annalen der a - Wiley Online Library · A theoretical approach to iron-based superconductors Page A15 G. W. Fuchs Annalen der Physik – a brief history of a living legend Full text

1© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

www.ann-phys.org

Multi-orbital band structure of iron-pnictide superconductorsby O. K. Andersen and L. Boeri

annalen der ad

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ISSN 0003-3804 · Ann. Phys. (Berlin), Sample Issue (2011)

physik

New i

n 201

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Sample Issue 201 1

www.ann-phys.org © 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim2

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Editor-in-ChiefGuido W. Fuchs

Section EditorChristian Joas

Max Planck Institute

for the History

of Science, Berlin,

Germany

Editorial Team

Regina Hagen

Lars Herrmann Cornelia Wanka

Dietmar Reichelt

Sonja Hoffmann

Editorial Offi ce

Wiley-VCH Verlag GmbH & Co. KGaA

Rotherstr. 21, 10245 Berlin, Germany

Phone: +49 (0) 30 – 47 03 13 21

Fax: +49 (0) 30 – 47 03 13 99

E-mail: [email protected]

Advisory BoardD. D. Awschalom, Santa Barbara, USAC. W. J. Beenakker, Leiden, The Netherlands

K. Blaum, Heidelberg, Germany

I. Bloch, Munich, GermanyC. Bruder, Basel, Switzerland

A. Caldwell, Munich, Germany

F. Capasso, Cambridge, USA

I. Cirac, Garching, Germany

G. Dvali, Munich, Germany R. Fazio, Pisa, Italy

R. Frésard, Caen, Frankreich

N. Gisin, Genève, SwitzerlandT. Hänsch, Munich, Germany S. Hell, Göttingen, Germany

A. Imamoglu, Zurich, SwitzerlandC. Kiefer, Cologne, Germany

P. Kim, New York, USAJ. Mannhart, Stuttgart, Germany

G. Schön, Karlsruhe, Germany

M. Schreiber, Chemnitz, Germany

Y. Tokura, Tokyo, JapanV. Vedral, Oxford, UKH. Zohm, Garching, Germany

P. Zoller, Innsbruck, Austria

Honorary Advisory Board

U. Eckern, F. W. Hehl, B. Kramer,

G. Röpke, A. Wipf, I. Peschel

How to citeAnnalen der Physik is cited as follows:Ann. Phys. (Berlin) vol. no. (issue no.), page(s) (year). Example: Ann. Phys. (Berlin) 524 (3), 320-334 (2012).Please make sure to always use Ann. Phys. (Berlin) as journal abbreviation.

Submission

Online manuscript submission: http://mc.manuscriptcentral.com/andp

www.ann-phys.org

annalen der ad

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Founded in 1790 by F. A. C. Gren

Continued by L. W. Gilbert,

J. C. Poggendorff, G. and E. Wiedemann,

P. Drude, W. Wien, M. Planck,

E. Grüneisen, F. Möglich, H. Kopfermann,

G. Richter, H.-J. Treder, W. Walcher,

B. Mühlschlegel, U. Eckern

Annalen der Physik publishes original

work in modern physics, overview articles

on topics of special interest, as well as

short letter contributions of exceptional

relevance. As a general physics journal

it covers theoretical, experimental and

applied physics and related areas of

physical sciences.

Scope

The journal covers the physics of � Condensed Matter / Solid State /

Materials� Optics / Photonics / Quantum

Information� Cosmology / Gravitation / Relativity� High Energy / Particles / Nuclear� Atoms and Molecules / Plasma � Biophysics / Biological and Medical

Applications� Geo / Climate / Environment

24 (3) 320 334

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annalen der ad

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New in 2012For more information visit: www.ann-phys.org/Relaunch2012

Browse this issue and discover the new Annalen der Physik


HIGHLIGHTS

Page A5

COVER PICTURE

Sample Issue 2011

Contents

EDITORIAL

Page A6

Page A7-A12

Page A13-A14

Highlights from

recent Annalen der Physik issues

E. Pavarini

Lattice distortions in KCuF3:

a paradigm shift?

PHYSICS FORUM

A. H. Romero and M. J. Verstraete

A theoretical approach to iron-based

superconductors

Page A15

G. W. Fuchs

Annalen der Physik –

a brief history of a living legend

Full text on our homepage at www.ann-phys.org

ContentsCo

nten

ts

A2

ADVISORY BOARD

Page A4

G. W. Fuchs

Annalen der Physik –

refreshed and renewed

The new Advisory Board

EXPERT OPINION

EXPERT OPINION

THEN & NOW

RETROSPECT

The Review Article by O. K. Andersen

and L. Boeri on p. 1 of this sample issue

investigates the electronic structure and

magnetic stripe order in iron-pnictide

superconductors. The cover picture

shows details of the magnetic energy in

k-space which are clearly related to the

peculiar propeller-shaped Fermi surface of

LaOFeAs.


Ann. Phys. (Berlin) A3 (2011)

Contents

A3

ORIGINAL PAPER

Sample Issue 2011

RAPID RESEARCH LETTER

Page 43 – 46

J. Deisenhofer, M. Schmidt, Zhe Wang,

Ch. Kant, F. Mayr, F. Schrettle,

H.-A. Krug von Nidda, P. Ghigna, V. Tsurkan,

and A. Loidl

Lattice vibrations in KCuF3

This paper reports on polarization depend-

ent refl ectivity measurements in KCuF3 in

the far-infrared frequency regime. The ob-

served IR active phonons at room tempera-

ture are in agreement with the expected

modes for tetragonal symmetry. A splitting

of one mode at 150 K is observed as is the

appearance of a new mode in the vicinity

of the Néel temperature.

Page 37 – 42

N. J. Popławski

Cosmological constant from quarks and

torsion

A simple and natural way to derive the ob-

served small, positive cosmological con-

stant from the gravitational interaction

of condensing fermions is presented. In

Riemann-Cartan spacetime, torsion gives

rise to the axial–axial vector four-fermion

interaction term in the Dirac Lagrangian for

spinor fi elds. This nonlinear term acts like a

cosmological constant if these fi elds have a

nonzero vacuum expectation value.

REVIEW ARTICLE

Page 1 – 36

O. K. Andersen and L. Boeri

On the multi-orbital band structure and

itinerant magnetism of iron-based super-

conductors

This paper explains the multi-orbital band

structures and itinerant magnetism of

the iron-pnictide and chalcogenide su-

perconductors. The presence of iron in a

superconductor implies that there is an

interplay between magnetism and super-

conductivity - a strange combination be-

cause the two effects should be exclusive.

Annalen der Physik is indexed in Chemical Abstracts Service/SciFinder, COMPENDEX, Current Contents®/Physical, Chemical & Earth Sciences, FIZ Karlsruhe Databases, INIS: International Nuclear Information System Database, INSPEC, Journal Citation Reports/Science Edition, Science Citation Index Expanded™, Science Citation Index®, SCOPUS, Statistical Theory & Method Abstracts, VINITI,Web of Science®, Zentralblatt MATH/Mathematics Abstracts

Recognized by the European Physical Society

www.ann-phys.org © 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim6A4

David D. Awschalom

California Nanosystems

Institute, University of

California, Santa Barbara,

CA, USA

Carlo W.J. Beenakker

Instituut-Lorentz,

Universiteit Leiden,

The Netherlands

Klaus Blaum

Max Planck Institute for

Nuclear Physics,

Heidelberg, Germany

Immanuel Bloch

Quantum Many-Body Sys-

tems Division, Max Planck

Institute for Quantum

Optics, Garching, Germany

Christoph Bruder

Department of Physics,

University of Basel,

Switzerland

Allen Caldwell

Max Planck Institute of

Physics, Munich, Germany

Federico Capasso

Harvard University,

Cambridge, MA, USA

Ignacio Cirac

Max Planck Institute

for Quantum Optics,

Maximilians University

Munich, Garching, Germany

The new Advisory Board

Georgi Dvali

Faculty of Physics,

Theoretical Physics, Ludwig


Munich, Germany

Rosario Fazio

Scuola Normale Superiore,

Faculty of Sciences, Pisa,

Italy

Raymond Frésard

Laboratoire Crismat-

ENSICAEN, France

Nicolas Gisin

GAP-Optique, Université

de Genève, Geneva,

Switzerland

Theodor Hänsch

Faculty of Physics, Ludwig


Munich, Germany

Stefan Hell


Biophysical Chemistry,

NanoBiophotonics,

Göttingen, Germany

Atac Imamoglu

Institute for Quantum

Electronics, ETH Zurich,

Switzerland

Claus Kiefer

Institute for Theoretical

Physics, Cologne University,

Cologne, Germany

Philip Kim

Department of Physics,

Columbia University,

New York, NY, USA

Jochen Mannhart


Solid State Research,

Stuttgart, Germany

Gerd Schön


Solid State Physics,

Karlsruhe, Germany

Yoshinori Tokura

Department of Applied

Physics, University of Tokyo,

Japan

Vlatko Vedral

Department of Atomic &

Laser Physics, Clarendon

Laboratory, University of

Oxford, UK

Hartmut Zohm


Plasma Physics, University

Munich, Garching, Germany

Peter Zoller


Physics, University of

Innsbruck, Austria


Dear Reader,

The time has come for a change and Annalen der Physik – AdP will ap-pear completely renewed in 2012. With this sample issue you get a fi rst impression of what the AdP will look like. The new AdP will have a com-pletely different and modern look, with monthly changing front cover pictures and a new journal and arti-cle layout. As in the past, the scope of the journal involves all aspects of physics. The aim is to attract scien-tists to publish about important and timely topics at the forefront of mod-ern physics. This will also include topics from applied physics. AdP will report about fast evolving areas and will organize special issues in re-search areas that leading scientists expect to be relevant in the future. For that, Annalen der Physik enables a new generation of young, talented or particularly creative physicists to participate more closely in the de-velopment of the journal by becom-ing Advisory Board members. With this new team new topical priorities can be set. It is an honor and a pleasure for me to build on Ulrich Eckern’s suc-cessful leadership as Editor-in-Chief of Annalen der Physik. I have served as Managing Editor for AdP since 2009, and have had the opportunity to gain insights into the journal that form the basis of the restructuring that now is taking shape.

EDITORIAL

Annalen der Physik –refreshed and renewed

For AdP authors there will be some changes, too. As can be seen in this sample issue, Rapid Research Letters will be introduced and Review Arti-cles will be solicited [1,2]. The manu-scripts have to be submitted via an online manuscript system [3]. AdP allows the online submission of vid-eo abstracts and supporting materi-al. The Einstein Lectures series, i.e. special invited articles from interna-tionally leading scientists, will be re-vived and continued. A new section Then & Now will be introduced, or-ganized by the Max Planck Institute for the History of Science (Berlin/Germany). Furthermore, there will be an Expert Opinion section where researchers comment on recent or co-published articles in AdP in a brief essay form. The peer-review system will continue to be fast and sound and all articles will be quickly available as Early View online publi-cations shortly after their accept-ance. Shaping the future of a journal is not completely in the hands of the editor. The most crucial part comes from the scientifi c community, i.e. scientists and interested researchers and enthusiasts like you. As author and reader you can signifi cantly con-tribute to the success of Annalen der Physik by submitting your fi rst-class scientifi c work and most distin-guished manuscripts to the journal.

It is only with your contributions that AdP can be attractive and keep its status as a highly respected jour-nal. I invite you to be a part of the new AdP!

For details please visit our webpage www.ann-phys.org/Relaunch2012.

With kind regards

Guido W. FuchsEditor-in-Chief 2012

HighlightsEditorial

Ann. Phys. (Berlin) A5 (2011)

References

[1] See author guidelines for letter articles on the journals homepage, www.ann-phys.org [2] There is a review proposal sheet available for this purpose on www.ann-phys.org (Wiley Online Library) [3] Submit your manuscript here: http://mc.manuscriptcentral.com/ andp

A5


Hig

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hts

RETROSPECT – Highlights of recent Annalen der Physik issues

Volume 523 | Issue 6 | Pages 439–449 (2011)

High precision thermal modeling of complex systems with application to the fl yby and Pioneer anomaly B. Rievers and C. Lämmerzahl

DOI 10.1002/andp.201100081

In the 1970s, the spacecrafts Pioneer 10 and 11 were launched for the exploration of

the outer solar system. Ever since J.C. Anderson (Jet Propulsion Laboratory, Pasade-

na, California) et al. in 1998 reported on a mysterious small acceleration of Pioneer

10 and 11 of about 10-9 m/s2 toward the Sun, attempts were made to explain this

“anomaly’’. Was it “new physics’’ (modifi ed general relativity, vacuum fl uctuations,

dark energy,...) or simply an effect overlooked in the analyses of the experiments?

You will fi nd the answer to this question in this remarkable paper of B. Rievers and

C. Lämmerzahl from ZARM in Bremen, Germany.

Volume 523 | Issue 1-2 | Pages 1-190 (2011)

Topical Issue: Optical and Vibrational Spectroscopy Special issue in honor of the 75th birthday of Manuel Cardona

Eds.: Aldo H. Romero and Jorge Serrano

http://onlinelibrary.wiley.com/doi/10.1002/andp.v523.1/2/issuetoc

Relevant review papers are reported here on the areas of superconductivity in iron

pnictides, optical properties of nanostructures, electron holography in nitrides, and

the quantum Boltzmann equation. The special issue has been prepared on the oc-

casion of the seventy fi fth birthday of Manuel Cardona.

Volume 522 | Issue 7 | Pages 467-519 (2010)

Probabilistic observables, conditional correlations, and quantum physics C. Wetterich

DOI: 10.1002/andp.201010451

The authors discuss the classical statistics of isolated subsystems. Only a small part

of the information contained in the classical probability distribution for the subsys-

tem and its environment is available for the description of the isolated subsystem.

The “coarse graining of the information” to micro-states implies probabilistic ob-

servables. Furthermore the classical statistical realization of entanglement within a

system corresponding to four-state quantum mechanics is discussed. It is concluded

that quantum mechanics can be derived from a classical statistical setting with infi -

nitely many micro-states.

f

e-

r

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A6

RETROSPECT – Highlights


THEN & NOW

Annalen der Physik – a brief history of a living legendGuido W. Fuchs

Just in time for its 222 anniversary the journal Annalen der Physik will experience a metamorphosis – crowned by its relaunch in January

2012. From next year onwards readers can expect a new content, a new look, and a new editorial team. And all this happens for good

reasons. Today, the publishing world is under constant pressure to change. This also holds for academic journals and consequently for

Annalen der Physik, too.

Ann. Phys. (Berlin) A7-A12 (2011)

Annalen der Physik – AdP1 appears as a landmark of modern physics, an institution, distinguished by works from Einstein, Planck and other ex-traordinary talents. But what makes it unique today? The age of print media is said to be over. Our time is dynamic and digital. Nowadays, science arti-cles are delivered electronically, e.g. as pdf or XML documents, right to the researchers offi ce desk or laboratory. Literature search is done via special-ized databases or general search en-gines like Google and the like. In addi-tion, successful journals advertise their content and use the internet for marketing purposes, e.g. utilizing news portals, newsletter, rss-feeds, fa-cebook, twitter, etc. Over the last 200 years the amount of published phys-ics articles has increased exponen-tially. None of the established and well-recognized journals can deal with the vast fl ood of information. Fil-tering out the essence, i.e. informa-tion that most likely will advance physics, is the main task of editorial manuscript selection and article compiling. High peer-review quality standards will be more and more im-portant. This especially holds for the general physics journal Annalen der Physik, which no longer claims to be a comprehensive manuscript archive, as in the early times, but rather focus-es on key aspects of modern physics.

This change in scope is good reason to refl ect on the past events of this journal.

Birth of a legend (1790–1824)

The story begins with Friedrich Gren, a natural scientist born in 1760 in Bernburg/Saale, who held a position as professor in Halle, Germany. The general progress in natural sciences in Europe at the end of the 18th century was remarkable. In comparison to other European coun-tries Germany was only scientifi c province at this time. Most new fi nd-ings were published in minutes of so-ciety meetings or academy reports,

e.g. in Paris, London or Saint Peters-burg, or were propagated by private communications in the form of let-ters. Thus, ideas could only circulate within small and elitist communities. Gren believed that the lack of a suita-ble communication and publication medium was jointly responsible for the weak performance of German re-search. Inspired by the 1778-founded chemical journal of his teacher Lorenz von Crell (“Crell’s Annalen”) Gren started his own journal “Journal der Physik” in Halle. In the preface of the fi rst issue in June 1790 he wrote: “My purpose of publishing this jour-nal is to make acquainted with the discoveries in mathematics and chemistry of the foreigners and na-

Editors-in-Chief of Annalen der Physik from 1790 until 1947

(top, from left) Friedrich Albert Carl Gren, Ludwig Wilhelm Gilbert,

Johann Christian Poggendorff, Gustav Heinrich Wiedemann,

(below, from left) Eilhard Wiedemann, Paul Drude, Wilhelm Wien, Max Planck

1 Engl.: Annals of Physics

A7

HighlightsPhysics Forum

www.ann-phys.org © 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim1 0

tives in the fi eld of the natural scienc-es […]“. Accordingly, translations of foreign works built an important base for the new journal. With his journal Gren also aimed to give amateurs (“Privatmann”) access to recent re-search, both as reader as well as au-thor. Important topics were thermo-dynamics, electricity and mag-netism. Gren died in 1798, only 38 years old. His journal marked the be-ginning of a legend – the home jour-nal of the most distinguished minds in physics. Ludwig W. Gilbert, born in 1769 in Berlin, was a mathematician and geo-grapher and in 1801 succeeded Gren as university professor in Halle. Al-ready, Gren had worked towards a re-launch of his journal under the new name Annalen der Physik. Now in 1799, Gilbert continued his mentor’s work and the journal appeared for the fi rst time under the new name. It was denoted as series1 number one out of eight series until today. Gilbert trans-lated, edited, and enriched many original foreign articles with didactic fi nesse to the benefi t of the German reader. He edited 76 volumes and served AdP for a full quarter-century. During his time physics did not have the rather well-defi ned topical focus and conformity that it has to-day. Thus, many articles appeared that nowadays belong to meteorolo-gy, climatology, geography, nautical science, or even biology. Still, most publications were in the core area of physics, like the translations of works by David Brewster, Michael Faraday or Joseph Gay-Lussac. Electrochem-

istry was a timely topic as well, with contributions from Johann Wilhelm Ritter, Sir Humphrey Davy and oth-ers. AdP reported on Ampere’s work about magnetic phenomena and their relation to moving electricity. However, the fi nal Ampere’s law from 1824 did not appear in the journal.From the fi rst issue of Annalen der Physik until volume 30 (1808) the journal appeared at the publisher Rengersche Buchhandlung (Renger’s Bookstore) in Halle. From volume 31 (1809) onwards, i.e. from series two of the AdP, Johann Ambrosius Barth (1760–1813) became the publisher of the journal [1]. As it turns out, the journal was published by the pub-lisher J.A. Barth for more than 180 years until 1992. Originally, Gilbert aimed for physics articles only, but this proved to be diffi cult and from 1819 to 1824 the name of the journal was extended to Annalen der Physik und der physikalischen Chemie 2.

The Poggendorff Era (1824–1877)

In 1820 Johann C. Poggendorff (1796–1877) studied natural sciences at the university in Berlin. Already in 1823 the young man was thinking about starting his own chemical-physics journal. After the unexpected death of Gilbert in 1824, Poggendorff real-ized that there was a chance of be-coming the editor of AdP and con-tacted the publisher Verlag J.A. Barth. Poggendorff knew exactly what he wanted: Either become editor of AdP or start his own journal that he in-tended to become the leading journal in physics and chemistry in Germany. He spoke with leading scientists to ensure their willingness to publish with him and used these connections to put pressure on the J.A. Barth pub-lisher. Surprisingly, his plan worked out. Poggendorff, only 28 years old, boldly managed to become editor of AdP and published his fi rst issue in

1824 under the name Annalen der Physik und Chemie3. The new editor arranged for the new name because he thought that both physics and chemistry could not be separated in a meaningful way. In the second half of the 19th cen-tury translations of foreign works lost their importance for the journal to the benefi t of original contributions and appeared only infrequently from that time onwards. This development was due to new physics institutes at Ger-man universities that were founded in the course of the Prussian university reform. These institutes had an ex-plicit order to promote and perform research, as opposed to the previous “Cabinette”. The fi rst institutes were founded in Leipzig and Göttingen and were inspired by the French Ecole Po-lytechnique. The amount of new fi nd-ings made Poggendorff publish in to-tal seven supplementary volumes in addition to the regular AdP volumes. In 1874, at the 50th anniversary of “his” Annalen, Poggendorff out-lined what he considered to be the most important topics: “Electrodynamics, induction, diamagnetism, photo-magnetism, thermochrosy, telegra-phy, photography, diffusion, fl uores-cence, spectral analysis, and me-chanical theory of thermodynamics”. From today’s point of view not all scientifi c-editorial decisions from Poggendorff were free of errors. For example, the works by Julius Mayer (1841) and Hermann v. Helmholtz (1847) about the principle of energy conservation were not accepted for publication in AdP. Also, Philip Reis’s invention of the telephone was not appreciated, neither was Sadi Car-not’s work from 1824 about the heat engine. Only nine years later, Benoît Clapeyron’s article appeared in AdP, where he explained Carnot’s thoughts in a more practical way. On the other hand, Rudolf Clausius’s concept from 1850 containing the fi rst and second law of thermody-

1 The term series is a translation of the

German ‘Folge’. However, in some cases a

‘Folge’ was subdivided into ‘Serien’, i.e.

subseries. In this essay series always

refers to ‘Folge’.2 Engl.: Annals of Physics and Physical

Chemistry3 Engl.: Annals of Physics and Chemistry

G.W. Fuchs: Annalen der Physik – a brief history of a living legendPh

ysic

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1 1© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

namics, which basically equals the concepts of Joule and Carnot, was well received and is one of the high-lights of AdP. In the area of electricity AdP re-ported about Ohm’s current–voltage law, as well as Faraday’s numerous experimental investigations that, for instance, contained his discovery of magnetic induction and its visualiza-tion through magnetic lines of forces, the behavior of dielectrics, the intro-duction of electric lines of forces and the discovery of diamagnetism. Poggendorff took care of the AdP for 53 years. He was the editor of 160 volumes. His Annalen der Physik und Chemie were simply called the Poggendorff Annalen. The heyday of the journal was between 1850 and 1920. During that time AdP devel-oped into one of the leading physics journals in Europe, if not the leading journal. With only a few exceptions, reading AdP suffi ced to keep oneself up-to-date in physics [2]. In addition, AdP was very popular and was not only subscribed by university librar-ies, but also by many secondary3 and technical schools.

The Heydays (1877–1914)

After Poggendorff’s death in 1877, the publisher Hans Barth appointed the 51-years-old Gustav H. Wiede-mann (1826–1899) as the new editor of AdP. Right at the beginning, AdP cooperated closely with the Physical Society of Berlin (PGzB)4, which was realized by appointing Hermann

Helmholtz as coeditor of the journal. The “extraordinary increase of the material [… ] and the fact, that in ad-dition to the Annalen also other comprehensive journals have been founded” (Helmholtz 1893), led to fewer and fewer articles being pub-lished in AdP that belonged to chem-istry, mineralogy, metrology and physical chemistry. As a conse-quence of this ongoing differentia-tion of the natural sciences into sub-fi elds, AdP began to focus on pub-lishing articles solely from physics. In addition, it became more diffi cult for authors to publish in AdP due to in-creased editorial selection criteria, as Helmholtz (1893) states: “The number of German manuscripts has gradually increased over time, so that by now, only a selection of those can be considered.” In 1893, Gustav’s son, Eilhard Wiedemann (1852–1928), became Co-Editor-in-Chief of AdP. After Helmholtz’s death in 1895 Max Planck (1858–1947) took over his role and supported the AdP as co-editor on behalf of the PGzB. Only four years later, in 1899, Gustav Wie-demann passed away in Leipzig. His son Eilhard, although himself a pro-fessor of physics at the University Er-langen, declined to take over full re-sponsibilities for the journal and fi -nally resigned as editor from AdP. Paul Drude (1863–1906), who nowa-days is considered as one of the pio-

neers of solid-state physics, became the new Editor-in-Chief of AdP. Thir-ty-six years old, talented, dynamic and already in permanent position as professor, Drude seemed to be an ide-al choice. In addition, he resided in Gießen, a medium-sized German town in Hesse, and thus did not be-long to the Berlin physicists commu-nity that in the rest of the German Reich was often perceived as too dominant. In 1900, with the change of editorship, Annalen der Physik und Chemie were renamed to Annalen der Physik and the journal has kept that name ever since. It was now the fourth series of AdP. One novelty was the in-troduction of an Advisory Board5 of fi ve professors, with Max Planck be-ing one of them. Despite Drude’s sci-entifi c brilliance he seemed to be rather less determined and less criti-cal in editorial matters. Very much to the displeasure of Planck, many man-uscripts of low quality passed Drude’s judgment. But it was also the time when legendary papers of modern physics were published in AdP. For example, Planck’s work about the en-ergy density distribution of the black-body radiation6 was published in AdP, where he also introduced the quan-tum of action ħ, the constant now named after him. This work was gen-erally regarded as the beginning of quantum theory. In 1905, Albert Ein-stein published seminal papers in

3 Here Secondary School is used as a

translation for the German Gymnasium.4 Orig.: Physikalische Gesellschaft zu

Berlin, PGzB5 Orig.: Kuratorium6 M. Planck, “Ueber das Gesetz der

Energieverteilung im Normalspektrum”,

Ann. Phys. (Berlin), 309(3), 553–563 (1901)

Hermann Helmholtz Albert Einstein (Credit: ÖND/Wien,

Bildnummer LSCII 0081-C)

Ann. Phys. (Berlin) 1-80 (2011)

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AdP that built the base for his later fame [3]. At that time, Einstein was mostly unknown to the relevant aca-demic circles and was not working in academia. It is thanks to Drude that Einstein’s works were published in AdP. However, Planck was one of the fi rst who realized Einstein’s genius and the importance of his work. Also, Planck helped this 26-year old patent offi ce clerk to start an academic ca-reer and later made great efforts in at-tracting Einstein to Berlin. On July 5, 1906 Drude committed suicide. The reasons remain un-known. Planck and Wilhelm Wien (1864–1928) became the new Edi-tors-in-Chief of equal rights. Howev-er, Wien was more involved in the day-to-day business of the journal, whereas Planck reserved the right to be consulted in all critical cases like manuscript rejections or revisions. At that time, Planck was already a well-known scientist and an accepted long-standing editor of the AdP. Planck appeared as an author of AdP already in 1881 and published pre-dominantly in this journal during his whole life. His last article in AdP ap-peared in 1941. In 1947, after the war,

he was involved in the reactivation of the journal [4]. Thus, Planck accom-panied AdP over 66 years – truly mo-mentous years of the journal.

Times of crisis (1914–1945) The political and economic crisis did not go unnoticed by the Annalen der Physik. As opposed to 3800 published pages in the year 1914, the number quickly reduced to 2100 pages in 1918 induced by the war – a decrease by 45%. In the following years, this number further decreased reaching a trough of 1800 pages in 1921. Besides the AdP and the 1899-founded jour-nal Physikalische Zeitschrift, a new journal Zeitschrift der Physik came into existence. In 1920, with the ac-ceptance of the German Physical So-ciety (Deutsche Physikalische Ge-sellschaft, abbrev. DPG), the publish-er Vieweg launched the new journal that soon turned out to be a strong competitor for AdP. The new journal managed to publish many important works of young researchers in the booming fi eld of quantum physics, like those from Max Born and Werner

Heisenberg. In view of these young scientists Annalen der Physik ap-peared no longer timely, because it was known that Planck and Wien were skeptical towards the new trends in quantum mechanics. Here the young Erwin Schrödinger was an exception. His four ground-breaking articles about the “Quantization as Eigenval-ue Problem”, published in 1926, ap-peared in AdP. In these works, Schrödinger outlined his wave-me-chanical approach that nowadays is a cornerstone of quantum mechanics. But there were also other examples of important contributions in quantum theory that appeared in AdP, like the works from Maria Göppert-Mayer from 1931 “Elementary processes with two quantum transitions”, Max Born and Robert Oppenheimer’s 1927 article “About the quantum theory of molecules” or Wolfgang Pauli’s 1922 contribution “On the model of the hy-drogen molecule ion”. In addition to the domestic competitors, interna-tional journals also appeared on the scene, like the Physical Review that al-ready used the modern peer-review procedure to quality check its manu-scripts. In 1928 Wien died. His successor Eduard Grüneisen (1877–1949) start-ed to serve the AdP in 1929 and this marks the start of a new AdP series, the fi fth. It was the time of Hitler’s rise and with the advent of the Nazis a turning point in German history had been reached, not only for the Anna-len der Physik but also for German science in general. A fl ood of German emigrants, persecuted because of their political opinion or their race, left the country, among them many authors of AdP. The myriads of per-sonal tragedies that took place was not directly refl ected in the AdP, how-ever, the absence of many important articles was signifi cant – mostly those from Jewish authors. Accordingly, the decrease in page numbers until 1939, i.e. already in prewar time, was signifi -

Editors-in-Chief of Annalen der Physik from 1947 until today

(top, from left) Eduard Grüneisen, Friedrich Möglich, Hans Kopfermann, Gustav Richter

(Photo: Th. Richter),

(below, from left) Hans-Jürgen Treder (Photo: bpk/Gerhard Kiesling), Wilhelm Walcher,

Bernhard Mühlschlegel, Ulrich Eckern


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cant. Planck and Grüneisen managed to keep the politics out of the AdP dai-ly business as much as possible. Thus, even in the late 1930s works from Lise Meitner, Rudolf Ladenburg, Paul Ewald, and Richard Gans appeared in Annalen der Physik. But over time, fewer and fewer emigrants published in German and preferred foreign, mostly English language journals. In spring 1938 Debye, together with oth-er guest editors, organized a special issue in honor of Arnold Sommer-feld’s 70th birthday. In this context, the publisher approached the organ-izers with the request to only publish articles from “Arian” authors. This un-paralleled case of open racism trig-gered protests and outrages by many physicists and most prominently by Wolfgang Pauli. But in the end, the special issue appeared as wanted by the publisher. With the outbreak of the second world war in 1939 the number of con-tributions again reduced signifi cant-ly. Shortly after the assassination at-tempt on Hitler on July 20, 1944 all companies and factories that had no direct war-relevance were closed and large parts of the population were obliged to work in the armaments in-dustry. In the course of these ‘total warfare’ measures the publishing house J.A. Barth in Leipzig was also closed down and with that Annalen der Physik de facto ceased to exist.

Divided but together (1946–1990)

Germany was broken, the war lost. The severity of destruction, ongoing resentments and loss of manpower made a restart diffi cult. Grüneisen, who lived in Marburg, which was sit-uated in the Western zone of oc-cupation, had no hope to get permis-sion from the Western allied powers to relaunch the Annalen der Physik. After Max von Laue’s discharge from

Farm Hall (U.K.), where he had been detained as a prisoner of war, and his return to Germany in 1946, he imme-diately started with the rebuilding and organization of the German sci-ence and physics program. Laue was involved in many projects East and West of the ideological border and in-dependent of the political landscape within Germany. He recommended his former PhD student Friedrich Möglich (1902–1957) as co-Editor-in-Chief of AdP. The appointment of a Western and an Eastern Editor-in-Chief of AdP remained common practice for the journal until 1992, i.e. until shortly after the German reuni-fi cation. Annalen der Physik adhered to the conviction that both parts of Germany belong together. Only dur-ing a short period, between 1950 and 1951, was this new tradition disrupt-ed. On August 1, 1946 the Soviet mili-tary administration granted permis-sion for the restart of AdP: “For the benefi t of German science and for the benefi t of humanity and internation-al understanding”. But the license came with some restrictions. AdP was not allowed to publish certain branches of physics like nuclear physics, semiconductor physics, high-frequency technology and elec-tronics. It was now series six of the Annalen der Physik. Grüneisen and Möglich, as well as Planck who died in 1947 shortly before the fi rst new is-sue appeared, were the fi rst editors after the war. The journal clearly emerged debilitated from the past crisis and published only 500 pages per year, only occasionally were 1000 pages realized. Though AdP still pub-lished articles of high quality and long-term importance until the 1940s and 1950s – at least from time to time – the heydays were clearly over. AdP lost ground compared to other inter-national journals like Physical Review that now took the lead. Relevant na-tions in the fi eld of physics were the

USA and the Soviet Union. As op-posed to the prewar situation there were almost no contributions from non-German authors in AdP which, continued to publish in German lan-guage. The successor to Grüneisen, who died in 1949, was Hans Kopfermann (1895–1963) who started to serve AdP in 1952 as the West German editor. After Friedrich Möglich’s death in 1957 Gustav Richter (1911–1999) be-came the new East German editor. This marked the beginning of a new series, series seven of Annalen der Physik. In East Germany the Socialist Unity Party was worried about its se-curity due to an allegedly ongoing mass migration of its citizens into the Western zones. It was decided to for-tify the national borders and the building of the Berlin Wall in August 1961 marked the beginning of a thir-ty-year physical isolation and separa-tion of West and East Germany. The AdP publishing house remained in Leipzig, i.e. in East Germany. Regard-less of the new political situation AdP followed its policy to appoint two Ed-itors-in-Chief from East and West Germany, respectively. The successor to Kopfermann was Wilhelm Walcher (1910–2005) for the Western Federal Republic of Germany and Hans-Jür-gen Treder (1928–2006) for the East-ern German Democratic Republic (GDR).

Times of reunifi cation (1992–2011)

With the end of the cold war and of communist regimes in the former Eastern Bloc a new era began for AdP. The journal was restructured in 1992. The Hüthig GmbH, Heidelberg/Ger-many took over AdP from the former J.A. Barth publishing house. At that time the J.A. Barth publisher was al-ready state property of the GDR since 1988. However, Hüthig published

Ann. Phys. (Berlin) 1-80 (2011)

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AdP still under the former publisher’s trademark ‘J.A. Barth Verlag’ until 1998. Once again, a new series start-ed: Series No. 8. Bernhard Mühl- schlegel (1925–2007) from Cologne/Germany became the new Editor-in-Chief of the AdP in 1992. The Adviso-ry Board was dissolved and replaced by three international co-editors, among them Alexei Abrikosov who later won the 2003 Nobel Prize in Physics. From that time onwards AdP published solely in English. The jour-nal intended to be globally more visi-ble, and attractive for young scien-tists. However, the manuscript sub-missions fell behind expectations and gave rise to concerns about the future of the journal. In 1998, Mühlschlegel was 73 years old and handed over editorship to the theoretical solid state physi-cists Ulrich Eckern from Augsburg. In the same year, in the course of a re-structuring measure Hüthig sold ten of its academic journals to the pub-lisher Wiley-VCH (Weinheim/Berlin) Among these journals was AdP. At the same time, the 120-year old coopera-tion with the DPG (and PGzB) ended. Now, for the fi rst time, and in addi-tion to the print issues, the journal appeared in electronic form. Further-more, old print issues from 1799 on-wards were scanned and refurbished, and have been available in electronic form since 2006. In the year 2005, in honor of Einstein’s annus mirabilis AdP introduced the Einstein Lectures. With this distinction contributions from important prize winners, like the Nobel Prize winners Theodor Hänsch (MPQ Garching), Roy J. Glau-ber (Harvard), or Peter Grünberg (FZ Jülich) were highlighted.

The new AdP (2012)

Ulrich Eckern will end his term as AdP Editor-in-Chief at the end of 2011, after 14 years of successful lead-

ership. From January 2012 onwards the journal will be run directly by the publisher with an in-house editorial team with Guido W. Fuchs as the new Editor-in-Chief. The former Editorial Board members Friedrich Hehl, Bernhard Kramer, Gerd Röpke and Andreas Wipf will continue to serve for AdP as Honorary Advisory Board members. They will be joined by Ul-rich Eckern and Ingo Peschel, who is currently an Advisory Board member. Ingo Peschel, for example, had been crucial and supportive in diffi cult times, right after the German reunifi -cation, during the start of the 8th se-ries in 1992, but also later when Bern-hard Mühlschlegel handed over edi-torship to Ulrich Eckern in 1998. The scope of the journal is still to publish general physics – in all its as-pects. This also includes topics in ap-plied physics. Letter articles will be newly introduced. The Einstein Lec-tures will be revived and continued. The section ‘100 years ago’ will be ceased. Translations of originally German articles into English will not be published as separate articles in current issues but appear as addi-tional material to the original articles. Historical essays Then & Now will be introduced with contributions from the Max Planck Institute for the His-tory of Science (Berlin/Germany). In addition, there will be an Expert Opinion section where authors can comment on recent or copublished articles in AdP in a brief essay form. In 2012, AdP will have changed completely. It is set up to serve an in-ternational readership, and although AdP has experienced several renam-ings, it is not considered to change the title into an English one because meanwhile the name Annalen der Physik belongs to our international cultural heritage. To emphasize the continuation of scientifi c publishing from its fi rst ap-pearance as Annalen der Physik in 1799 until today, already in 2009, the

volume counts were offi cially changed [5]. Previously, volume numbers restarted with the begin-ning of a new series (Folge), e.g. the latest series No. 8 started with vol-ume 1 in 1992. Now, all volumes are counted from the fi rst one in 1799, so that volume 523 refers to the volume published in 2011. The relaunch of AdP in 2012 will not trigger a new se-ries. Instead this concept of series is abandoned. The progress of AdP will simply be denoted by its volume number. Shaping the future of a journal is not completely in the hands of the editor or publisher. The most crucial input has to come from the scientifi c community. It remains to hope that AdP will be well received by the phys-icists and interested scientists. An-nalen der Physik has good intentions. It wants to serve the physics commu-nity. It has always been a journal act-ing as a mirror of current research and this is also its guiding theme for the future: Knowing Annalen der Physik means knowing physics.

Acknowledgements. The author thanks Dieter Hoffmann and Ulrich Eckern for their kind support and sugges-tions.

References

[1] K. Wiecke, 200 Jahre Johann Ambrosius Barth (Verlag Johann Ambrosius Barth, Leipzig, 1980), pp. 17–30. [2] F. Hund, Die Annalen im Wandel ihrer Aufgabe, Ann. Phys. (Berlin), 502(4), 289–295 (1990).[3] J. Renn (ed.), Einstein’s Annalen Papers (Wiley-VCH, Weinheim- Berlin, 2005).[4] D. Hoffmann (ed.), Max Planck: Annalen Papers (Wiley-VCH, Weinheim-Berlin, 2008).[5] G. W. Fuchs and U. Eckern, Ann. Phys.

(Berlin) 522(6), 371 (2010).


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Ann. Phys. (Berlin) 523, No. 7, 580–581 (2011) / DOI 10.1002/andp.201110469

EXPERT OPINION

A theoretical approach to iron-based superconductors*

Aldo H. Romero and Matthieu J. Verstraete

Very recently, in 2008, Hosono and collaborators [1] reported a new su-perconducting material with a tran-sition temperature of 26 K. Besides setting the right tone in renewing the race to increase the supercon-ducting critical temperature, Ho-sono gained attention because the material was based on a layered iron arsenide compound. By substitut-ing some oxygen in the starting iron arsenide structure, giving LaAsOFe, and after fl uorination doping, the new superconducting material is obtained. This composition is strange - the presence of iron in a superconductor implies there is an interplay between magnetism and superconductiv-ity. As we all learn in undergradu-ate physics, the two effects should be exclusive: magnetism tries to break Cooper pairs and inhibits the appearance of superconductivity, whereas superconductivity tends to expel magnetic fi elds. The fact that now a single material is able to show both of these phenomena is quite a revolution: the case for magnetic ef-fects (spin fl uctuations) in cuprate superconductors was much less clear-cut. In only 3 years the paper has received almost 2000 citations, an average of 700 per year - clearly a very hot topic! At low fl uorine doping the iron atoms couple antiferromagnetically,

but as the doping concentration is increased the magnetic coupling decreases; it is the weakening of the antiferromagnetic order which allows the rise of superconductiv-ity. Very quickly, a full family of iron compounds was reported in the lit-erature, with the same basic structure and reaching critical temperatures of 38K [2]. Since the report by Hosono, the related compounds were con-structed by trying to keep the layer arrangement, but with distortions, or using other chemical species. The original work was based on arsenic, but by now we know that similar be-havior can be obtained by exchang-ing As with P or Se or Te. In most of those structures, the iron plane is not perfectly fl at and binds to the period-VI element in the formulae, creating tetrahedra. This is in stark contrast to the octahedra in cuprate supercon-ductors. In particular, it was demon-strated that the higher the symmetry in the tetrahedral structure the larger the increase of the superconducting temperature [3,4]. Most calculations indicate that electrons fl ow along the planes formed by the irons, which probably points (surprise!) to elec-trons coupling to spin fl uctuations. It was initially speculated that the physics of this new superconductor is related to that of the cuprates, but

soon demonstrated that the situa-tion was much more complex. Both systems are antiferromagnetic, but LaOFeAs is also a spin-density wave metal, with electrons which are much more delocalized than in the cuprates. Another difference appears in experimental measurements in-dicating that the bands around the electronic gap are nicely symmetric in the pnictides, while they are not in the cuprates. The asymmetry in the cuprate gap was explained using the d-wave argument [5], which does not apply to this new system. The sym-metry around the energy gap is still under discussion, but it is strongly system dependent. What is clear is the interrelation between the elec-tronic structure, specifi cally the to-pology of the bands around the Fer-mi energy, and the superconducting behavior. To make the puzzle more complicated, the electron-phonon interaction is fairly small and clearly insuffi cient to explain the global be-havior.Since the discovery of superconduc-

* Published in Ann. Phys. (Berlin) 523, No. 7,

580–581 (2011); slightly modifi ed for the

sample issue, with permission from the

authors.

Figure 1 The set of fi ve Fe d-like Wannier

orbitals (downfolded and orthonormalized

NMTOs) which span the fi ve LaOFeAs bands

extending from -1.g eV below to 2.2 eV above

the Fermi level. For more information see [6].

A13



A.H. Romero / M. J. Verstraete: A theoretical approach to iron-based superconductorsPh

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tivity in pnictides, a large number of theoretical papers have appeared, trying to explain the properties of these new superconductors, and in particular trying to reconcile the dif-ferent theoretical approaches with the experimental observations. It is very hard to follow the full literature because of the plethora of different systems and approximations. A com-plete understanding of this problem has yet to come out. The paper by Andersen and Boeri in the present volume [6] presents a comprehen-sive approach of the band structure by using the same methodology and explaining, quite pedagogically, the contributions of the different orbitals to the energy bands. They also gener-ate the corresponding tight binding parameters, which allows them to get deeper insight into the spin wave behavior and the interplay with the

structural symmetry. They fi nish the paper with a discussion on the con-tribution of the spin polarization to some of the observed properties, in particular considering spin spirals. This remarkable contribution gives the most comprehensive theo-retical overview to date of the elec-tronic structure of the iron pnictides compounds and how their properties could give rise to superconductivity.

Aldo H. Romero

CINVESTAV, Unidad Querétaro, Libramiento

Norponiente 2000, Real de Juriquilla,

Querétaro CP 76230, Mexico


Matthieu J. Verstraete

Department of Physics, Universite de Liege,

Av du 6 Aout, 17, B-4000 Liege, Belgium

E-mail: [email protected].

References

[1] Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono, J. Am. Chem. Soc. 130, 3296 (2008).[2] M. Rotter, M. Tegel and D. Johrendt, Phys. Rev. Lett. 101, 107006 (2008).[3] C.H. Lee, A. Iyo, H. Eisaki, H. Kito, M.T. Fernandez-Diaz, T. Ito, K. Kihou, H. Matsuhata, M. Braden and K. Yamada, J. Phys. Soc. Jpn. 77, 083704 (2008). [4] D.C. Johnston, Adv. Phys. (Berlin) 59, 803 (2010).[5] A.D. Christianson, E. A. Goremychkin, R. Osborn, S. Rosenkranz, M.D. Lumsden, C.D. Malliakas, I.S. Todorov, H. Claus, D.Y. Chung, M.G. Kanatzidis, R. I. Bewley and T. Guidi, Nature 456, 930 (2008).[6] O.K. Andersen and L. Boeri, Ann. Phys. (Berlin) 523, 8 (2011).

A14


EXPERT OPINION

Lattice distortions in KCuF3: a paradigm shift?Eva Pavarini

KCuF3 is the paradigmatic compound for the co-operative Jahn-Teller effect.

But do we really know its structure?

Co-operative Jahn-Teller distortions are ubiquitous. But do we really know where they come from? Usually they go along with other distortions and ordering phenomena, which make it diffi cult to identify the actual driving mechanism. KCuF3 is believed to be a beautiful exception, the cleanest re-alization of a co-operative Jahn-Teller system. Its CuF6 octahedra are slightly compressed along z, and have a long (l) and a short (s) CuF bond in the xy plane. The electronic confi guration of Cu is 3d

9, a single hole in the eg states;

the distortions split the otherwise de-generate eg orbitals, and the hole goes into the |s2−z

2 〉 state. The spatial alter-

nation of l and s bonds in all direction produces the orbital pattern shown in Fig. 1. Despite its simple structure, the origin of the co-operative Jahn-Teller distortion in KCuF3 remained a puz-zle. Is it driven by electron-phonon coupling or by many-body superex-

change [1]? Early-on static mean-fi eld LDA+U calculations showed that the stability of the Jahn-Teller distor-tion (total energy gain) is strongly enhanced by Coulomb repulsion, a result recently confi rmed by dynami-cal mean-fi eld (DMFT) calculations [2]. Does this mean that manybody super-exchange is driving the co-operative distortion? The answer remained elusive for half a century. Only recently, by using DMFT and a new approach to separate super-exchange and electron-phonon cou-pling effects, the puzzle was fi nally solved. It was shown [3,4] that many-body super-exchange alone gives a critical temperature of about 350 K, very large, but far too low to explain experimental facts: the co-operative Jahn-Teller distortion persists up to TOO ∼ 800 K, and probably at even higher temperatures. Hence the static Jahn-Teller distortions must be driv-en by electron-phonon coupling. But, resourceful as ever, KCuF3 has new surprises in store for us. Far below TOO, a new, dynamic, phase appears to manifest itself. The work of Dei-senhofer et al. [5] reports a splitting of the infrared-active phonon mode Eu(3) at ∼ 150 K, indication of symme-try lowering; an analogous splitting of the Eg(2) mode is seen in Raman scat-tering slightly above the Neel tem-perature, TN = 40 K. This makes KCuF3 remarkable in yet another way – as a compound whose low temperature properties are dominated by dynam-ics. Indeed, the evolution of the Eg(2) and Eu(3) modes with temperature

could be understood if strong lattice fl uctuations around a lower symme-try orthorhombic lattice were present. Remarkably, above TN KCuF3 behaves as a one-dimensional anti-ferromag-netic Heisenberg chain, characterized by strong spin fl uctuations. Strong lattice fl uctuations can couple to these spin fl uctuations, and give rise to novel spin-lattice effects, even in the paramagnetic phase. On the time-scale of lattice fl uctuations, spin orbit could give rise to a dynamical Dzya-loshinsky-Moriya interaction, which on lowering the temperature eventu-ally becomes static and probably cru-cial in establishing three-dimensional magnetic order. New experiments and theoretical work will tell us if this dynamical scenario is correct.

Eva Pavarini

Institute for Advanced Simulation,

Forschungszentrum Jülich, 52425 Jülich,

Germany


References

[1] K.I. Kugel and D.I. Khomskii, Zh. Eksp. Teor. Fiz. 64, 1429 (1973) [Sov. Phys. JEPT 37, 725 (1973)].[2] I. Leonov et al., Phys. Rev. Lett. 101, 096405 (2008).[3] E. Pavarini, E. Koch, A.I. Lichten- stein, Phys. Rev. Lett. 101, 266405 (2008)[4] E. Pavarini and E. Koch, Phys. Rev. Lett. 104, 086402 (2010).[5] J. Deisenhofer et al., Ann. Phys. (Berlin) 523 (8-9), 645 (2011)Figure 1 Orbital order in KCuF3 [3].


A15

Ann. Phys. (Berlin) 523, No. 7, 580–581 (2011) / DOI 10.1002/andp.201110469


On the multi-orbital band structure and itinerant magnetism of iron-based superconductors* Ole Krogh Andersen** and Lilia Boeri

Received 7 November 2010, accepted 26 November 2010,

Published online 4 January 2011

* Published in Ann. Phys. (Berlin) 523, No. 1–2, 8–50 (2011);

modifi ed for the sample issue, with permission from the

authors.** Corresponding author:


Max-Planck-Institute for Solid State Research,

Heisenbergstrasse 1, 70569 Stuttgart, Germany

Ann. Phys. (Berlin) 523, No. 1-2, 8-50 (2011) / DOI 10.1002/andp.201000149

This paper explains the multi-orbital band structures and itin-

erant magnetism of the iron-pnictide and chalcogenide super-

conductors. We fi rst describe the generic band structure of a

single, isolated FeAs layer. Use of its Abelian glide-mirror group

allows us to reduce the primitive cell to one FeAs unit. For the

lines and points of high symmetry in the corresponding large,

square Brillouin zone, we specify how the one-electron Hamil-

tonian factorizes. From density-functional theory, and for the

observed structure of LaOFeAs, we generate the set of eight

Fe d and As p localized Wannier functions and their tight-bind-

ing (TB) Hamiltonian, h(k). For comparison, we generate the set

of fi ve Fe d Wannier orbitals. The topology of the bands, i. e.

allowed and avoided crossings, specifi cally the origin of the d6

pseudogap, is discussed, and the role of the As p orbitals and

the elongation of the FeAs4 tetrahedron emphasized. We then

couple the layers, mainly via interlayer hopping between As pz

orbitals, and give the formalism for simple tetragonal and

body-centered tetragonal (bct) stackings. This allows us to ex-

plain the material-specifi c 3D band structures, in particular the

complicated ones of bct BaFe2As2 and CaFe2As2 whose interlayer

hoppings are large. Due to the high symmetry, several level

1 Introduction

The first report of superconductivity in an iron pnictide, specifically in F-doped LaOFeP below 5K in 2006 [1, 2], was hardly noticed and only two years later, when F-doped LaOFeAs was reported to su perconduct below 28 K, the potential of iron pnictides as high-temperature superconducing materials was realized [3]. Following this discovery, more than 50 new iron superconductors with the same basic structure were discovered [4] with Tc reaching up to 56 K [5]. This structure is shown in Fig. 1 for the case of LaOFeAs. The common motive is a planar

inversions take place as functions of kz or pressure, and linear

band dispersions (Dirac cones) are found at many places. The

underlying symmetry elements are, however, easily broken by

phonons or impurities, for instance, so that the Dirac points are

not protected. Nor are they pinned to the Fermi level because

the Fermi surface has several sheets. From the paramagnetic

TB Hamiltonian, we form the band structures for spin spirals

with wavevector q by coupling h(k) and h(k+q). The band struc-

ture for stripe order is studied in detail as a function of the ex-

change potential, Δ, or moment, m, using Stoner theory. Gap-ping of the Fermi surface (FS) for small Δ requires matching of FS dimensions (nesting) and d-orbital characters. The interplay

between pd hybridization and magnetism is discussed using

simple 4×4 Hamiltonians. The origin of the propeller-shaped

Fermi surface is explained in detail. Finally, we express the

magnetic energy as the sum over band-structure energies and

this enables us to understand to what extent the magnetic en-

ergies might be described by a Heisenberg Hamiltonian, and to

address the much discussed interplay between the magnetic

moment and the elongation of the FeAs4 tetrahedron.

FeAs layer in which the Fe atoms form a square lat tice, tetrahedrally coordinated with As atoms placed alternat-ingly above and below the hollow centers of the squares.

1

HighlightsReview

Article


Instead of As, the ligand could be another pnictogen (P) or a chal-cogen (X=Se or Te), but for sim-plicity, in this paper we shall refer to it as As. These superconduc-tors are divided in four main fam-ilies depending on their 3D crys-tal structure [6]: The iron chal-cogenides are simple tetragonal (st) with the FeX layers stacked on top of each other (11 family). The iron pnictides have the FeAs layers separated by alkali met-als (111 family), or by rare-earth oxygen/fluoride blocking layers (1111 family as in Fig. 1), in st stacking, or by alkali-earth met-als (122 family) in body-centered tetragonal (bct) stacking. Iron-based superconductors share some general physical properties, although the de-tails are often specific to families, or even to compounds. With the exception of LiFeAs, the undoped compounds are spin-density wave (SDW) metals at low tempera-ture with the Fe spins ordered anti-ferromagnetically between nearest neighbors in the one direction and fer-romagnetically in the other, thus forming stripe or dou-ble-stripe (FeTe) patterns. The values of the measured magnetic moments range from 0.4 μB/Fe in LaOFeAs [7], to ∼ 1μB in BaFe2As2 compounds, to over 2 μB in doped tellurides [9–11]. At a temper ature above or at the Neel temperature, which is of order 100K, there is a tetragonal-to-orthorhombic phase transition in which the in-plane lattice constant contracts by 0.5-1.0% in the direction of ferro magnetic order. Superconductivity sets in when the magnetic order is suppressed by pressure, electron or hole doping, or even isovalent doping on the As site, and at a much lower temperature. Both super-conductivity and magnetism are found to depend cru-cially on the details of the crystal structure; for example is it often observed that the highest Tc s occur in those compounds where the FeAs4 tetrahedra are regular [8]. Critical temperatures range from a few K in iron-phos-phides to 56 K in SmOFeAs. The variations in the phonon spectra are, however, small and seem uncorrelated with Tc . This, together with the proximity of magnetism and superconductivity in the phase diagram, was a first in-dication that the superconductivity is unconventional. A stronger indication seems to come from the symmetry of the superconducting gap, which is currently a strongly debated issue [12]. Depending on the sample, and on the experimental technique, multiple gaps with s symmetry

and various degrees of anisotropy – but also of nodes – have been reported [9–11]. It now seems as if the gap symmetry is not universal, but material specific in these compounds. Current understanding of the basic electronic struc-ture has been reached mainly by angle-resolved pho-toemission (ARPES) [13–22], quantum oscillation, and de-Haas-van-Alphen (dHvA) experiments [23– 29] in combination with density-functional (DFT) calcula-tions [30–41]. All parent compounds have the electronic configuration Fe d6 and are metallic. In all known cases, the Fermi surface (FS) in the para magnetic tetragonal phase has two concentric hole pockets with dominant dxz /dyz character and two equivalent electron pockets with respectively dxz /dxy and dyz /dxy character. A third hole pocket may also be present, but its character, dxy or d

3z2

−1, as well as the sizes and shapes of all sheets, vary

among different families of compounds, and, within the same family, with chemical composition and pres sure. In all stoichiometric compounds, the volumes of the hole sheets compensate those of the electron sheets. The magnetically stripe-ordered phase remains metallic, but

Figure 1 The layered structure of simple tetragonal LaOFeAs. The 3D primitive cell contains one Fe2As2 and one La2O2 layer, each contain-

ing three sheets: a square planar Fe (red) or O (blue) sheet sand-

wiched between two planar As (green) or La (yellow) sheets. c =

874pm. The coordination of Fe with As, or O with La, is tetrahedral. x

and y are the vectors between the Fe-Fe or O-O nearest neighbors

(separated by α = 285 pm) and X and Y are those between As-As or La-La nearest neighbors in the same sheet. The directions of those

vectors we shall denote x, y, X , and Y .

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the FS becomes much smaller and takes the shape of a propeller [16] plus, possibly, tiny pockets [23]. Given the strong tendency to magnetism, and the low value of the calculated electron-phonon in teraction [42–44], spin fluctuations are the strongest candidate for mediating the superconductivity. Al ternative scenarios have been proposed, in which superconductivity is due to magnetic interactions in the strong-coupling limit, polarons, or orbital fluctuations [45]. Models for spin fluctuations are based on the weak-coupling, itinerant limit, with superconductivity related to the presence of strong nesting between hole and electron sheets of the paramagnetic Fermi surface, which is also held respon-sible for the instability towards magnetism [40, 41, 46]. This possibility has been investigated using more ore less sound models of the band structure, combined with dif-ferent many-body methods (RPA, FLEX, frG, model ME calculations) which do seem to agree on a picture with competing instabilities towards mag netism and super-conductivity [40, 41, 47–58]. The superconducting phase should be characterized by multiple gaps, with s and d symmetries almost degenerate. Modifying the shape and orbital characters of the different sheets of the Fermi sur-face by doping, pressure, or chemistry can influence the leading instability and affect the structure of the gap. As a result, a reasonable, qualitative picture of the materi als trend, such as the dependence of Tc and gap symmetry on the tetrahedral angle, has evolved [50,55]. Most ex-perimental evidence seems to support this picture, but several points remain controversial. A badly understood issue is how to include 3D effects, which is particularly serious for the bct 122 com pounds. Another problem concerns the magnetism: While it is true that spin-polarized DFT (SDFT) calcula tions repro-duce the correct atomic coordinates and stripe-order of the moment, the magnitude of the moment is, except in doped FeTe, at least two times larger than what is mea-sured by neutron scattering, or inferred from the gaps measured by ARPES [28, 59], dHvA, and optics [60], albeit much smaller than the saturation moment of 4 μB /Fe. Suppressing the too large moments in the calculations will, however, ruin the good agreement for the structure and the phonon spectra [43, 61–64]. This over-estimation of the moment is opposite to what was found 25 years ago for the superconducting cuprates where the SDFT gave no moment, but is typical for itinerant magnets close to a magnetic quantum critical point (QCP) [61]. The magnetic fluctuations in time and space have been described [65] using a localized Heisenberg model with competing ferro-and antiferromagnetic interactions be-tween respectively first and second-nearest neighbors, but to reconcile this model with the partly metallic band

structure is a problem [46, 66–69]. Another possible solu-tion of the moment problem in SDFT is that moments of the predicted size are present, but fluctuate on a time scale faster than what is probed by the experi ments [61]. In fact, two recent studies of realistic, DFT-derived multi-band Hubbard models solved in the dynamical mean-field approximation (DMFT) show that the magnetism has two different energy scales [70, 71]. It is therefore possible that the electronic correlations after all do play a role in these multi-band, multi-orbital materials [72, 73]. Experiments and calculations have revealed a marked interplay between the details of the band structure and the superconducting properties. Most of these observa-tions are empirical and we feel that there is a need to ex-plain the origin of such details. In this paper, we therefore attempt to give a self contained, pedagogical description of the paramagnetic and spin-polarized band structures. Specifi cally, we discuss the Fe d As p band-structure to-pology, causing the pseudogap at d6 as well as numer ous Dirac cones, the interlayer hopping in the simple-tetrag-onal and body-centered-tetragonal struc tures, the spin-spiral band structures, and the band-resolved magnetic energies. In all of this, the co valency between Fe d and As p is found to play a crucial role. Applications to super-conductivity are beyond the scope of the present paper. In Sect. 2 we explain the structure of a single, isolated FeAs layer and use the glide mirror to reduce the primi-tive cell to one FeAs unit and have k running in the large, square Brillouin zone (BZ) known from the cuprates. Halving the number of bands will prove important when it comes to understanding the multi-orbital band struc-ture. In Sect. 3 we show that this band structure may be generated and un derstood from downfolding [74], of the DFT Hilbert space for LaOFeAs to a basis set consisting of the five Fe d, localized Wannier orbitals, or – as we prefer – including explicitely also the three As p orbitals. Even the latter 8 × 8 tight-binding (TB) Hamiltonian, h (k), has long-ranged pp and pd hoppings due to the diffuseness of the As p orbitals, and its accurate, analytical matrix elements are so spacious that they will be published at a different place [75]. The crucial role of the As p orbit-als for the low-energy band structure, the electron bands in particular, and the presence of a d 6 pseudogap is em-phasized. The different sheets of the FS are discussed. In Fig. 2 we show the factorization of the Bloch waves along the lines and points of high symmetry in the large BZ. The high symmetry of the single, tetragonal layer allows many bands to cross and leads to linear dispersions, and even to Dirac cones. Our understanding of this generic band structure of a single layer then allows us to discuss standard DFT calculations for specific materials. This is done in Sect. 4, where we first see that increasing the As


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Figure 2 Upper-right quarter of the large Brillouin zone (BZ) for the glide mirror space group of the single FeAs layer (black), the factori-

zation of the band Hamiltonian (blue), and the LaOFeAs Fermi sur-

face (red). The BZ for merely the translational part of the space group

has half the area and is folded-in as indicated by the dashed black

lines. In order to distinguish the corners, M, and edge mid points, X,

of these two square BZs, we use an overbar for the large BZ. Hence

Γ= Γ , M= X , and X is the com mon midpoint of the XY and ΓM-lines. The folding causes all three hole pockets to be centered at Γ and the two electron pockets be centered at M with their axes

crossed. The blue boxes along the lines of high symmetry contain

the orbitals whose Bloch-sums may hybridize (belong to the same

irreducible representa tion). At the high-symmetry points, this fac-

torization of the Hamiltonian into diagonal blocks is as follows: Γ[xy][XY] [Xz, X] [Yz,Y][zz,z], X [xz][xy,y] [yz, z], [XY, zz,x], and M [XY ][zz][xy, z][Xz, X ][Yz, Y ]. With of ten used notations [41], the inner and outer sheet of the M-centered xz/yz-like hole pock-ets are respectively α1 and α2 while the X and Y -centered xy/xz and xy/yz-like electrons sheets are respectively β1 and β2, and the Γ -centered xy-like hole pocket is γ.

height moves an anti bonding pz /dxy level down towards the degenerate top of the dxz /dyz hole bands, with which it cannot cross, and thereby causes the inner, longitudinal band to develop a linear dispersion. In-terlayer hopping is shown to pro-ceed mainly via the As pz orbital and to have a strength and (kx, ky) -dependence which depends on the material family. This hopping is strongest for the bct structure where the As atoms in neighboring layers face each oth-er. In st SmOFeAs and for kz at the edge of the 3D BZ, the antibonding pz /dxy level reaches the top of the hole bands and forms a Dirac cone together with the longitudinal hole band. In LiFeAs and FeTe the Dirac point is inside the BZ. The interlayer hopping not only causes the As pz -like 2D bands to disperse with kz , but also folds the bands into the conventional, small BZ, i. e. it cou-ples h (k)and h (k + πx + πy). The formalism for interlayer hopping is given in Sect. 4.2, and its increasing

influence on the band structures of BaFe2As2, CaFe2As2, and collapsed CaFe2As2 is shown and explained, for the first time, we believe. In CaFe2As2, we find that the nearly linear dispersion of the dxy /pz -like electron band has de-veloped into a full Dirac cone. The effects of spin polarisation on the generic 2D band structure are discussed in Sect. 5. We con sider spin spirals which have a translationally invariant magnitude but a spiralling orientation which is given by q. Their band Hamiltonian possesses translational symmetry both in configurational and in spin-space, but indepen-dently of each other as long as spin-orbit coupling is ne-glected. The spin spiral therefore simply couples h (k) to h (k + q) , regardless of whether q is commensurable or not. For h (k) we use the DFT pd Hamiltonian derived in Sect. 3. In order to keep the analysis transparent and amenable to generalization, we shall treat the exchange coupling using the Stoner model rather than full SDFT. This has the avantage that it decouples the band struc-ture and self-consistency problems, so that we can study the band structure as a function of the exchange poten-tial, Δ. In Sect. 5.2 we discuss the bands and FSs for the observed stripe order. As long as the moment is a linear function of Δ, gapping requires matching of d-orbital

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characters as well as FS dimensions (nesting). For larger moments, and ferromagnetic order in the x direction, the FS is different and shaped like a two-blade propeller in the ky direction. It is formed by crossing dxy /pz -dyz↓ and dzz↓/dXY ↑ bands, which cannot hybridize along the line through the blades and the hub. The resulting Dirac cone has been predicted before [76] and also observed [29, 77]. The interplay between pd hybridization and magne-tism is discussed using sim ple, analytical 4 × 4 models. In Sect. 5.3 we first show the static spin-suceptibility, m (Δ)/Δ, calculated for stripe and checkerboard orders as functions of the electron doping in the rigid-band approxima tion. The low-moment solution – maybe for-tuitously – resembles the behaviour of the observed mo-ment as a function of doping and q. We then discuss the electronic origin of the magnetic energies and first show how the magnetic energy may be interpreted as the dif-ference between double-counting corrected magnetic and non-magnetic band-structure energies. This directly relates the magnetism to the band structure and we specifically look at the origin of the magnetic energy. We find that the mag netic energy gain is caused by the cou-pling of the paramagnetic dxy hole and dxy /pz electron bands, as well as by that of the dxz parts of the two other electron and hole bands. The Fermi-surface contribu-tions to the magnetic energy are comparatively small. We can then explain why increasing the distance between the As and Fe sheets increases the stripe-ordered mo-ment, and vice versa. At the end, we compare our results with those of fully self-consistent SDFT spin-spiral calcula tions of moments and energies as functions of q and doping in the virtual-crystal approximation, for LaO1−xFxFeAs and Ba1−2yK2yFe2As2.

2 Structure

The basic structural unit for the iron-based supercon-ductors is a planar FeAs layer consisting of three sheets: (Fig. 1). In the high-temperature paramagnetic tetrago-nal phase, the iron atoms form a square sublattice (a ≡ 1) with each Fe tetrahedrally coordinated by four As li-gands. The latter thus form two 2 × 2 square lattices above and below the Fe plane at a vertical distance of ap-proximately half the a-constant of the Fe sublattice. The Fe and As positions are thus described by respectively :

where x and y are the orthogonal vectors between the Fe nearest neighbors and nx and ny take all integer val-ues. z is perpendicular to x and y, and has the same length. For perfect tetrahedra, η = 1, and for LaOFeAs, η = 0.93. Instead of η ≡ 2cot θ/2 ≡ 2 2zAs, it is customary to specify the As-Fe-As tetrahedral angle, θ, or the inter-nal parameter, zAs. While t are the translations of the Fe sublattice, T ≡ nX X + nY Y are those of the As sublattice whose primitive translations are X ≡ y + x and Y ≡ y − x. The latter are turned by 45° with respect to x and y, and

2 longer. The translation group of the FeAs layer is T and has two FeAs units per cell. These are, however, re-lated by a glide mirror. Rather than using the irreducible representations of the 2D translation group, it is there-fore simpler to use those of the group generated by the primitive Fe-translations, x and y, combined with mir-roring in the Fe-plane. These glide-mirror operations (“take a step and stand on your head”) generate an Abe-lian group with only one FeAs unit per cell and irreduc-ible representations, exp (ik · r) , which are periodic for k in the reciprocal lattice, hx 2πx+hy 2πy, with hx and hy integer. The corresponding Brillouin zone (BZ) shown in Fig. 2 is a square, centered at the Γ -point k = 0, with corners at the M -points, k = πy ±πx and−πy

±

πx, i. e. at ±πX and ±πY, and edge-centers at the X and Y-points, k =±πx and ±πy. In this paper we shall use this more heavy notation instead of e.g. (π, π) for M and (π,0) for X as done for cuprates, because for the iron superconductors, no consensus exists about whether to use the (x, y) or the (X , Y ) coordinate system. The overbar is used to designate the high-symmetry points in the 2D reciprocal space for the glide-mirror group. In conclusion, use of the glide-mirror group reduces the number of bands by a factor of two, and this is impor-tant when attempting to understand the intricacies of the band structure. In Fig. 3 we sketch the antibonding Bloch sums of the Fe dxy (top) and dxz (bottom) orbitals, and realize that with the glide-mirror notation the former has k = 0 and the latter k · x = π. Accordingly, the top of the pure Fe dxy band is at Γ , while the degenerate top of the pure dxz and dyz bands is at M . We shall often return to this. (Authors who unfold without reference to the glide-mirror group, may have Γ and M interchanged, with the result that the xy hole pocket and the two xz/yz hole pockets are re-spectively at M and Γ . In order to avoid this confusion, it is useful to remember that the two xz/yz hole pockets are those towards which the electron superellipses at Xand Y are pointing). The real 3D crystals consist of FeAs layers stacked in the z-direction with other layers intercalated, although the iron chalcogenides, FeX, have no intercalation. Fig 1


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specifically shows LaOFeAs, for which all our Wannier-orbital (3D) calculations were done, unless otherwise stated. The interlayer coupling is weak but not negligible, and it depends on the material. Although the 2D glide-mirror may take the 3D crystal into itself, as is the case for LnOFeAs, FeX, and LiFeAs, we do want to use kz to enumerate the states in the third direction. For the 3D crystals we shall therefore use the standard 3D transla-tion group according to which only the X and Y transla-tions, combined with an out-of plane translation, leave the crystal invariant. The corresponding 2D reciprocal lattice is hX πX+hY πY = hX + hY πy+hX − hY πx. Hence, the 3D Brillouin zone is as shown by the dashed lines in Fig. 2 (for kz =π/2c), with M falling onto Γ and with corners at X and Y , now named M. Interlayer hopping may thus couple the glide-mirror states at k with those at k+πx+πy. This material-dependent coupling will be considered in Sect. 4 after we have explained the generic electronic structure of a single FeAs layer.

Spin-orbit interaction also invalidates the glide-mirror symmetry, but the splitting of states degen erate at k and k +πx+πy is at most 32 ζFe3d 0.1 eV, and this only oc-curs if all three xy, yz, and xz states happen to be degen-erate and purely Fe d-like.

3 Paramagnetic 2D band structure

In this section we shall describe the generic 2D band structure of an isolated FeAs layer. We start by observing that the bands are grouped into full and empty, separat-ed by a pseudogap. We then discuss the grouping of the bands into Fe 3d and As 4p, and derive two sets of Wan-nier orbitals from DFT, one set describing merely the five Fe d-like bands and another set describing the eight Fe d-and As p-like bands. Armed with those sets, we can return to a detailed description of the low-energy band-structure, i. e. the one which forms the pseudogap at d6 and the Fermi surface. This is done in subsection 3.3 where we shall see that the hybridization between – or covalency of – the As p and the Fe d orbitals is crucial for the band topology. Bringing this out clearly, was in fact our original reason for deriving the eight-orbital pd set, although the five-orbital d set suffices to describe the low-energy band structure. For FeTe and LaOFeAs the formal ionic states are respectively Fe2+Te2− and La3+O2−Fe2+As3−. In fact, for all parents of the iron-based superconductors, the nomi-nal electronic configuration is ligand p6 Fe d6. The ge-neric 2D band structure is shown in Fig. 4 for energies ranging from 4.5 eV below to 2.5 eV above the Fermi lev-el and along the high-symmetry lines of the BZ (Fig. 2). In the energy range considered, there are eight bands which are seen to separate into three low-energy and five high-energy bands. They may be called respectively the ligand p-and iron d-bands, and the correspond-ing electron count is as written on the figure. At p6d6

the two uppermost bands are seen to be detached from the rest, except at one (Dirac) point along the XM -line where two bands cross, because their Bloch functions are respectively even and odd with respect to reflection in a vertical mirror parallel to XM and containing near-est-neighbor As atoms. If the energy of this crossing could be moved up, above the relative band maxima atΓ and M, it would drag the Fermi level along and the material would transform into a zero-gap semiconduc-tor. For the iron-based superconductors, however, the Fermi level is merely in a pseudogap and the Fermi sur-face (FS) consists of a Γ -centered hole pocket, two M-centered hole pockets, and two compensating electron pockets centered at respectively X and Y (Fig. 2).

Figure 3 Sketch of the anti bonding Bloch sum of Fe dxy orbitals in the xy-plane (top) and of the antibonding Bloch sum of Fe dxz orbit-als in the xz-plane (bottom). A Bloch sum is formed by adding the glide-mirrored π orbital multiplied by exp i k · t , where the glide, t, is a primitive translation, x or y, and the mirror is the Fe plane. The antibond ing Bloch sum of dxy orbitals has k=0 and that of dxz or-bitals has k·x=π. That the lobes of the real Wannier orbitals avoid the As sites (Fig. 6) is indicated by enhancing the countours of the lobes

pointing towards the reader.

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3.1 Fe d five-orbital Wannier basis

Characterizing the five upper bands as Fe d is sound, be-cause they can be spanned exactly by five Wan nier func-tions [41] which behave like Fe d-orbitals. This can be seen in Fig. 5. Our Wannier functions were constructed [74] to have d character on the central Fe site and no d character on any other Fe site. This makes them localized Wannier

orbitals. The five bands of course have characters other than Fe d, and those characters are mixed into the Fe d Wannier orbitals. This by-mixing follows the point sym-metry in the crystal. Specifically, the Fe dxy Wannier orbital has on-site Fe pz character breaking the horizontal-mirror symmetry of the pure dxy orbital, as well as strong off-site pz character on all four As neighbors. The sign of the As pz character is antibonding to Fe dxy because the As p hy-bridization pushes the Fe d band up in energy. The cor-responding nodes between the Fe d and As p tails make neighboring lobes difficult to see in the figure. Hence, only the As pz lobes pointing towards the La lay ers are big. Sim-ilarly, the Fe dXz Wannier orbital antibonds with pX on the two As neighbors in the X direction, and Fe dY z antibonds with pY on the two As neighbors in the Y direction. If the Fe-site sym metry had been exactly tetragonal, the three above-mentioned Wannier orbitals would have been de-generate and transformed according to the t2 irreducible representation. However, the non-tetrahedral environ-ment, e.g. flattening of the tetrahedron (η < 1) , increases the energy of the dxy orbital above that of the d orbitals be-longing to t, i. e. dXz and dY z or, equivalently, dxz and dyz. In LaOFeAs, the energy of dxy is ∼0.1 eV above that of dt . The two remaining Wannier orbitals, d

3z2−1≡dzz and dy2−x2 ≡dXY ,

antibond less with As p because their lobes point between the arsenics. Fe dzz is seen to antibond with pz on the four As neighbors and Fe dXY antibonds with pY on the two As neighbors in the X direc tion, and with

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