Superconductivity and

Low Temperature Physics II

Lecture Notes Summer Semester 2013

R. Gross and A. Marx

© Walther-Meißner-Institute

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General Remarks on the Courses to the Field

Superconductivity and Low Temperature Physics

The following lectures are offered on a regular basis: 1. Superconductivity and Low Temperature Physics I

Foundations of Superconductivity

2. Superconductivity and Low Temperature Physics II (SS 2013: Thu., 12:30h, HS 3) Foundations of Low Temperature Physics and Techniques

3. Applied Superconductivity (SS 2013: Mon. & Wed., 14:15h, WMI) Josephson-Effects, Superconducting Electronics, Quantum Circuits

4. Several Seminars (see announcements)

Documents and Hints: http://www.wmi.badw.de Teaching (announcement of lectures) Lecture Notes (download of scripts, handouts, etc.)

Seminars (announcement of seminars)

SS 2013: - Advances in Solid-State Physics Tue. 10:15 – 11:30h Seminar room 143, WMI - Superconducting Quantum Circuits Tue. 14:30 – 16:00h Library, WMI

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Applied Superconductivity Superconductivity and Low Temperature Physics II

Spin Electronics

Sum

mer

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01

3

VO, ÜB,

Skript

Seminar: Superconducting Quantum Circuits

Tue., 14.30 – 16.00 h, Seminar room, WMI

Seminar: Advances in Solid State Physics

Tue., 10.15 – 11.45 h, Seminar room, WMI

Seminar: Spin Mechanics and Spin Dynamics

Wed., 10.15 – 11.45 h Seminar room, WMI

Mon. and Wed., 14.15 – 15.45 h Seminar room, WMI

Tue, 13.30 – 15.00 h Seminar room, WMI

VO, ÜB,

Skript

VO, ÜB,

Skript

Rudolf Gross Frank Deppe

Thu, 12.30 – 14.00 h Physics Department, HS3

Hans Hübl

S. Gönnenwein

Walther-Meißner-Institut (www.wmi.badw.de)

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year name discovery

1913 Heike Kamerlingh Onnes "For his investigations on the properties of matter at low temperatures which led, inter alia, to the production of liquid helium"

1972 John Bardeen, Leon Neil Cooper und Robert Schrieffer

"for their jointly developed theory of superconductivity, usually called the BCS-theory"

1973 Brian David Josephson "for his theoretical predictions of the properties of a supercurrent through a tunnel barrier, in particular those phenomena which are generally known as the Josephson effect"

1978 Pjotr Kapiza "for his basic inventions and discoveries in the area of low-temperature physics"

1985 Klaus von Klitzing "for the discovery of the quantized Hall effect"

1987 Johannes Georg Bednorz und Karl Alex Müller

"for their important break-through in the discovery of superconductivity in ceramic materials"

1996 David M. Lee, Douglas D. Osheroff und Robert C. Richardson

"for their discovery of superfluidity in helium-3"

1997 Steven Chu, Claude Cohen-Tannoudji und William D. Phillips

"for development of methods to cool and trap atoms with laser light" See Laser cooling.

1998 Robert B. Laughlin, Horst Ludwig Störmer und Daniel Chee Tsui

"for their discovery of a new form of quantum fluid with fractionally charged excitations". See Quantum Hall effect.

2001 Eric A. Cornell, Wolfgang Ketterle und Carl E. Wieman

"for the achievement of Bose-Einstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of the condensates"

2003 Alexei Abrikosov, Witali Ginsburg und Anthony James Leggett

"for pioneering contributions to the theory of superconductors and superfluids"

Nobel Prizes in Physics related to low temperature physics

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Superconductivity and

Low Temperature Physics II

Contents of the Lecture

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I.1 Foundations and General Properties I.1.1 Quantum Fluids I.1.2 Helium I.1.3 Van der Waals Bonding I.1.4 Zero-Point Fluctuations I.1.5 Helium under Pressure I.1.6 pT-Phase Diagram of 4He and 3He I.1.7 Characteristic Properties of 4He and 3He I.1.8 Specific Heat of 4He and 3He

I.2 4He as an Ideal Bose Gas I.2.1 Bose-Einstein Condensation I.2.2 Bose-Einstein Condensation of 4He

I.3 Superfluid 4He I.3.1 Experimental Observations I.3.2 Two-Fluid Model I.3.3 Excitation Spectrum of 4He

I.4 Vortices I.4.1 Quantization of Circulation I.4.2 Experimental Study of Vortices

Contents Part I: Quantum Fluids

I.5 3He I.5.1 normal fluid 3He I.5.2 solid 3He and Pomeranchuk effect I.5.3 superfluid 3He I.6 3He / 4He mixtures

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II.1 Specific Heat II.1.1

II.2 Thermal Conductance II.2.1

II.3 Phonons and Electrons II.3.1

II.4 Magnetic Moments II.4.1

Contents Part II: Solids at Low Temperature

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III.1 Introduction III.1.1 General Remarks III.1.2 Mesoscopic Systems III.1.3 Characteristic Length Scales III.1.4 Characteristic Energy Scales III.1.5 Transport Regimes

III.2 Description of Electron Transport by Scattering of Waves III.2.1 Electron Waves and Waveguides III.2.2 Landauer Formalism III.2.3 Multi-terminal Conductors

III.3 Quantum Interference Effects III.3.1 Double Slit Experiment III.3.2 Two Barriers – Resonant Tunneling III.3.3 Aharonov-Bohm Effect III.3.4 Weak Localization III.3.5 Universal Conductance Fluctuations

III.4 From Quantum Mechanics to Ohm‘s Law

III.5 Coulomb Blockade

Contents Part III: Quantum Transport in Nanostructures

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IV.1 Generation of Low Temperatures IV.1.1 Introduction IV.1.2 Expansion Machine IV.1.3 Regenerative Machine IV.1.4 Joule-Thomson Cooling IV.1.5 Summary IV.1.6 Evaporation Cooling IV.1.7 Dilution Cooling IV.1.8 Pomeranchuk Cooling IV.1.9 Adiabatic Demagnetization

IV.2 Thermometry IV.2.1 Introduction IV.2.2 Primary Thermometers IV.2.3 Secondary Thermometers

Contents Part IV: Cryogenic Techniques:

Generation and Measurement of LT

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• F. Pobell Matter and Methods at Low Temperatures, Springer 1996

• D.R. Tilley and J. Tilley Superfluidity and Superconductivity, Adam Hilger 1990

• C. Enss and S. Hunklinger Low-Temperature Physics, Springer 2005

• P.V.E. McClintock, D.J. Meredith, J.K. Wigmore Matter at Low Temperatures, Blackie 1984

• J. Wilks, D.S. Betts Introduction to Liquid Helium, Oxford 1987

• A. Kent Experimental Low Temperarure Physics, MacMillan, New York

• G.K. White, P.J. Meeson Experimental Techniques in Low Temperature Physics Oxford University Press, 2002

• K.H. Bennemann, J.B. Ketterson The Physics of Liquid and Solid Helium I and II, Wiley 1978

• H. Frey, R.A. Haefer Tieftemperaturtechnologie, VDI-Verlag, Düsseldorf 1981

• Yoseph Imry Introduction to Mesoscopic Physics Oxford University Press, Oxford (1997)

• Supriyoto Datta Electronic Transport in Mesoscopic Systems Cambridge University Press, Cambridge (1995)

• Thomas Heinzel Mesoscopic Electronic in Solid State Nanostructures Wiley VCH, Weinheim (2003)

Literature

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•magnetism

•mesoscopic physics

•nanoscale superconducting and spintronic devices

•superconducting quantum bits

•………

an appetizer

Low Temperature Physics at WMI

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25 nm

Nb Au

Flux Qubit WMI

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Pr1.85Ce0.15CuO4

Crystal Growth Lab

YBa2Cu3O7-d

Bi2Sr2CaCu2O8+d Image Furnace

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fiber for IR laser heating

substrate manipulators

excimer laser optics

target manipulators

pyrometer

casing of RHEED screen and camera

operator tool

AFM/STM system

atomic oxygen source

Laser-Molecular Beam Epitaxy

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[1] R. Gross et al., SPIE Conf. Proc. Vol. 4058 (2000), pp. 278-294

[2] J. Klein, C. Höfener, L. Alff, and R.Gross, Supercond. Sci. Technol. 12, 1023 (1999).

[3] J. Klein, C. Höfener, L. Alff, and R.Gross, J. Magn. and Magn. Mat. 211, 9 (2000).

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SrTiO3

La2/3Ba1/3MnO3

Oxide Heterostructures for Oxide Electronics

Example: Magnetic Tunnel Junction for

Magnetic Random Access Memories (MRAM)

SrTiO3

La2/3Ba1/3MnO3

La2/3Ba1/3MnO3

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Clean Room: 50m², class 100

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Electron Beam Lithography

Philips XL30 SFEG

Lithography System:

Raith ELPHY plus

2µm

Al

JJs

Al

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Intel dual-core 45 nm

(2007)

first transistor (1947)

Bardeen, Brattain, & Shockley

vacuum tubes

ENIAC (1946)

Enigma (1940)

physics

technology

superconducting Qubit

20 µm

WMI

From mechanical to quantum mechanical IP

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Collaborative Research Center 631 Cluster of Excellence NIM

CeNS

F

WSI

F

Semiconductor Quantum Dots

MPQ

Trapped Atoms and Ions

2 µm

Al

WMI

Superconducting Qubits

Development of Hardware Platform for QIP Systems

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Superconducting Quantum Devices and Circuits

Flux Qubit

coplanar waveguide resonator 1.25 GHz

Q > 105

hybrid ring S23 = - 3 dB S31 = - 50 dB

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• minimum temperature ~20 mK • HF shielded room • silver box for HF-shielding • magnetic shielding: cryoperm and

double µ-metal shielding • low temperature low-pass filter (GHz) • room temperature low-pass filter

experimental setup for qubit characterization

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Low temperature scanning probe techniques

Omicron 5K-UHV-STM

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„Dry“ dilution refrigerator (~ 20 mK)

commercial exploitation by Vericold GmbH, Ismaning

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27

innovative cryoengineering

…..WMI develops first dry dilution fridge

K. Uhlig, Cryogenics 42, 73 – 77 (2002)

Oxford Instruments Triton family

market share of dry dilution fridges: > 90%

„Dry“ dilution refrigerator (~ 20 mK)

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WMI Quantum Science Laboratory

Dezember 2011

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New mK Facilities for Circuit-QED Experiments

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Helium-Liquefaction

• Helium liquefier at WMI: Linde TCF 20

• supply of LHe to both Munich Universities

• liquefaction power: > 150 000 l/year

• market price: about 1 Mio. €

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Some Introductory

Remarks

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Temperature Scale

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

104

105

106

107

108

109

tem

per

atu

re (

K)

same amount of new physics on every decade of log T scale

center of hottest stars

center of the sun, nuclear energies

electronic energies, chemical bonding

surface of sun, highest boiling temperatures

organic life

liquid air

liquid 4He universe

superfluid 3He

lowest temperatures of condensed matter

elec

tro

nic

m

ag

net

ism

nu

clea

r-

ma

gn

etis

m

sup

erco

nd

uct

ivit

y

low

te

mp

era

ture

re

se

arc

h

lowest temperature in nuclear spin system achieved by adiabatic demagnetization of Rhodium nuclei: ≈ 100 pK

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Year

low

tem

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atu

res

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ra-l

ow

tem

per

atu

res

paramagnetic refrigeration

nuclear demagnetization

Generation of Low Temperatures - History

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Carl Paul Gottfried von Linde * 11. Juni 1842 in Berndorf, Oberfranken

† 16. November 1934 in Munich

Low Temperature Technology in Germany

1868 offer of chair at the Polytechnische Schule München (now TUM)

1873 development of cooling machine allowing the temperature stabilization in beer brewing

21. 6. 1879 foundation of „Gesellschaft für Linde’s Eismaschinen AG“ together with two beer brewers and three other co-founders

1892 - 1910 re-establishment of professorship

12.5.1903 patent application: „Lindesches Gegenstrom- verfahren“ liquefaction of oxygen (-182°C = 90 K)

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Walther Meißner * 16. Dezember 1882 in Berlin

† 15. November 1974 in Munich

1913 – 1934 building and heading of low temperature laboratory at the Physikalisch-Technischen- Reichsanstalt, liquefaction of H2 (20K)

7.3.1925 first liquefaction of He in Germany (4.2 K, 200 ml), 3rd system world-wide besides Leiden and Toronto

1933 discovery of perfect diamagnetism of superconductors together with Ochsenfeld Meißner-Ochsenfeld Effect

1934 offer of chair at the Technische Hochschule München (now TUM)

1946 – 1950 president of the Bayerischen Akademie der Wissenschaften

1946 foundation of the commission for Low Temperature Research Walther-Meißner-Institut

Walther Meißner - der Mann, mit dem die Kälte kam W. Buck, D. Einzel, R. Gross, Physik Journal, Mai 2013

Low Temperature Technology in Germany

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@ 1 bar

Cryogenic Liquids