Zlatko Tesanovic, Johns Hopkins University zbt@pha.jhu.edu http://www.pha.jhu.edu/~zbt

o Strongly correlated normal state exhibiting a “BCS-ish” pairing instability (?pnictides, 3He, heavy fermions, organics, e-doped cuprates, …)

o Intrinsic strongly correlated SC, exerting major influence on surrounding “normal” state(s) (?pnictides, h-doped cuprates, …)

Correlated superconductivity comes in (at least) two varieties:

Electron Correlations and HTS in Fe-Pn

122

Correlated Superconductors: Cu-oxides vs Fe-pnictides

However, there are also many differences! This may add up to new and interesting physics

FeAs

ORE1111

11

111

Key Difference: 9 versus 6 d-electrons

In CuO2 a single hole in a filled 3d orbital shell

A suitable single band model might workIn FeAs large and even number of d-holes

A multiband model is likely necessary

ZT, Physics 2, 60 (2009)

Phase diagram of Cu-oxides

Cu-oxides: Mott Insulators Superconductors

?? How Mott insulators turn into superconductors, particularly in the pseudogap region, remains one of great intellectual challenges of condensed matter physics

U

Only when doped with holes (or electrons) do cuprates turn into superconductors

All superconductors havethermal fluctuations

No such ground state in BCS theory (at weak coupling) !!

Correlated superconductors havequantum (anti)vortex fluctuations

Ground state with enhancedpairing (and other!) correlations but no SC !!(gauge theories, QED3, chiral SB, AdS/CMT,…PW Anderson, Balents, Burkov, MPA Fisher, Nayak, Nikolic, Sachdev, Senthil, PA Lee, Franz, Vafek,,ZT)

How Correlated Superconductors turn into Mott Insulators

Near Tc these are alwaysphase fluctuations

ZT, Nature Physics 4, 408 (2008)P. Nikolic and ZT, PRB 83, 064501 (2011)

BCS-Eliashberg-Migdal

Optimal Tc in HTS is determined by quantum fluctuations

Giant Nernst Effect and Quantum Diamagnetism in HTS

Vortex fluctuations and enhanced quantum diamagnetism in pseudogap state !!

Z. A. Xu et al., Nature 406, 486 (2000)

L. Li et al., Nature-Phys (2007)

Vortex excitations in conductivity !! N. P. Armitage et al, Nature Physics

A sequence of thermal KT transitions as Tc drops from 40K to 2K

However, there is a clear break below ~ 30K indicating Tc -2(0) s (0)

magnitude of Tc(x) is dictated byQuantum critical SC fluctuations !!

Quantum Superconducting Fluctuations in Underdoped Cuprates

“Thermal metal” in non-SC YBCOM. Sutherland et al., PRL 94, 147004 (2005)

I. Hetel et al., Nature Physics 3, 700 (2007)

d-wave nodal liquid in highly underdoped BSCCO U. Chatterjee et al., Nature Physics 6, 99 (2009)dHvA Small Fermi surfaces (pockets) in underdoped YBCO?

C. Jaudet et al., PRL 100, 187005 (2008); S. E. Sebastian et al., PNAS 107, 6175 (2010) d-wave pseudogap in YBCO in very high fields S. C. Riggs . et al., NHMFL preprint (2010)

Pockets & Nodes?

Millis & NormanChubukov Johnson et al.

Fermi sea

+

+

- -

Cooper pairing driven by repulsion (No BEC limit) !!

HTS, other correlated SCs Cooper pairing is a way of reducing repulsion !! Competition with other states !!

P. W. Anderson, KITP Conference on Higher Tc, June 2009

Projection eliminates doubly occupied sites

Phase diagram of underdoped cuprates from a wave-function?

This is just d-wave BCS SC. However,inside © there is:

ij must start fluctuating as x 0

and system becomes Mott insulator.

Including fluctuations in ij leads to

improved ground state wavefunction.

N & 1PW AndersonPA Lee, Senthil, Wen, Hermele Balents, MPA Fisher, Nayak Franz, Vafek, Melikyan, ZTSenthil & MPA Fisher,Balents, Burkov, Sachdev, …Salk et al, …

Pockets !?Nodes !?Pockets & Nodes !?

Correlated s-wave superconductor

Quantum s-wave/bosonic duality:

Automatic conservation of vorticity Cooper pairs, bound by strong attraction !!

view i - j as a gauge field aij coupled to electrical charge

P. Nikolic and ZT, PRB 83, 064501 (2011)

Quantum Phase Fluctuations on SITES: Formation of Local Spin Singlets (Strong Attraction, U < 0)

Real space Cooper pairs (center-of-mass motion only)

CDWSC

Strong local attraction favors formation of spin singlet Cooper “molecules” (BEC limit):

Bond Phases (dSC) versus Site Phases (sSC)

Automatic conservation of vorticity Cooper pairs !!

Vafek, Melikyan, ZT

d-wave SC Duality is More Complex

Quantum d-wave/fermionic duality (U > 0):

Monopole-antimonopole configurations Non-conservation of vorticity Cooper pairs !!

Quantum s-wave/bosonic duality (U < 0):

Automatic conservation of vorticity Cooper pairs !!

Translation: Cooper pairs can fall apart !! They are held together by kinetic energy and cannot survive without motion in a correlated medium (No BEC) !

ZT, Nature Physics 4, 408 (2008)P. Nikolic and ZT, PRB 83, 064501 (2011)

What controls fluctuations in µij ? Kinetic energy.

view ij as gauge field aij coupled to staggered charge

ZT, Nature Physics 4, 408 (2008)

Formation of Local Singlets on BONDS (Strong Repulsion, U >> t) !!

For CuO2 plane this translatesinto a d-wave superconductor Or an antiferromagnet !!

dSC or AF as the ground state depends on kinetic energy and dynamics of center-of-mass versus relative motion of bond Cooper pairs

If center-of-mass moves aroundfreely while relative motion is suppressed

CuO2 plane dSC CuO2 plane is Neel AF !!

If relative motion becomes too strong Cooper pairs break up !!

As relative fluctuations become too strong and motion ceases, bond Cooper pairs fade away !! charge e insulator !! Dual of dSC is AF

Strong local repulsion favors formation of spin singlets on bonds:

Cooper pairs are held together by electronic motion repulsion is minimized

ZT, Nature Physics 4, 408 (2008)

Wave-function ©BCS is not enough Quantum disorder in

µij !!

Must include quantumfluctuations of:

dSC

dSCnodal fermions

AF+x

Lu Li & Ong

Phase diagram of Cu-oxides

Fe-pnictides: Semimetals Superconductors

In contrast to CuO2, all d-bands in FeAs are either nearly empty (electrons) or nearly full (holes) and far from being half-filled. This makes it easier for electrons (holes) to avoid each other. FeAs are less

correlated than CuO2

(correlations are still important !! )

C. de la Cruz, et al., Nature 453, 899 (2008)

Phase diagram of Fe-pnictides

Like CuO2, phase diagram of FeAs has SDW (AF) in proximity to the SC state.

SC coexists with SDW (AF) in 122 compounds

H. Chen, et al., arXiv/0807.3950

However, unlike CuO2, all regions of FeAs phase diagram are (bad) metals !!

SmFeAsO1-xFx

parent (SDW)

SCx = 0.0

x = 0.18

T. Y. Chen, et al..

Important: Near EF e and h bands contain significant admixture of all five Wannier d-orbitals, dxz and dyz of odd parity (in FeAs plane) and the remaining three d-orbitals of even parity in FeAs plane

Minimal Model of FeAs LayersV. Cvetkovic and ZT, EPL 85, 37002 (2009)C. Cao, P. J. Hirschfeld, and H.-P. Cheng, PRB 77, 220506 (2008)K. Kuroki et al, PRL 101, 087004 (2008)

dxz odd parity

even parity

dyz

dxy dxx-yy d2zz-xx-yy

Nesting in Fe-pnictides

Turning on moderate interactions VDW = itinerant multiband CDW (structural), SDW (AF) and orbital orders at q = M = (¼,¼)

Cvetkovic & ZT, Korshunov & Eremin

Semiconductor Semimetal

m

d

c

ed

ec

SDW, CDW, ODW or combinations thereof VDW

Interactions in FeAs IV. Cvetkovic and ZT, PRB 80, 024512 (2009); J. Kang and ZT, PRB 83, 020505 (2011)

Interactions in FeAs II

Typically, we find Ws is dominant Valley density-wave(s) (VDW) in FeAs

h1 h2 e1

e-h

These “Josephson” terms are not crucial for SDW Could they be the cause of SC ?

Hirschfeld, Kuroki, Bernevig, Thomale, Chubukov, Eremin,

Interband pairing acts like Josephson coupling in k-space. If G2 is repulsive antibound Cooper pairs (s’SC)M

Two Kinds of Interband Superconductivity

Type-A interband SC:

c

FS

c d

d

Type-B (intrinsic) interband SC:

c d

FS

sSC

s’SC

G2

sSC

s’SC

G2

ZT, Physics 2, 60 (2009)

If G1 , G2 << U, W relevant vertices: U, W, & G2

Interactions in FeAs III V. Cvetkovic & ZT (RG) ; A. V. Chubukov, I. Eremin et al (parquet);F. Wang, H. Zhai, Y. Ran, A. Vishwanath & DH Lee (fRG)R. Thomale, C. Platt, J. Hu, C. Honerkamp & A. Bernevig (fRG)

The condition for interband SC is actually milder: suffices to have G2* > U* even if G2 << U

RG flows (near SDW):

RG Theory of Interband Mechanism of SC in FeAs V. Cvetkovic and ZT, PRB 80, 024512 (2009)

In Fe-pnictides interband superconductivity (s’ or s+- state) is a strong possibility but there is some fine tuning with SDW/CDW/ODW

What is a (THE) Model for Iron-Pnictides ? U(4)£U(4) Theory of Valley-Density Wave (VDW)

Key assumption I:

Eremin, Knolle

Hirschfeld, Kuroki, Bernevig, Thomale, Chubukov, Eremin,

Key assumption II:

U(4)£U(4) Theory of Valley-Density Wave (VDW)

U(4)£U(4) symmetry unified spin and pocket/orbital flavors

V. Cvetkovic and ZT, PRB 80, 024512 (2009); J. Kang and ZT, PRB 83, 020505 (2011)

Hierarchy of RG Energy Scales U, W >> G1, G2 U(4)£U(4) Theory of Valley-Density Wave (VDW)

VDW in Fe-pnictides is a (nearly) U(4)£U(4)symmetric combination: SDW/CDW/ODW

(. . .)

D. K. Pratt, et al., arxiv/0903.2833

TS (K) TN (K) mord (μB)

LaFeAsO 155 137 0.36

CeFeAsO 155 140 0.83

PrFeAsO 153 127 0.48

NdFeAsO 150 141 0.9

CaFeAsF 134 114 0.49

SrFeAsF 175 120

CaFe2As2 173 173 0.8

SrFe2As2 220 220 0.94-1.0

BaFe2As2 140 140 0.9

V. Cvetkovic and ZT, PRB 80, 024512 (2009); J. Kang and ZT, PRB 83, 020505 (2011)

Hierarchy of RG Energy Scales U, W >> G1, G2 U(4)£U(4) Theory of Valley-Density Wave (VDW)

U(4)£U(4) symmetry at high energies Spin and pocket/orbital flavors all mixed VDW ground state (any combination of SDW/CDW/ODW)

D. K. Pratt, et al., arxiv/0903.2833

At low energies, numerous terms break this U(4)£U(4) symmetry

Key assumptions:

V. Cvetkovic and ZT, PRB 80, 024512 (2009); J. Kang and ZT, PRB 83, 020505 (2011)

U(4)£U(4) Symmetry vs Reality

Since ¸1 » 0 el-ph interactionor dynamical polarization from Pn bands could easily lead to ¸1 < 0 Pnictides are near ¸1 = 0 QCP !!

J. Kang and ZT, PRB 83, 020505 (2011)

“Near” U(4)£U(4) Symmetry and Experiments

Orbital “AF” Can this modulated current pattern be observed by neutrons? ¹SR?

J. Kang and ZT, PRB 83, 020505 (2011)