Correlated Superconductivity in Cuprates and Pnictides Zlatko Tesanovic, e-mail: zbt@pha.jhu.edu web: http://www.pha.jhu.edu/~zbt

Collaborators: V. Cvetkovic (JHU UCR), V. Stanev, J. Kang, J. Murray, C. Broholm (JHU), …

o Strongly interacting FL + Unconventional SC (3He, heavy fermions, cuprates, pnictides ?)

o Non-FL “normal” state + Unconventional SC (cuprates, pnictides ?)

o Non-FL “normal” state Correlated SC (cuprates ?)o Exotic “normal” state + Unconventional SC (cuprates,

pnictides, AdS/CMT ?)

January 2010

Based on D. Pendlebury (ISI Thomson-Reuters) citations analysis for ScienceWatch

#6- Iron-based Superconductors,which rivaled swine-flu for citations among scholars…

1111 122

FeAs

ORE

122

Cu-oxides versus Fe-pnictides

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

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 correlations but no SC !!(gauge theories, QED3, chiral SB,…)

How Correlated Superconductors turn into Mott Insulators

Near Tc these are alwaysphase fluctuations

ZT, Nature Physics 4, 408 (2008)

BCS-Eliashberg-Migdal

Optimal Tc in HTS is determined by quantum fluctuations

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)

0 20 40 60 80

0

10

20

30 LBCO1 LBCO2 LSCO 7% Shen's LSCO 6.3%

|| (m

eV

)

0.0 0.1 0.2 0.30

10

20

30

0 (m

eV

)

x

0

100

200 TC (LSCO)

TC (LBCO)

TC (

K)

Nodes in pseudogap ground state (LBCO) at x=1/8T. Valla et al., Science 314, 1914 (2006)

non SC

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

d-wave nodal liquid in highly underdoped BSCCO U. Chatterjee et al., Nature Physics (2009)

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

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

N & 1Balents, MPA Fisher, Nayak Franz, Vafek, Melikyan, ZTSenthil & MPA Fisher,Balents , Bartosch, Burkov, Sachdev, SenguptaHermele, Wen, PA Lee, Senthil, …PW Anderson

What controls fluctuations in µij ? Kinetic energy.

view ij as gauge field aij coupled to staggered charge

Bond Phases versus Site Phases

Automatic conservation of vorticity Cooper pairs !!

Vafek, Melikyan, ZT

d-wave Duality is More Complex

Quantum d-wave/fermionic duality:

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

Quantum s-wave/bosonic duality:

Automatic conservation of vorticity Cooper pairs !!

Cooper pairs can fall apart !!

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 !!

If relative motion becomes too strong bond Cooper pairs break up !! charge e insulator !! Dual of dSC is AF

Strong local repulsion favors formation of local spin singlets on bonds:

ZT, Nature Physics 4, 408 (2008)

Wave-function © is not enough Quantum disorder in µij !!

Must include quantumfluctuations of:

dSC

dSCnodal fermions

AF+x

Lu Li & Ong

Phase diagram of Cu-oxides

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

Phase diagram of cuprates

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..

J. G. Storey et al., arXiv:1001.0474

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 !! )

ARPES and dHvA see coherent (metallic) bands in rough agreement with LDA.

ARPES

L. X. Yang, et al., arxiv/0806.2627

C. Liu, et al., arxiv/0806.2147

1111

122

+ dHvA

1111 A. I. Coldea, et al., arxiv/0807.4890

Minimal Model of FeAs Layers

“Puckering” of FeAs planes is essential:i) All d-orbitals are near EF

ii) Large overlap with As p-orbitals below EF enhanced itinerancy of d electrons

defeats Hund’s rule and large local moment

V. Cvetkovic and ZT, EPL 85, 37002 (2009)K. Kuroki et al ; S. Raghu et al

Hund’s Rule Defeated (but Lurking !)

“Puckering” of FeAs planes is essential:i) All d-orbitals are near EF

ii) Large overlap with As p-orbitals below EF enhanced itinerancy of d electrons

defeats Hund’s rule and large local moment

Hund’s rule rules for Mn2+ :all five d-electrons line up to

minimize Coulomb repulsion S = 5/2

Haule, Shim and Kotliar, PRL 100, 226402 (2008)

Y. Singh et al., arXiv/0907.4094 (MnAs)

Bands, Nesting and Valley Density-Wave in Fe-pnictides

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

Semiconductor Semimetal

m

d

c

ed

ec

SDW, CDW, ODW or combinations thereof VDW

K. Kuroki et alV. Cvetkovic et alS. Raghu et al

SC state in FeAs superconductors

Conclusions: Conventional phonon-mechanism is unlikely but so is Mott limit-induced repulsion of the cuprate d-wave kind. We have something new !!

Only a “single” superconducting gap – sign/phase could be different for holes and electrons.

T. Y. Chen et al., Nature 453, 1224 (2008)

NMR seesnodal behavior (» T2 ) in 1111

Emerging consensus (PCAR, ARPES, STM, ¹w, SQUID, …):nodeless “single” ¢ in 1111, “two” ¢’s in 122, nodes in lower Tc SC ??

H. Ding, et al., arxiv/0807.0419

122L. Wray, et al., PRB 78 184508 (2008),

122

Multiband superconductivityin Fe-pnictides !?

C. Liu, et al., arxiv/0806.2147

1111

1111

1111

122R. T. Gordon et al., arxiv/0810.2295

C. Hicks, et al., arxiv/0903.5260

1111

K. Hashimoto, et al., PRL 102 017002 (2009),

Interactions in FeAs I

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 essential for the SDW (VDW) Could they cause real SC ?

V. Cvetkovic et alA. V. Chubukov et al

F. Wang et al

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

Yes 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

V. Stanev, J. Kang, ZT, PRB 78, 184509 (2008)ZT, Physics 2, 60 (2009)

Valley Density-Wave (VDW) and SC in FeAs

The condition for interband SC is actually milder:

but

– Inter (intra) band energy scales

RG calculations indicate, near a (¼, ¼) VDW state:

In Fe-pnictides interband superconductivity (s’ or s+- state) is a strong possibility (perhaps with little help from phonons)

V. Stanev, J. Kang, ZT, PRB 78, 184509 (2008)

V. Cvetkovic et al

I. I. Mazin et al M. Parish, J. Hu, and B. A. Bernevig, PRB 78, 144514 (2008)

A. V. Chubukov et al

F. Wang, H. Zhai, Y. Ran, A. Vishwanath & DH Lee

If G1 , G2 << U, W

relevant vertices: U, W, & G2

Interactions in FeAs V. Cvetkovic & ZT (RG) ; A. V. Chubukov et al (parquet);F. Wang, H. Zhai, Y. Ran, A. Vishwanath & DH Lee

(FRG)

RG (near VDW):

This is true interband SC since U > 0 – different from U < 0 :

Interplay of VDW and SC in FeAs I

Proximity to VDW is crucial:

In Fe-pnictides interband superconductivity (s’ or s+- state) is a strong possibility but it is a fine tuning with SDW/CDW/ODW (little help from phonons in reducing U* would not hurt)

RG flows (near VDW):

Interplay of VDW and SC in FeAs II

A. V. Chubukov et al, PRB 78, 134512 (2008);Also F. Wang et al, PRL 102, 047005 (2009)

V. Cvetkovic and ZT, PRB 80, 024512 (2009)

Conclusions

o Iron pnictides are semimetals turned superconductors

o Correlations are significant, hence a SDW in parent compounds, but weaker than in cuprates

o Superconducting gap has substantial s-wave character

o Both magnetism and superconductivity are intrinsically multiband in nature – s’ interband SC is a likely possibility near a nesting-driven SDW

new physics, beyond the “standard” model?

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

Johns Hopkins

Princeton