Correlated Superconductivity in Cuprates and Pnictides Zlatko Tesanovic, web: 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…

Fe As O RE 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 CuO 2 a single hole in a filled 3d orbital shell  A suitable single band model might work In 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 have thermal fluctuations No such ground state in BCS theory (at weak coupling) !! Correlated superconductors have quantum (anti)vortex fluctuations Ground state with enhanced pairing correlations but no SC !! (gauge theories, QED 3, chiral SB,…) How Correlated Superconductors turn into Mott Insulators Near T c these are always phase fluctuations ZT, Nature Physics 4, 408 (2008) BCS-Eliashberg-Migdal Optimal T c in HTS is determined by quantum fluctuations

A sequence of thermal KT transitions as T c drops from 40K to 2K However, there is a clear break below ~ 30K indicating T c  -2 (0)   s (0)   magnitude of T c (x) is dictated by Quantum critical SC fluctuations !! Quantum Superconducting Fluctuations in Underdoped Cuprates “Thermal metal” in non-SC YBCO M. Sutherland et al., PRL 94, (2005) Nodes in pseudogap ground state (LBCO) at x=1/8 T. 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  ij must start fluctuating as x  0 and system becomes Mott insulator N & 1 Balents, MPA Fisher, Nayak Franz, Vafek, Melikyan, ZT Senthil & MPA Fisher, Balents, Bartosch, Burkov, Sachdev, Sengupta Hermele, Wen, PA Lee, Senthil, … PW Anderson

What controls fluctuations in µ ij ? Kinetic energy. view  ij as gauge field a ij 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 CuO 2 plane this translates into 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 around freely while relative motion is suppressed CuO 2 plane  dSC CuO 2 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 µ ij !! Must include quantum fluctuations of: dSC nodal 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 CuO 2, 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/ Phase diagram of cuprates Unlike CuO 2, all regions of FeAs phase diagram are (bad) metals !! SmFeAsO 1-x F x parent (SDW) SC x = 0.0 x = 0.18 T. Y. Chen et al.. J. G. Storey et al., arXiv:

Fe-pnictides: Semimetals  Superconductors In contrast to CuO 2, 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 CuO 2 (correlations are still important !! )

ARPES and dHvA see coherent (metallic) bands in rough agreement with LDA. ARPES L. X. Yang, et al., arxiv/ C. Liu, et al., arxiv/ dHvA 1111 A. I. Coldea, et al., arxiv/

Minimal Model of FeAs Layers “Puckering” of FeAs planes is essential: i)All d-orbitals are near E F ii)Large overlap with As p-orbitals below E F  enhanced itinerancy of d electrons defeats Hund’s rule and large local moment V. Cvetkovic and ZT, EPL 85, (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 E F ii)Large overlap with As p-orbitals below E F  enhanced itinerancy of d electrons defeats Hund’s rule and large local moment Hund’s rule rules for Mn 2+ : all five d-electrons line up to minimize Coulomb repulsion  S = 5/2 Haule, Shim and Kotliar, PRL 100, (2008) Y. Singh et al., arXiv/ (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 ) SemiconductorSemimetal  d c dd cc SDW, CDW, ODW or combinations thereof  VDW K. Kuroki et al V. Cvetkovic et al S. Raghu et al

SC state in FeAs superconductors 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 sees nodal behavior ( » T 2 ) in 1111 Emerging consensus (PCAR, ARPES, STM, ¹ w, SQUID, …): nodeless “single” ¢ in 1111, “two” ¢ ’s in 122, nodes in lower T c SC ?? H. Ding, et al., arxiv/ L. Wray, et al., PRB (2008), 122 Multiband superconductivity in Fe-pnictides !? C. Liu, et al., arxiv/ R. T. Gordon et al., arxiv/ C. Hicks, et al., arxiv/ K. Hashimoto, et al., PRL (2009),

Interactions in FeAs I

Interactions in FeAs II Typically, we find W s is dominant  Valley density-wave(s) (VDW) in FeAs h1h1 h2h2 e1e1 e-h These “Josephson” terms are not essential for the SDW (VDW)  Could they cause real SC ? V. Cvetkovic et al A. V. Chubukov et al F. Wang et al

Interband pairing acts like Josephson coupling in k-space. If G 2 is repulsive  antibound Cooper pairs (s’SC) M Yes  Two Kinds of Interband Superconductivity Type-A interband SC: c FS cd d Type-B (intrinsic) interband SC: cd FS sSC s’SC G2G2 sSC s’SC G2G2 V. Stanev, J. Kang, ZT, PRB 78, (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, (2008) V. Cvetkovic et al I. I. Mazin et al M. Parish, J. Hu, and B. A. Bernevig, PRB 78, (2008) A. V. Chubukov et alF. Wang, H. Zhai, Y. Ran, A. Vishwanath & DH Lee

If G 1, G 2 << U, W  relevant vertices: U, W, & G 2 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, (2008); Also F. Wang et al, PRL 102, (2009) V. Cvetkovic and ZT, PRB 80, (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?  new physics, beyond the “standard” model? Zlatko Tesanovic, Johns Hopkins University Web: