1. 2004: Room Temperature Superconductivity: Dream or Reality? 1972: High Temperature Superconductivity: Dream or Reality? Annual Review of Materials Science, August 1972, Vol. 2, Pages 663-696 Ginzburg V L, Kirzhnits D A (Eds) Problema Vysoko- temperaturnoi Sverkhprovodimosti (The Problem of High- Temperature Superconductivity) (Moscow: Nauka, 1977 ) [English Translation: High-Temperature Superconductivity (New York: Consultants Bureau, 1982)] 1977: Not If, When! ```` One can presume that the coming decade will be decisive for the problem of High- Temperature Superconductivity

2. Electronic Structure, Magnetism and Superconductivity in Na x CoO 2 Acknowledgements: D. Agterberg (UWM) A. Liebsch (Juelich) M.J. Mehl (NRL) D.A. Papaconstantopoulos (NRL) Igor Mazin, Michelle Johannes (Naval Research Laboratory) David Singh (ORNL) Instant superconductor: Just Add Water!

3. The Distorted Octahedral Environment of Co Ions NaCoO 2 : Co 3+ (3d 6 ) => band insulator CoO 2 : Co 4+ (3d 5 ) => Mott insulator? But Na x CoO 2 behaves almost oppositely… CoO 2 planes

4. Na content phase diagram 0 M, µ B 1 OBSERVED For x < 0.5, system is a simple metal For x > 0.5, system go through a sequence of magnetic metallic phases EXPECTED At x =0, system is a magnetic insulator At x=1, system is a band insulator For x < 0.5, system is a magnetic metal For x > 0.5, system is a simple metal Consistent overestimation of magnetism suggests spin fluctuations LDA typically finds smaller magnetic moments than experiment Exception: the vicinity of a quantum critical point

5. Multi-Orbital Nature of Fermi Surfaces Na 0.7 CoO 2 Two distinct Fermi surface types are predicted by calculation. a 1g = (xy) + (yz) + (zx) = 3z 2 -r 2 e g ’= (xy) + e  2  i/3 (yz) + e  4  i/3 (zx) Small pockets carry 70% of the weight in hydrated compound (Note that FS is 2D!)

6. Comparison with Experiment The large (a 1g )Fermi Surface is clearly seen by ARPES The smaller (e g ’) surfaces are absent M.Z. Hasan et al H. B. Yang et al WHY? Correlations beyond LDA Surface effects (relaxation, surface bands, Na content) Matrix elements

7. How does correlation affect the electronic structure? Strongly correlated systems are characterized by large U/t What is U in Na x CoO 2 ? LMTO: 3.7 eV (for all 5 d-bands) Narrow t 2g bands screened by Empty e g orbitals … U < 3.7eV (A.Liebsch) LDA+U: Corrects on-site Coulomb repulsion Gets good FS match for U= 4 eV (P. Zhang, PRL 93 236402) But U=4 eV > U C = 3eV for unobserved charge disproportionation ( K-W. Lee PRL 94 026403) For U<2.5 eV, small pockets remain Spin fluctuations: Renormalize bands, similarly to phonons Fermi surface is preserved, less weight

8. Optics: A Probe of Bulk Electronic Structure There are three basic peaks: . Peak shifts with changing Na content are reproduced. Peak heights and energy positions are exaggerated.   

9. Optics: Effect of LDA+U Application of LDA+U worsens agreement with experiment. Mott-Hubbard type correlation is not exhibited for any x!   How does electronic correlation manifest itself? 

10. Dynamical Correlation: DMFT Small e g ’ holes grow Some spectral weight shifts downward Dynamical Mean Field Theory gives a very different picture of correlation effects: LDA+U A.Liebsch, ‘05

11. Summary of Part I Na x CoO 2 has an unusual magnetic phase diagram The system does not behave as a Mott-Hubbard insulator, despite a rather narrow t 2g bandwidth The LDA+U method worsens agreement with optical measurements Dynamical correlations show weight transfer from a 1g  e g i.e. holes grow! Calculations, in conjunction with experiment, suggest the presence of spin fluctuations

12. Part II: Superconductivity What kind of superconductor is Na 0.35 CoO 2  yH 2 O ? Pairing state: Singlet? Triplet? Order parameter: s,p,d,f …?

13. Experimental evidence for pairing state...singlet order parameter with s-wave symmetry is realized in NaxCoO2.yH2O - JPSJ 72, 2453 (2003)...an unconventional superconducting symmetry with line nodes - cond-mat/0410517 (2004) Unconventional superconductivity in NaxCoO2 yH2O - cond- mat/0408426 (2004) Possible singlet to triplet pairing transition in NaxCoO2 H2O - PR B70, 144516 (2005) Possible unconventional super- conductivity in NaxCoO2.yH(2)O probed by muon spin rotation and relaxation - PR B70, 13458 (2005) Evidence of nodal superconductivity in Na0.35CoO2. 1.3 H2O - PR B71, 20504 (2005)...magnetic fluctuations play an important role in the occurrence of superconductivity - JPSJ 74, 867 (2005) Our results make superconducting NaxCoO2 a clear candidate for magnetically mediated pairing - cond-mat/0503010 (2005) … superconducting electron pairs are in the singlet state - JPSJ 74 (2005)

14. » Superconducting state not fully gapped What pairing states can we exclude? » No states with L≠ 0 » k z -dependent order parameter unphysical After Sigrist and Ueda RMP 63 240 (1991) 9 representations 25 total states  SR No static magnetic moments » No states with L  0 » No non-unitary triplet states Two dimensionality c/a ratio ~ 3.5  ab /  c ~ 10 3 » k z -dependent order parameter unrealistic DOS Probes Non-exponential decay of C/T vs. T No coherence peak in 1/T 1 Non-exponential decay of relaxation time » Superconducting state not fully gapped

15. How can pairing state be further resolved? f states Presently, results are contradictory All remaining states are triplet f Both f states are axial Knight Shift can distinguish: Spin direction is  to vector order parameter KS constant across T C for planar spins (axial order parameter) KS decreases across T C for axial spins (planar order parameter)

16. Evidence of Spin Fluctuations in Na 0.35 CoO 2  1.4H 2 O Curie-Weiss like behavior of 1/T 1 (above T C ), with negative  Correlation of T C with magnetic fluctuations as measured by NQR Direct neutron observation of spin fluctuations in related compounds LDA calculations indicate proximity to quantum critical point There is growing evidence that SF have a role in the superconductivity: Details of pairing/pair-breaking in a particular system depend on: i) Fermiology ii) spin fluctuation spectrum - Im  (q,  )

17. Is pairing interaction always attractive? Consider BCS formula (in this notation, attractive V>0): If  k  and  q  are of the same sign, V must be positive. But if they are of the opposite sign, the corresponding V can be negative (repulsive) and still be pairing! 17 Charge fluctuations are attractive regardless of parity (V>0) Spin fluctuations are repulsive (V<0) in a singlet channel (BCS, HTSC) Spin fluctuations are attractive (V<0) in a triplet channel (He 3, Sr 2 RuO 4 ?)

18. Spin fluctuations in Na x CoO 2 yH 2 O AD=G/2 AC=AB=G/4 Im  0 (q,  )/  |  0 Re  0 (q,0)   (q,  =  k f(  k+q ) - f(  k )  k+q -  k -  - i   (q,    (q,  1- I(q,  ) For a Mott-Hubbard system, I(q,  ) is main factor For Na x CoO 2 yH 2 O, we expect peaks to come from non-interacting part:

19. Primary nesting SF’s are pair breaking for every state The secondary-nesting SF are either pair-breaking (s) or mutually canceling (d,p) Spin fluctuations: pairing and pair-breaking  k  = V kq,   q  F(  q ,T)  qq V<0 V>0  k  = V kq,   q  F(  q ,T)  qq V>0

20. Odd gap superconductivity  (  )= -  ( -  ) Now spatial+spin Pauli principle for a pair is reversed: (Berezinskii, ‘74 … Balatsky et al, ‘92

21. What to expect from a triplet s-wave superconductor Severely reduced Hebel-Slichter peak - by at least (T c /E F ) 2 Impurities should have small effect on T c Finite DOS even at T=0 (gapless) - noexponential thermodynamics Vanishing of pair tunneling in even-odd Josephson junction

22. Summary of Part II Calculated spin fluctuations are compatible only with odd gap, triplet superconductivity - this is consistent with experiment so far. The current body of experimental evidence strongly suggests unconventional superconductivity Both experiment and calculation point to the presence of spin fluctuations, possibly connected to the superconductivity

23. NQR, Fujimoto et al C/T, Lorenz et al  SR, Kanigel et al, Knight, Higemoto et alAbsence of mag. fields, Higemoto et al Hc2, Maska et al Superconductivity: symmetry (experiment)