2004 Room Temperature Superconductivity Dream or Reality 1977

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

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

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

0 M, µB 1 Na content phase diagram LDA typically finds smaller magnetic moments than experiment Exception: the vicinity of a quantum critical point 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 OBSERVED • For x < 0. 5, system is a simple metal • For x > 0. 5, system go through a sequence of magnetic metallic phases Consistent overestimation of magnetism suggests spin fluctuations

Multi-Orbital Nature of Fermi Surfaces Na 0. 7 Co. O 2 a 1 g= (xy) + (yz) + (zx) = 3 z 2 -r 2 eg’= (xy) + e 2 i/3(yz) + e 4 i/3(zx) Two distinct Fermi surface types are predicted by calculation. Small pockets carry 70% of the weight in hydrated compound (Note that FS is 2 D!)

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

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

Optics: A Probe of Bulk Electronic Structure a g b There are three basic peaks: a, b, g. Peak shifts with changing Na content are reproduced. Peak heights and energy positions are exaggerated.

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

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

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

Part II: Superconductivity What kind of superconductor is Na 0. 35 Co. O 2 y. H 2 O ? Pairing state: Singlet? Triplet? Order parameter: s, p, d, f …?

Experimental evidence for pairing state. . . singlet order parameter with s-wave symmetry is realized in Nax. Co. O 2. y. H 2 O - JPSJ 72, 2453 (2003). . . an unconventional superconducting symmetry with line nodes cond-mat/0410517 (2004) Unconventional superconductivity in Nax. Co. O 2 y. H 2 O - condmat/0408426 (2004) Possible unconventional superconductivity in Nax. Co. O 2. y. H(2)O Possible singlet to triplet probed by muon spin rotation and pairing transition in Nax. Co. O 2 relaxation - PR B 70, 13458 (2005) H 2 O - PR B 70, 144516 (2005) Evidence of nodal superconductivity in Na 0. 35 Co. O 2. 1. 3 H 2 O - PR B 71, 20504 (2005). . . magnetic fluctuations play an important role in the occurrence of superconductivity 74, 867 (2005) Our results make superconducting Nax. Co. O 2 a … superconducting- JPSJ electron pairs are in the singlet clear state candidate for magnetically mediated pairing cond-mat/0503010 (2005) - JPSJ 74 (2005)

What pairing states can we exclude? SR • No static magnetic moments After Sigrist and Ueda RMP 63 240 (1991) » No states with L 0 » No states with L≠ 0 » No non-unitary triplet states Two dimensionality • c/a ratio ~ 3. 5 9 representations 3 • / ~ 10 » 25 kz-dependent order ab c total states parameter » unphysical kz-dependent order parameter unrealistic DOS Probes • Non-exponential decay of C/T vs. T • No coherence peak in 1/T 1 » Non-exponential Superconducting stateofnot fully gapped decay relaxation time • » Superconducting state not fully gapped

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

Evidence of Spin Fluctuations in Na 0. 35 Co. O 2 1. 4 H 2 O There is growing evidence that SF have a role in the superconductivity: • Curie-Weiss like behavior of 1/T 1 (above TC), with negative • Correlation of TC with magnetic fluctuations as measured by NQR • Direct neutron observation of spin fluctuations in related compounds • LDA calculations indicate proximity to quantum critical point Details of pairing/pair-breaking in a particular system depend on: i) Fermiology ii) spin fluctuation spectrum - Im (q, )

Is pairing interaction always attractive? 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 Ru. O 4? ) 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! 1

Spin fluctuations in Nax. Co. O 2 y. H 2 O 0(q, ) = 1 - I(q, ) 0(q, ) For a Mott-Hubbard system, I(q, ) is main factor For Nax. Co. O 2 y. H 2 O, we expect peaks to come from non-interacting part: 0(q, ) = f(ek+q) - f(ek) k (ek+q - ek - - id) AD=G/2 AC=AB=G/4 Im 0(q, )/ | 0 Re 0(q, 0)

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

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

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

Summary of Part II • 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 • Calculated spin fluctuations are compatible only with odd gap, triplet superconductivity - this is consistent with experiment so far.

Superconductivity: symmetry (experiment) NQR, Fujimoto et al Knight, Higemoto et al C/T, Lorenz et al Absence of mag. fields, Higemoto et al SR, Kanigel et al, Hc 2, Maska et al