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2004: Room Temperature Superconductivity: Dream or Reality?. 1972: High Temperature Superconductivity: Dream or Reality?. 1977: Not If, When! ````. Annual Review of Materials Science, August 1972, Vol. 2, Pages 663-696.

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2004: Room Temperature Superconductivity: Dream or Reality?

1972: High Temperature Superconductivity: Dream or Reality?

1977: Not If, When!


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)]

One can presume that the coming decade will be decisive for the problem of High-Temperature Superconductivity

Instant superconductor: Just Add Water!

Electronic Structure, Magnetism and Superconductivity in NaxCoO2

Igor Mazin,Michelle Johannes

(Naval Research Laboratory)

David Singh (ORNL)


D. Agterberg (UWM)

A. Liebsch (Juelich)

M.J. Mehl (NRL)

D.A. Papaconstantopoulos (NRL)

The Distorted Octahedral Environment of Co Ions

CoO2 planes

CoO2: Co4+ (3d5) => Mott insulator?

NaCoO2: Co3+ (3d6) => band insulator

But NaxCoO2 behaves almost oppositely…

0 M, µB 1

LDA typically finds smaller magnetic moments than experiment

Exception: the vicinity of a quantum critical point

Consistent overestimation of magnetism suggests spin fluctuations

Na content phase diagram


  • 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


  • For x < 0.5, system is a simple metal

  • For x > 0.5, system go through a sequence of magnetic metallic phases

Small pockets carry 70% of the weight

in hydrated compound

(Note that FS is 2D!)

Multi-Orbital Nature of Fermi Surfaces


a1g= (xy) + (yz) + (zx) = 3z2-r2

eg’= (xy) + e2i/3(yz) + e4i/3(zx)

Two distinct Fermi surface types

are predicted by calculation.

H. B. Yang et al

M.Z. Hasan et al

The large (a1g )Fermi Surface is clearly seen by ARPES

The smaller (eg’) surfaces are absent


  • Correlations beyond LDA

  • Surface effects (relaxation, surface bands, Na content)

  • Matrix elements

Comparison with Experiment

Narrow t2g bands screened by

Empty eg orbitals … U < 3.7eV


LDA+U: Corrects on-site Coulomb repulsion

Gets good FS match for U= 4 eV(P.Zhang, PRL 93 236402)

But U=4 eV > UC= 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

How does correlation affect the electronic structure?

Strongly correlated systems are characterized by large U/t

What is U in NaxCoO2?

LMTO: 3.7 eV (for all 5 d-bands)

Optics: A Probe of Bulk Electronic Structure




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



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:


Small eg’ holes grow

A.Liebsch, ‘05

Some spectral weight shifts downward

Summary of Part I

  • NaxCoO2 has an unusual magnetic phase diagram

  • The system does not behave as a Mott-Hubbard insulator,

  • despite a rather narrow t2g bandwidth

  • The LDA+U method worsensagreement with optical

  • measurements

  • Dynamical correlations show weight transfer from a1g eg

  • i.e. holes grow!

  • Calculations, in conjunction with experiment, suggest

  • the presence of spin fluctuations

Part II: Superconductivity

What kind of superconductor is Na0.35CoO2yH2O ?

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 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 unconventional super-conductivity in NaxCoO2.yH(2)O probed by muon spin rotation and relaxation - PR B70, 13458 (2005)

Possible singlet to triplet pairing transition in NaxCoO2 H2O - PR B70, 144516 (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)

  • SR

  • No static magnetic moments

  • »No states with L0

  • » No non-unitary triplet states

  • DOS Probes

  • Non-exponential decay of C/T vs. T

  • No coherence peak in 1/T1

  • Non-exponential decay of relaxation time

  • »Superconducting state not fully gapped

  • Two dimensionality

  • c/a ratio ~ 3.5

  • ab/ c ~ 103

  • » kz-dependent order parameter

  • unrealistic

What pairing states can we exclude?

After Sigrist and Ueda RMP 63 240 (1991)

9 representations

25 total states

»No states with L≠ 0

» kz-dependent order parameter


» Superconducting state not fully gapped

How can pairing state be further resolved?

f states

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 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 Na0.35CoO21.4H2O

There is growing evidence that SF have a role in the superconductivity:

  • Curie-Weiss like behavior of 1/T1 (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 singletchannel(BCS, HTSC)

Spin fluctuations are attractive (V<0) in a tripletchannel(He3, Sr2RuO4?)

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!



c0(q,w) = Sk

f(ek+q) - f(ek)

(ek+q - ek - w - id)

c(q,w) =


1- I(q,)

Spin fluctuations in NaxCoO2 yH2O

For a Mott-Hubbard system,

I(q,) is main factor

For NaxCoO2 yH2O, we expect peaks to come from non-interacting part:



Im 0(q,)/|0

Re 0(q,0)




k = Vkq,qF(q,T)

k = Vkq,qF(q,T)



Spin fluctuations: pairing and pair-breaking

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)

SR, Kanigel et al,

C/T, Lorenz et al

NQR, Fujimoto et al

Hc2, Maska et al

Knight, Higemoto et al

Absence of mag. fields, Higemoto et al