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)
Acknowledgements:
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
Small pockets carry 70% of the weight
in hydrated compound
(Note that FS is 2D!)
Multi-Orbital Nature of Fermi Surfaces
Na0.7CoO2
a1g= (xy) + (yz) + (zx) = 3z2-r2
eg’= (xy) + e2i/3(yz) + e4i/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
WHY?
Comparison with Experiment
Narrow t2g bands screened by
Empty eg 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 > 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
a
b
g
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.
b
Mott-Hubbard type
correlation is not exhibited
for any x!
g
a
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
Part II: Superconductivity
What kind of superconductor is Na0.35CoO2yH2O ?
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)
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
unphysical
» 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
Presently, results are contradictory
Evidence of Spin Fluctuations in Na0.35CoO21.4H2O
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,)
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!
17
c0(q,w)
c0(q,w) = Sk
f(ek+q) - f(ek)
(ek+q - ek - w - id)
c(q,w) =
c0(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:
AD=G/2
AC=AB=G/4
Im 0(q,)/|0
Re 0(q,0)
V>0
V<0
V>0
k = Vkq,qF(q,T)
k = Vkq,qF(q,T)
q
q
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
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