The document discusses room temperature superconductivity and summarizes past research on high temperature superconductivity. It also examines the electronic structure and superconducting properties of NaxCoO2. Specifically: 1) Prior research from the 1970s explored whether high temperature superconductivity was possible. 2) Calculations and experiments on NaxCoO2 suggest it has unusual magnetic and electronic properties, including spin fluctuations that may be important to superconductivity. 3) Studies of the superconducting state in NaxCoO2 indicate it is unconventional and not fully gapped, with triplet f-wave pairing being a leading hypothesis to explain experimental results.

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 NaxCoO2
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
NaCoO2: Co3+
(3d6
) => band insulator
CoO2: Co4+
(3d5
) => Mott insulator?
But NaxCoO2 behaves almost oppositely…
CoO2 planes

4. Na content phase diagram0M,µB1
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
Na0.7CoO2
Two distinct Fermi surface types
are predicted by calculation.
a1g= (xy) + (yz) + (zx) = 3z2
-r2
eg’= (xy) + e±2πi/3
(yz) + e±4πi/3
(zx)
Small pockets carry 70% of the weight
in hydrated compound
(Note that FS is 2D!)

6. Comparison with Experiment
The large (a1g )Fermi Surface is clearly seen by ARPES
The smaller (eg’) 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 NaxCoO2? LMTO: 3.7 eV (for all 5 d-bands)
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

8. Optics: A Probe of Bulk Electronic Structure
There are three basic peaks: α, β, γ.
Peak shifts with changing Na content are reproduced.
Peak heights and energy positions are exaggerated.
α
β
γ

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

10. Dynamical Correlation: DMFT
Small eg’ 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
• 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 worsens agreement 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

12. Part II: Superconductivity
What kind of superconductor is Na0.35CoO2•yH2O ?
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
» kz-dependent order parameter
unphysical
After Sigrist and Ueda RMP 63 240 (1991)
9 representations
25 total states
µSR
• No static magnetic moments
» No states with L≠0
» No non-unitary triplet states
Two dimensionality
• c/a ratio ~ 3.5
• ρab/ ρc ~ 103
» kz-dependent order parameter
unrealistic
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

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 TC for planar spins (axial order parameter)
• KS decreases across TC for axial spins (planar order parameter)

16. Evidence of Spin Fluctuations in Na0.35CoO2•1.4H2O
•Curie-Weiss like behavior of 1/T1 (above TC), with negative θ
•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
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 - Imχ(q,ω)

17. Is pairing interaction always attractive?
),(, TFV β
β
βαβα q
q
qkqk ∆∆=∆ ∑
Consider BCS formula (in this notation, attractive V>0):
If ∆kα and ∆qβ 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 (He3
, Sr2RuO4?)

18. Spin fluctuations in NaxCoO2 yH2O
AD=G/2
AC=AB=G/4
Im χ0(q,ω)/ω|ω→0 Re χ0(q,0)
χ0(q,ω) = Σk
f(εk+q) - f(εk)
(εk+q - εk - ω - iδ)
χ(q,ω) =
χ0(q,ω)
χ0(q,ω)1- I(q,ω)
For a Mott-Hubbard system,
I(q,ω) is main factor
For NaxCoO2 yH2O, 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
∆kα = Vkq,αβ ∆qβF(∆qβ,T)
Σqβ
V<0 V>0
∆kα = Vkq,αβ ∆qβF(∆qβ,T)
Σqβ
V>0

20. Odd gap superconductivity
∆(ω)= -∆(-ω)
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 (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

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 µSR, Kanigel et al,
Knight, Higemoto et al Absence of mag. fields, Higemoto et al Hc2, Maska et al
Superconductivity: symmetry (experiment)