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
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!
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
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
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
椯i
(yz)
+ e
4
椯i
(zx)
Small pockets carry 70% of the weight
in hydrated compound
(Note that FS is 2D!)
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
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
Optics: A Probe of Bulk Electronic Structure
There are three basic peaks:
a, b, g
.
健欠獨楦k猠睩瑨桡湧h湧n乡N捯湴敮琠慲攠数e潤畣敤
Peak heights and energy positions are exaggerated.
a
b
g
Optics: Effect of LDA+U
Application of LDA+U
worsens
agreement with
experiment.
Mott

Hubbard type
correlation is not exhibited
for any x!
b
a
䡯眠摯e猠敬散瑲潮挠捯牲敬慴a潮浡湩晥獴瑳敬昿
g
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
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
Part II: Superconductivity
What kind of superconductor is Na
0.35
CoO
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
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)
» 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
〠†††††††
» 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
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)
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
,
)
Is pairing interaction always attractive?
)
,
(
,
T
F
V
b
b
b
ab
a
q
q
q
kq
k
Consider BCS formula (in this notation, attractive
V
>0):
If
k
a
and
q
b
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
7
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
?)
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)
0
(
q
,
)
=
S
k
f(
e
k
+
q
)

f(
e
k
)
(e
k
+
q

e
k


i
d)
(
q
,
)
0
(
q
,
)
0
(
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:
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
a
=
V
kq
,
ab
q
b
F
(
q
b
,
T
)
S
q
b
V<0
V>0
k
a
=
V
kq
,
ab
q
b
F
(
q
b
,
T
)
S
q
b
V>0
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 (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
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
NQR, Fujimoto et al
C/T, Lorenz et al
SR,
Kanigel et al,
Knight, Higemoto et al
Absence of mag. fields, Higemoto et al
Hc2, Maska et al
Superconductivity: symmetry (experiment)
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