Dream or Reality?

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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)