Multi-orbital Analysis on the
Superconductivity in NaxCoO2 yH2O
Youichi YANASE, Masahito MOCHIZUKI and Masao OGATA
J. Phys. Soc. Jpn. 74 (2005) 430
2006/1/30
Suzuki-Kusakabe group
Fumiya Kanetake
Contents
1.
2.
3.
4.
Introduction
- NaxCoO2yH2O vs. High-Tc cuprates
- Gap function (order parameter)
Theory
- Multi-orbital Hubbard model
- 2nd order perturbation Green’s function method
Calculation Result
Summary
NaxCoO2yH2O vs. High-Tc cuprates(La2-xSrxCuO4)
G. Baskaran
Phys.Rev.Lett.91(2003)097003
K. Takada et al , Nature 422 (2003) 53
超伝導 黒木和彦・青木秀夫
NaxCoO2 yH2O(2003)
High-Tc cuprates(1986)
Structure
2-dimentional triangular CoO2
lattice
2-dimentional square CuO2
lattice
Tc (Superconductive
transition temperature)
～5[K] (x~0.35, y~1.3)
～40[K] (La2-xSrxCuO4;x~0.15)
Main conduction band
t2g(dxy,dyz,dzx) (electron)
dx2-y2 (hole)
Gap function
(pair symmetry)
p-wave triplet? d-wave singlet?
f-wave triplet?
dx2-y2-wave singlet (La2-xSrxCuO4)
3
NaxCoO2yH2O vs. La2-xSrxCuO4
eg
NaxCoO2 yH2O…
NaxCoO2 →(Na1+)xCo(4-x)+(O2-)2 →3d5+x
main conduction band: t2g(dxy,dyz,dzx) ( (5+x)/6 electron )
La2-xSrxCuO4 …
La2-xSrxCuO4→(La3+)2-x(Sr2+)xCu(2+x)+(O2-)4→3d9-x
main conduction band: dx2-y2 ( (1+x)/2 hole )
3d
t2g
eg
x2-y2
t2g
3z2-r2
xy
3d
yz,zx
Na1/3CoO2
K.-W. Lee et al, Phys.Rev.B.70(2004)045104
La2CuO4
L.F.Mattheiss Phys.Rev.Lett.58(1987)1028
4
Gap function (order parameter)
Gap function indicates Energy gap, Symmetry of superconductivity.
s-wave, p-wave, d-wave, f-wave…(from symmetry of lattice)
BCS S.C. … s-wave.
Gap equation
The others …not s-wave.
s-wave
π/a
dx2-y2-wave
f1-wave
p-wave
+
+
ky
--
-
+
-π/a
-π/a
kx
--
--
-
+
++
+
+
-
++
π/a
5
Motivation


They want to decide gap function of NaxCoO2 yH2O because it has
not been decided in experiment and theory.
It is necessary to consider 3-orbital that is not considered in theory
up to now.
6
Single-orbital Hubbard model
It suites Electron localized system. ( f.e. d-orbital, f-orbital)
parameters
・Hopping energy (kinetic energy) t (t1,t2,t3…)
・On site coulomb energy (potential energy) U
t2
t1
t3
7
Multi-orbital Hubbard model
NaxCoO2yH2O…
main conduction band: t2g (dxy, dyz, dzx)3-orbital
⇒3-orbital Hubbard model
Hopping energy tij fits LDA band structure.
ky
εk
kx
tayz,zy
taxy,xy
+
-
-
+ +
-
-
+
+
-
-
+ +
-
Fitting
-
+
a=0.8
K.-W. Lee et al,
Phys.Rev.B.70(2004)045104
8
2nd order perturbation Green’s function method
This method considers only 1st and 2nd order Feynman diagrams.
V(k,k’)
k
k’
=
-k
2nd
1st
+
+
3rd
+
+
+
+
-k’
+
+
2nd order perturbation
+
+
+
+
+
+
more
+…
3rd order perturbation
9
Method of decision of gap function
1.
Setting of Parameters (‘a’, U, U’, ne)
‘a’: hopping energy scale, U: on-site intra-orbital coulomb energy,
U’: on-site inter-orbital coulomb energy, ne: hole density
2.
Calculation of Green’s function
3.
Solving gap equation
10
(U’=U/2)
Calculation Result
Hopping energy scale


p-wave and f1-wave is
dominant. (a little difference)
There is no method of
decision of ‘a’.
Eigen value
(a=0.8)
hole density
11
(U’=U/2,a=0.8)
Calculation Result
3-orbital
effective 2-orbital


The rank doesn’t change.
Absolute value of λe changes.
12
Calculation Result
(ne=0.35, a=0.6, U’=U/3)


There is no reversal of p-wave and f1-wave.
There is no method of decision of U,U’.
→ Kusakabe theory (cond-mat/0505703).
13
Summary

The calculation results indicates that p-wave or f1-wave gap function
is stable. (little difference)

There is no method of decision of ‘a’ and U,U’ in this paper.
14

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