Particle-hole asymmetry in fluctuating thermoelectric and Hall effects
A. Sergeev,
1
M. Yu. Reizer,
2
and V. Mitin
1
1
Department of ECE, Wayne State University, Detroit, Michigan 48202
2
5614 Naiche Road, Columbus, Ohio 43213
Received 10 April 2002; published 4 September 2002
Thermoelectric and Hall currents arise due to particle-hole asymmetry PHA in the electron system. Qua-
dratic electron spectrum alone is a source of PHA. This asymmetry, not associated with expansion of the
density of states DOS near the Fermi surface, leads to singular fluctuation thermopower and Hall conductivity
in electron systems with two-dimensional spectrum. In impure films new contributions dominate over the
contributions due to DOS expansion by parameter ( T
c
)
-1
, where is the electron-impurity scattering time.
In agreement with experimental observations in high-T
c
cuprates, sign of the fluctuation Hall correction is
opposite to the sign of the Hall conductivity in the normal state.
DOI: 10.1103/PhysRevB.66.104504 PACS numbers: 74.40.+k, 73.63.-b, 74.72.-h, 73.50.Lw
In recent years fluctuations effects in superconductors
near the critical temperature T
c
attracted much attention in
strongly anisotropic high-T
c
cuprates with two-dimensional
electron transport along layers and weak coupling between
layers. Near T
c
the fluctuation conductivity of ordinary su-
perconductors is described by the Aslamazov-Larkin AL
correction.
1
The excess conductivity of high-T
c
cuprates is
also well described by AL theory if anisotropy effects are
included.
2–4
The current situation with the fluctuations ther-
mopower TEP and Hall effect is rather confusing. The most
intriguing problem is that the sign of the calculated fluctua-
tion Hall conductivity
5–7
contradicts to experimental data on
high-T
c
superconductors.
8–11
All theories to date predict that AL correction to thermo-
electric coefficient and Hall conductivity in two-dimensional
conductors are absent.
3,5–7
Electrons and holes drifting in
perpendicular magnetic and electric fields or in the tempera-
ture gradient give contributions to the electric current of op-
posite signs. Therefore, thermoelectric and Hall currents
arise due to the difference between electron and hole states,
i.e., due to the particle-hole asymmetry PHA. To obtain
nonzero fluctuations thermopower and Hall coefficient one
should extract the PHA terms in the fluctuation propagator.
Previous works took into account PHA in the electron den-
sity of states DOS, which is constant in two-dimensional
conductors. Therefore, one could conclude that the AL-
corrections to the thermopower and Hall conductivity is ab-
sent. Interlayer coupling results in nonzero fluctuation TEP
and Hall conductivity along layers due to modification of
two-dimensional electron spectrum. However, experimental
measurements in various cuprates exhibit no significant de-
pendence on the interlayer coupling.
8–11
We show that complete treatment of all sources of PHA
can resolve the problems of sign and magnitude of fluctua-
tions TEP and Hall effects. To elucidate main idea of our
paper, we remind that for noninteracting electrons TEP re-
quires expansion of electron parameters, v
2
( v is the ve-
locity, is the density of states, and is the momentum
relaxation rate near the Fermi surface to extract PHA. For
the Hall conductivity no such expansion is necessary, and
PHA due to quadratic electron spectrum alone results in non-
vanishing effect.
12
Note, that for the linear Dirac spectrum
there is no PHA and the Hall effect is absent. For TEP and
Hall conductivity of interacting electrons, both sources of
PHA mentioned above should be taking into account on the
same footing. However, PHA effects from the quadratic elec-
tron spectrum have been lost in all previous calculations of
fluctuation TEP and Hall effect.
In the present paper we show that PHA from the electron
spectrum results in singular fluctuation thermopower and
Hall conductivity in 2D systems. The effects under consider-
ation are also important for 3D conductors. In particular, we
show that, in impure thin films the obtained TEP and Hall
corrections are T
c
times larger than found in earlier
papers.
5–7,13,14
In pure films our corrections are of the same
order as corrections due to expansion of DOS.
6,13
First, we calculate the PHA terms in the fluctuation propa-
gator, which describes the interaction in the Cooper channel.
In equilibrium the retarded propagator is
L
0
R
q , =
-1
- P
R
q ,
-1
, 1
where is a constant of the electron-electron interaction and
P ( q , ) is the polarization operator
P
R
q , =i
d
2
S
0
q ,
1 - q ,
, 2
where S
0
( ) =-tanh(/2T ). The function ( q , ) is given
by
q , =
1
d p
2
2
G
0
A
p, G
0
R
q-p, -
=-
i
d
2
1
2 - +
q -p
F
-i /
, 3
where is the angle between p and q, and the retarded R
and advanced A electron Green functions are
G
0
R
p, = G
0
A
p, * =
-
p
+i /2
-1
, 4
where
p
=( p
2
- p
F
2
)/2m .
Equations 1 – 4 are well known and widely used in the
microscopic theory of fluctuations.
1,5–7,13,14
An important
PHYSICAL REVIEW B 66, 104504 2002
0163-1829/2002/6610/1045044/$20.00 ©2002 The American Physical Society 66 104504-1