8 research outputs found
Fermi liquid theory for the Anderson model out of equilibrium
We study low-energy properties of the Anderson impurity under a finite bias
voltage using the perturbation theory in of Yamada and Yosida in the
nonequilibrium Keldysh diagrammatic formalism, and obtain the Ward identities
for the derivative of the self-energy with respect to . The self-energy is
calculated exactly up to terms of order , and , and the
coefficients are defined with respect to the equilibrium ground state. From
these results, the nonlinear response of the current through the impurity has
been deduced up to order .Comment: 8 pages, 1 figur
Determination of the phase shifts for interacting electrons connected to reservoirs
We describe a formulation to deduce the phase shifts, which determine the
ground-state properties of interacting quantum-dot systems with the inversion
symmetry, from the fixed-point eigenvalues of the numerical renormalization
group (NRG). Our approach does not assume the specific form of the Hamiltonian
nor the electron-hole symmetry, and it is applicable to a wide class of quantum
impurities connected to noninteracting leads. We apply the method to a triple
dot which is described by a three-site Hubbard chain connected to two
noninteracting leads, and calculate the dc conductance away from half-filling.
The conductance shows the typical Kondo plateaus of Unitary limit in some
regions of the gate voltages, at which the total number of electrons N_el in
the three dots is odd, i.e., N_el =1, 3 and 5. In contrast, the conductance
shows a wide minimum in the gate voltages corresponding to even number of
electrons, N_el = 2 and 4.
We also discuss the parallel conductance of the triple dot connected
transversely to four leads, and show that it can be deduced from the two phase
shifts defined in the two-lead case.Comment: 9 pages, 12 figures: Fig. 12 has been added to discuss T_
Perturbation Study of the Conductance through an Interacting Region Connected to Multi-Mode Leads
We study the effects of electron correlation on transport through an
interacting region connected to multi-mode leads based on the perturbation
expansion with respect to the inter-electron interaction. At zero temperature
the conductance defined in the Kubo formalism can be written in terms of a
single-particle Green's function at the Fermi energy, and it can be mapped onto
a transmission coefficient of the free quasiparticles described by an effective
Hamiltonian. We apply this formulation to a two-dimensional Hubbard model of
finite size connected to two noninteracting leads. We calculate the conductance
in the electron-hole symmetric case using the order self-energy. The
conductance shows several maximums in the dependence in some parameter
regions of , where () is the hopping matrix element in the
- (-) directions. This is caused by the resonance occurring in some of
the subbands, and is related with the dependence of the eigenvalues of the
effective Hamiltonian.Comment: 17 pages, 12 figures, to be published in J.Phys.Soc.Jpn. 71(2002)No.
NRG approach to the transport through a finite Hubbard chain connected to reservoirs
We study the low-energy properties of a Hubbard chain of finite size N_C
connected to two noninteracting leads using the numerical renormalization group
(NRG) method. The results obtained for N_C = 3 and 4 show that the low-lying
eigenstates have one-to-one correspondence with the free quasi-particle
excitations of a local Fermi liquid. It enables us to determine the transport
coefficients from the fixed-point Hamiltonian. At half-filling, the conductance
for even N_C decreases exponentially with increasing U showing a tendency
towards the development of a Mott-Hubbard gap. In contrast, for odd N_C, the
Fermi-liquid nature of the low-energy states assures perfect transmission
through the Kondo resonance. Our formulation to deduce the conductance from the
fixed-point energy levels can be applied to various types of interacting
systems.Comment: One typo found in Eq.(3) in previous version has been correcte
Fermi liquid theory for the nonequilibrium Kondo effect at low bias voltages
In this report, we describe a recent development in a Fermi liquid theory for
the Kondo effect in quantum dots under a finite bias voltage . Applying the
microscopic theory of Yamada and Yosida to a nonequilibrium steady state, we
derive the Ward identities for the Keldysh Green's function, and determine the
low-energy behavior of the differential conductance exactly up to terms
of order for the symmetric Anderson model. These results are deduced
from the fact that the Green's function at the impurity site is a functional of
a nonequilibrium distribution , which at
coincides with the Fermi function. Furthermore, we provide an alternative
description of the low-energy properties using a renormalized perturbation
theory (RPT). In the nonequilibrium state the unperturbed part of the RPT is
determined by the renormalized free quasiparticles, the distribution function
of which is given by . The residual interaction between
the quasiparticles , which is defined by the full vertex part at
zero frequencies, is taken into account by an expansion in the power series of
. We also discuss the application of the RPT to a high-bias
region beyond the Fermi-liquid regime.Comment: 8 pages, to appear in a special edition of JPSJ "Kondo Effect -- 40
Years after the Discovery", typos are correcte
Out-of-equilibrium Anderson model at high and low bias voltages
We study the high- and low-voltage properties of the out-of-equilibrium
Anderson model for quantum dots, using a functional method in the Keldysh
formalism. The Green's function at the impurity site can be regarded as a
functional of a nonequilibrium distribution function. The dependence of the
Green's function on the bias voltage V and temperature T arises through the
nonequilibrium distribution function. From this behavior as a functional, it is
shown that the nonequilibrium Green's function at high-voltage limit is
identical to the equilibrium Green's function at high-temperature limit. This
correspondence holds when the couplings of the dot and two leads, at the left
and right, are equal. In the opposite limit, for small eV, the low-energy
behavior of the Green's function can be described by the local Fermi-liquid
theory up to terms of order . These results imply that the correlation
effects due to the Coulomb interaction U can be treated adiabatically in the
two limits, at high and low bias voltages.Comment: 6 pages, 4 figures: to appear in J. Phys. Soc. Jpn. 71, No.12 (2002
Quasi-particle description for the transport through a small interacting system
We study effects of electron correlation on the transport through a small
interacting system connected to reservoirs using an effective Hamiltonian which
describes the free quasi-particles of a Fermi liquid. The effective Hamiltonian
is defined microscopically with the value of the self-energy at .
Specifically, we apply the method to a Hubbard chain of finite size (), and calculate the self-energy within the second order in in
the electron-hole symmetric case. When the couplings between the chain and the
reservoirs on the left and right are small, the conductance for even
decreases with increasing showing a tendency toward a Mott-Hubbard
insulator. This is caused by the off-diagonal element of the self-energy, and
this behavior is qualitatively different from that in the special case examined
in the previous work. We also study the effects of the asymmetry in the two
couplings. While the perfect transmission due to the Kondo resonance occurs for
any odd in the symmetric coupling, the conductance for odd decreases
with increasing in the case of the asymmetric coupling.Comment: 27 pages, RevTeX, 14 figures, to be published in Phys. Rev.