2,261 research outputs found
Gate-voltage dependence of Kondo effect in a triangular quantum dot
We study the conductance through a triangular triple quantum dot, which are
connected to two noninteracting leads, using the numerical renormalization
group (NRG). It is found that the system shows a variety of Kondo effects
depending on the filling of the triangle. The SU(4) Kondo effect occurs at
half-filling, and a sharp conductance dip due to a phase lapse appears in the
gate-voltage dependence. Furthermore, when four electrons occupy the three
sites on average, a local S=1 moment, which is caused by the Nagaoka mechanism,
is induced along the triangle. The temperature dependence of the entropy and
spin susceptibility of the triangle shows that this moment is screened by the
conduction electrons via two separate stages at different temperatures. The
two-terminal and four-terminal conductances show a clear difference at the gate
voltages, where the SU(4) or the S=1 Kondo effects occurring.Comment: 4 pages, 4 figs: typos just below (4) are corrected, results are not
affecte
Transmission Coefficient as a Three-Point Retarded Function
We show that the transmission probability through a small interacting region
connected to noninteracting leads, can be written in terms of a retarded
product of a three-point correlation function defined in the real time. Our
proof is based on the Kubo formalism, and uses an Eliashberg theory for
analytic properties of vertex functions. The aim of this short report is to add
a new viewpoint to the transport theory described in the previous paper: A.O.,
J. Phys. Soc. Jpn. 70 (2001) 2666.Comment: 2 pages, 2 figures, submitted to J. Phys. Soc. Jp
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.
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_
Transport through a finite Hubbard chain connected to reservoirs
The dc conductance through a finite Hubbard chain of size N coupled to two
noninteracting leads is studied at T = 0 in an electron-hole symmetric case.
Assuming that the perturbation expansion in U is valid for small N (=1,2,3,...)
owing to the presence of the noninteracting leads, we obtain the self-energy at
\omega = 0 analytically in the real space within the second order in U. Then,
we calculate the inter-site Green's function which connects the two boundaries
of the chain, G_{N1}, solving the Dyson equation. The conductance can be
obtained through G_{N1}, and the result shows an oscillatory behavior as a
function of N. For odd N, a perfect transmission occurs independent of U. This
is due to the inversion and electron-hole symmetries, and is attributed to a
Kondo resonance appearing at the Fermi level. On the other hand, for even N,
the conductance is a decreasing function of N and U.Comment: 11 pages, RevTeX, 6 figures, to be published in Phys. Rev. B 59
(1999
Effects on the Non-Relativistic Dynamics of a Charged Particle Interacting with a Chern-Simons Potential
The hydrogen atom in two dimensions, described by a Schr\"odinger equation
with a Chern-Simons potential, is numerically solved. Both its wave functions
and eigenvalues were determined for small values of the principal quantum
number . The only possible states correspond to . How the result
depends on the topological mass of the photon is also discussed. In the case
, the energy of the fundamental state corresponding to different choice
for the photon mass scale are found to be comprehended in the interval , corresponding to a mean
radius of the electron in the range ~cm
~cm. In any case, the planar
atom is found to be very weekly bounded showing some features similar to the
Rydberg atoms in three dimensions with a Coulombian interaction.Comment: 6 pages, 5 figure
The Kondo crossover in shot noise of a single quantum dot with orbital degeneracy
We investigate out of equilibrium transport through an orbital Kondo system
realized in a single quantum dot, described by the multiorbital impurity
Anderson model. Shot noise and current are calculated up to the third order in
bias voltage in the particle-hole symmetric case, using the renormalized
perturbation theory. The derived expressions are asymptotically exact at low
energies. The resulting Fano factor of the backscattering current is
expressed in terms of the Wilson ratio and the orbital degeneracy as
at zero temperature. Then,
for small Coulomb repulsions , we calculate the Fano factor exactly up to
terms of order , and also carry out the numerical renormalization group
calculation for intermediate in the case of two- and four-fold degeneracy
(). As increases, the charge fluctuation in the dot is suppressed,
and the Fano factor varies rapidly from the noninteracting value to the
value in the Kondo limit , near the crossover region
, with the energy scale of the hybridization .Comment: 10 pages, 4 figure
Mixed-state aspects of an out-of-equilibrium Kondo problem in a quantum dot
We reexamine basic aspects of a nonequilibrium steady state in the Kondo
problem for a quantum dot under a bias voltage using a reduced density matrix,
which is obtained in the Fock space by integrating out one of the two
conduction channels. The integration has been carried out by discretizing the
conduction channels preserving the two-fold degeneracy due to the left-going
and right-going scattering states. The remaining subspace is described by a
single-channel Anderson model, and the statistical weight is determined by the
reduced density matrix. In the noninteracting case, it can be constructed as
the mixed states that show a close similarity to the high-temperature
distribution in equilibrium. Specifically, if the system has an inversion
symmetry, the one-particle states in an energy window between the two chemical
potentials \mu_R and \mu_L are occupied, or unoccupied, completely at random
with an equal weight. The Coulomb interaction preserves these aspects, and the
correlation functions can be expressed in a Lehmann-representation form using
the mixed-state statistical weight.Comment: 8 pages, 3 figure
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