566 research outputs found
Ground state spin and Coulomb blockade peak motion in chaotic quantum dots
We investigate experimentally and theoretically the behavior of Coulomb
blockade (CB) peaks in a magnetic field that couples principally to the
ground-state spin (rather than the orbital moment) of a chaotic quantum dot. In
the first part, we discuss numerically observed features in the magnetic field
dependence of CB peak and spacings that unambiguously identify changes in spin
S of each ground state for successive numbers of electrons on the dot, N. We
next evaluate the probability that the ground state of the dot has a particular
spin S, as a function of the exchange strength, J, and external magnetic field,
B. In the second part, we describe recent experiments on gate-defined GaAs
quantum dots in which Coulomb peak motion and spacing are measured as a
function of in-plane magnetic field, allowing changes in spin between N and N+1
electron ground states to be inferred.Comment: To appear in Proceedings of the Nobel Symposium 2000 (Physica
Scripta
A nearly closed ballistic billiard with random boundary transmission
A variety of mesoscopic systems can be represented as a billiard with a
random coupling to the exterior at the boundary. Examples include quantum dots
with multiple leads, quantum corrals with different kinds of atoms forming the
boundary, and optical cavities with random surface refractive index. The
specific example we study is a circular (integrable) billiard with no internal
impurities weakly coupled to the exterior by a large number of leads with one
channel open in each lead. We construct a supersymmetric nonlinear
-model by averaging over the random coupling strengths between bound
states and channels. The resulting theory can be used to evaluate the
statistical properties of any physically measurable quantity in a billiard. As
an illustration, we present results for the local density of states.Comment: 5 pages, 1 figur
Scalar and vector Keldysh models in the time domain
The exactly solvable Keldysh model of disordered electron system in a random
scattering field with extremely long correlation length is converted to the
time-dependent model with extremely long relaxation. The dynamical problem is
solved for the ensemble of two-level systems (TLS) with fluctuating well depths
having the discrete Z_2 symmetry. It is shown also that the symmetric TLS with
fluctuating barrier transparency may be described in terms of the planar
Keldysh model with dime-dependent random planar rotations in xy plane having
continuous SO(2) symmetry. The case of simultaneous fluctuations of the well
depth and barrier transparency is subject to non-abelian algebra. Application
of this model to description of dynamic fluctuations in quantum dots and
optical lattices is discussed.Comment: 6 pages, 5 eps figures. Extended version of the paper to be published
in JETP Lett 89 (2009
Finite Size Corrections for the Pairing Hamiltonian
We study the effects of superconducting pairing in small metallic grains. We
show that in the limit of large Thouless conductance one can explicitly
determine the low energy spectrum of the problem as an expansion in the inverse
number of electrons on the grain. The expansion is based on the formal exact
solution of the Richardson model. We use this expansion to calculate finite
size corrections to the ground state energy, Matveev-Larkin parameter, and
excitation energies.Comment: 22 pages, 1 figur
Nonequilibrium theory of Coulomb blockade in open quantum dots
We develop a non-equilibrium theory to describe weak Coulomb blockade effects
in open quantum dots. Working within the bosonized description of electrons in
the point contacts, we expose deficiencies in earlier applications of this
method, and address them using a 1/N expansion in the inverse number of
channels. At leading order this yields the self-consistent potential for the
charging interaction. Coulomb blockade effects arise as quantum corrections to
transport at the next order. Our approach unifies the phase functional and
bosonization approaches to the problem, as well as providing a simple picture
for the conductance corrections in terms of renormalization of the dot's
elastic scattering matrix, which is obtained also by elementary perturbation
theory. For the case of ideal contacts, a symmetry argument immediately allows
us to conclude that interactions give no signature in the averaged conductance.
Non-equilibrium applications to the pumped current in a quantum pump are worked
out in detail.Comment: Published versio
Discrete charging of metallic grains: Statistics of addition spectra
We analyze the statistics of electrostatic energies (and their differences)
for a quantum dot system composed of a finite number of electron islands
(metallic grains) with random capacitance-inductance matrix , for which the
total charge is discrete, (where is the charge of an electron and
is an integer). The analysis is based on a generalized charging model,
where the electrons are distributed among the grains such that the
electrostatic energy E(N) is minimal. Its second difference (inverse
compressibility) represents the spacing between
adjacent Coulomb blockade peaks appearing when the conductance of the quantum
dot is plotted against gate voltage. The statistics of this quantity has been
the focus of experimental and theoretical investigations during the last two
decades. We provide an algorithm for calculating the distribution function
corresponding to and show that this function is piecewise
polynomial.Comment: 21 pages, no figures, mathematical nomenclature (except for Abstract
and Introduction
Spin and Charge Correlations in Quantum Dots: An Exact Solution
The inclusion of charging and spin-exchange interactions within the Universal
Hamiltonian description of quantum dots is challenging as it leads to a
non-Abelian action. Here we present an {\it exact} analytical solution of the
probem, in particular, in the vicinity of the Stoner instabilty point. We
calculate several observables, including the tunneling density of states (TDOS)
and the spin susceptibility. Near the instability point the TDOS exhibits a
non-monotonous behavior as function of the tunneling energy, even at
temperatures higher than the exchange energy. Our approach is generalizable to
a broad set of observables, including the a.c. susceptibility and the
absorption spectrum for anisotropic spin interaction. Our results could be
tested in nearly ferromagnetic materials.Comment: JETPL class, 6 pages, 2 figure
Role of a parallel magnetic field in two dimensional disordered clusters containing a few correlated electrons
An ensemble of 2d disordered clusters with a few electrons is studied as a
function of the Coulomb energy to kinetic energy ratio r_s. Between the Fermi
system (small r_s) and the Wigner molecule (large r_s), an interaction induced
delocalization of the ground state takes place which is suppressed when the
spins are aligned by a parallel magnetic field. Our results confirm the
existence of an intermediate regime where the Wigner antiferromagnetism
defavors the Stoner ferromagnetism and where the enhancement of the Lande g
factor observed in dilute electron systems is reproduced.Comment: 4 pages, 3 figure
Interactions and Disorder in Quantum Dots: Instabilities and Phase Transitions
Using a fermionic renormalization group approach we analyse a model where the
electrons diffusing on a quantum dot interact via Fermi-liquid interactions.
Describing the single-particle states by Random Matrix Theory, we find that
interactions can induce phase transitions (or crossovers for finite systems) to
regimes where fluctuations and collective effects dominate at low energies.
Implications for experiments and numerical work on quantum dots are discussed.Comment: 4 pages, 1 figure; version to appear in Phys Rev Letter
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