648 research outputs found
The semiclassical tool in mesoscopic physics
Semiclassical methods are extremely valuable in the study of transport and
thermodynamical properties of ballistic microstructures. By expressing the
conductance in terms of classical trajectories, we demonstrate that quantum
interference phenomena depend on the underlying classical dynamics of
non-interacting electrons. In particular, we are able to calculate the
characteristic length of the ballistic conductance fluctuations and the weak
localization peak in the case of chaotic dynamics. Integrable cavities are not
governed by single scales, but their non-generic behavior can also be obtained
from semiclassical expansions (over isolated trajectories or families of
trajectories, depending on the system). The magnetic response of a
microstructure is enhanced with respect to the bulk (Landau) susceptibility,
and the semiclassical approach shows that this enhancement is the largest for
integrable geometries, due to the existence of families of periodic orbits. We
show how the semiclassical tool can be adapted to describe weak residual
disorder, as well as the effects of electron-electron interactions. The
interaction contribution to the magnetic susceptibility also depends on the
nature of the classical dynamics of non-interacting electrons, and is
parametrically larger in the case of integrable systems.Comment: Latex, Cimento-varenna style, 82 pages, 21 postscript figures;
lectures given in the CXLIII Course "New Directions in Quantum Chaos" on the
International School of Physics "Enrico Fermi"; Varenna, Italy, July 1999; to
be published in Proceeding
Unbounded fluctuations in transport through an integrable cavity
We derive a semiclassical scheme for the conductance through a rectangular
cavity. The transmission amplitudes are expressed as a sum over families of
trajectories rather than a sum over isolated trajectories. The contributing
families are obtained from the evaluation of a finite number of continued
fractions. We find that, contrary to the chaotic case, the conductance
fluctuations increase with the incoming energy and the correlation function
exhibits a singularity at the origin.Comment: 9 pages + 3 figures, accepted for Eur. Phys. J.
Quantum Mesoscopic Scattering: Disordered Systems and Dyson Circular Ensembles
We consider elastic reflection and transmission of electrons by a disordered
system characterized by a scattering matrix . Expressing
in terms of the radial parameters and of the four
unitary matrices used for the standard transfer matrix parametrization, we
calculate their probability distributions for the circular orthogonal (COE) and
unitary (CUE) Dyson ensembles. In this parametrization, we explicitely compare
the COE--CUE distributions with those suitable for quasi-- conductors and
insulators. Then, returning to the usual eigenvalue--eigenvector
parametrization of , we study the distributions of the scattering phase
shifts. For a quasi-- metallic system, microscopic simulations show that
the phase sift density and correlation functions are close to those of the
circular ensembles. When quasi-- longitudinal localization breaks into
two uncorrelated reflection matrices, the phase shift form factor
exhibits a crossover from a behavior characteristic of two uncoupled COE--CUE
(small ) to a single COE--CUE behavior (large ). Outside quasi--one
dimension, we find that the phase shift density is no longer uniform and
remains nonzero after disorder averaging. We use perturbation theory to
calculate the deviations to the isotropic Dyson distributions. When the
electron dynamics is noComment: 39 pages, 14 figures available under request, RevTex, IPNO/TH 94-6
Semiclassical analysis of level widths for one-dimensional potentials
We present a semiclassical study of level widths for a class of
one-dimensional potentials in the presence of an ohmic environment. Employing
an expression for the dipole matrix element in terms of the Fourier transform
of the classical path we obtain the level widths within the Golden rule
approximation. It is found that for potentials with an asymptotic power-law
behavior, which may in addition be limited by an infinite wall, the width that
an eigenstate of the isolated system acquires due to the coupling to the
environment is proportional to its quantum number.Comment: 8 pages, 2 figures, RevTe
Universal Quantum Signatures of Chaos in Ballistic Transport
The conductance of a ballistic quantum dot (having chaotic classical dynamics
and being coupled by ballistic point contacts to two electron reservoirs) is
computed on the single assumption that its scattering matrix is a member of
Dyson's circular ensemble. General formulas are obtained for the mean and
variance of transport properties in the orthogonal (beta=1), unitary (beta=2),
and symplectic (beta=4) symmetry class. Applications include universal
conductance fluctuations, weak localization, sub-Poissonian shot noise, and
normal-metal-superconductor junctions. The complete distribution P(g) of the
conductance g is computed for the case that the coupling to the reservoirs
occurs via two quantum point contacts with a single transmitted channel. The
result P(g)=g^(-1+beta/2) is qualitatively different in the three symmetry
classes. ***Submitted to Europhysics Letters.****Comment: 4 pages, REVTeX-3.0, INLO-PUB-94032
Transmission phase of a quantum dot and statistical fluctuations of partial-width amplitudes
Experimentally, the phase of the amplitude for electron transmission through
a quantum dot (transmission phase) shows the same pattern between consecutive
resonances. Such universal behavior, found for long sequences of resonances, is
caused by correlations of the signs of the partial-width amplitudes of the
resonances. We investigate the stability of these correlations in terms of a
statistical model. For a classically chaotic dot, the resonance eigenfunctions
are assumed to be Gaussian distributed. Under this hypothesis, statistical
fluctuations are found to reduce the tendency towards universal phase
evolution. Long sequences of resonances with universal behavior only persist in
the semiclassical limit of very large electron numbers in the dot and for
specific energy intervals. Numerical calculations qualitatively agree with the
statistical model but quantitatively are closer to universality.Comment: 8 pages, 4 figure
Partial local density of states from scanning gate microscopy
Scanning gate microscopy images from measurements made in the vicinity of
quantum point contacts were originally interpreted in terms of current flow.
Some recent work has analytically connected the local density of states to
conductance changes in cases of perfect transmission, and at least
qualitatively for a broader range of circumstances. In the present paper, we
show analytically that in any time-reversal invariant system there are
important deviations that are highly sensitive to imperfect transmission.
Nevertheless, the unperturbed partial local density of states can be extracted
from a weakly invasive scanning gate microscopy experiment, provided the
quantum point contact is tuned anywhere on a conductance plateau. A
perturbative treatment in the reflection coefficient shows just how sensitive
this correspondence is to the departure from the quantized conductance value
and reveals the necessity of local averaging over the tip position. It is also
shown that the quality of the extracted partial local density of states
decreases with increasing tip radius.Comment: 16 pages, 9 figure
Spin-orbit effects in nanowire-based wurtzite semiconductor quantum dots
We study the effect of the Dresselhaus spin-orbit interaction on the
electronic states and spin relaxation rates of cylindrical quantum dots defined
on quantum wires having wurtzite lattice structure. The linear and cubic
contributions of the bulk Dresselhaus spin-orbit coupling are taken into
account, along with the influence of a weak external magnetic field. The
previously found analytic solution for the electronic states of cylindrical
quantum dots with zincblende lattice structures with Rashba interaction is
extended to the case of quantum dots with wurtzite lattices. For the electronic
states in InAs dots, we determine the spin texture and the effective g-factor,
which shows a scaling collapse when plotted as a function of an effective
renormalized dot-size dependent spin-orbit coupling strength. The
acoustic-phonon-induced spin relaxation rate is calculated and the transverse
piezoelectric potential is shown to be the dominant one.Comment: 12 pages, 5 figure
- âŠ