64 research outputs found
Adiabatic quantization of Andreev levels
We identify the time between Andreev reflections as a classical adiabatic
invariant in a ballistic chaotic cavity (Lyapunov exponent ), coupled
to a superconductor by an -mode point contact. Quantization of the
adiabatically invariant torus in phase space gives a discrete set of periods
, which in turn generate a ladder of excited states
. The largest quantized period is the
Ehrenfest time . Projection of the invariant torus
onto the coordinate plane shows that the wave functions inside the cavity are
squeezed to a transverse dimension , much below the width of
the point contact.Comment: 4 pages, 3 figure
Commensurability effects in Andreev antidot billiards
An Andreev billiard was realized in an array of niobium filled antidots in a
high-mobility InAs/AlGaSb heterostructure. Below the critical temperature T_C
of the Nb dots we observe a strong reduction of the resistance around B=0 and a
suppression of the commensurability peaks, which are usually found in antidot
lattices. Both effects can be explained in a classical Kubo approach by
considering the trajectories of charge carriers in the semiconductor, when
Andreev reflection at the semiconductor-superconductor interface is included.
For perfect Andreev reflection, we expect a complete suppression of the
commensurability features, even though motion at finite B is chaotic.Comment: 4 pages, 4 figure
Statistical Properties of Fano Resonances in Atomic and Molecular Photoabsorption
Statistical properties of Fano resonances occurring in photoabsorption to
highly excited atomic or molecular states are derived. The situation with one
open and one closed channel is analyzed when the classical motion of the
excited complex in the closed channel is chaotic. The closed channel subspace
is modeled by random matrix theory. The probability distribution of the Fano
parameter is derived both for the case of time reversal symmetry (TRS) and
broken time reversal symmetry. For the TRS case the area distribution under a
resonance profile relevant for low resolution experiments is discussed in
detail.Comment: 4 pages, 4 figure
Universal spectral statistics of Andreev billiards: semiclassical approach
The classification of universality classes of random-matrix theory has
recently been extended beyond the Wigner-Dyson ensembles. Several of the novel
ensembles can be discussed naturally in the context of superconducting-normal
hybrid systems. In this paper, we give a semiclassical interpretation of their
spectral form factors for both quantum graphs and Andreev billiards.Comment: final improved version (to be published in Physical Review E), 6
pages, revtex
A pseudointegrable Andreev billiard
A circular Andreev billiard in a uniform magnetic field is studied. It is
demonstrated that the classical dynamics is pseudointegrable in the same sense
as for rational polygonal billiards. The relation to a specific polygon, the
asymmetric barrier billiard, is discussed. Numerical evidence is presented
indicating that the Poincare map is typically weak mixing on the invariant
sets. This link between these different classes of dynamical systems throws
some light on the proximity effect in chaotic Andreev billiards.Comment: 5 pages, 5 figures, to appear in PR
Threshold Laws for the Break-up of Atomic Particles into Several Charged Fragments
The processes with three or more charged particles in the final state exhibit
particular threshold behavior, as inferred by the famous Wannier law for (2e +
ion) system. We formulate a general solution which determines the threshold
behavior of the cross section for multiple fragmentation. Applications to
several systems of particular importance with three, four and five leptons
(electrons and positrons) in the field of charged core; and two pairs of
identical particles with opposite charges are presented. New threshold
exponents for these systems are predicted, while some previously suggested
threshold laws are revised.Comment: 40 pages, Revtex, scheduled for the July issue of Phys.Rev.A (1998
Quantum Disorder and Quantum Chaos in Andreev Billiards
We investigate the crossover from the semiclassical to the quantum
description of electron energy states in a chaotic metal grain connected to a
superconductor. We consider the influence of scattering off point impurities
(quantum disorder) and of quantum diffraction (quantum chaos) on the electron
density of states. We show that both the quantum disorder and the quantum chaos
open a gap near the Fermi energy. The size of the gap is determined by the mean
free time in disordered systems and by the Ehrenfest time in clean chaotic
systems. Particularly, if both times become infinitely large, the density of
states is gapless, and if either of these times becomes shorter than the
electron escape time, the density of states is described by random matrix
theory. Using the Usadel equation, we also study the density of states in a
grain connected to a superconductor by a diffusive contact.Comment: 20 pages, 10 figure
Mesoscopic Fano Effect in a Quantum Dot Embedded in an Aharonov-Bohm Ring
The Fano effect, which occurs through the quantum-mechanical cooperation
between resonance and interference, can be observed in electron transport
through a hybrid system of a quantum dot and an Aharonov-Bohm ring. While a
clear correlation appears between the height of the Coulomb peak and the real
asymmetric parameter for the corresponding Fano lineshape, we need to
introduce a complex to describe the variation of the lineshape by the
magnetic and electrostatic fields. The present analysis demonstrates that the
Fano effect with complex asymmetric parameters provides a good probe to detect
a quantum-mechanical phase of traversing electrons.Comment: REVTEX, 9 pages including 8 figure
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