167 research outputs found
Quantal Andreev billiards: Semiclassical approach to mesoscale oscillations in the density of states
Andreev billiards are finite, arbitrarily-shaped, normal-state regions,
surrounded by superconductor. At energies below the superconducting gap,
single-quasiparticle excitations are confined to the normal region and its
vicinity, the essential mechanism for this confinement being Andreev
reflection. This Paper develops and implements a theoretical framework for the
investigation of the short-wave quantal properties of these
single-quasiparticle excitations. The focus is primarily on the relationship
between the quasiparticle energy eigenvalue spectrum and the geometrical shape
of the normal-state region, i.e., the question of spectral geometry in the
novel setting of excitations confined by a superconducting pair-potential.
Among the central results of this investigation are two semiclassical trace
formulas for the density of states. The first, a lower-resolution formula,
corresponds to the well-known quasiclassical approximation, conventionally
invoked in settings involving superconductivity. The second, a
higher-resolution formula, allows the density of states to be expressed in
terms of: (i) An explicit formula for the level density, valid in the
short-wave limit, for billiards of arbitrary shape and dimensionality. This
level density depends on the billiard shape only through the set of
stationary-length chords of the billiard and the curvature of the boundary at
the endpoints of these chords; and (ii) Higher-resolution corrections to the
level density, expressed as a sum over periodic orbits that creep around the
billiard boundary. Owing to the fact that these creeping orbits are much longer
than the stationary chords, one can, inter alia, hear the stationary chords of
Andreev billiards.Comment: 52 pages, 15 figures, 1 table, RevTe
Interfaces within graphene nanoribbons
We study the conductance through two types of graphene nanostructures: nanoribbon junctions in which the width changes from wide to narrow, and curved nanoribbons. In the wide-narrow structures, substantial reflection occurs from the wide-narrow interface, in contrast to the behavior of the much studied electron gas waveguides. In the curved nanoribbons, the conductance is very sensitive to details such as whether regions of a semiconducting armchair nanoribbon are included in the curved structure -- such regions strongly suppress the conductance. Surprisingly, this suppression is not due to the band gap of the semiconducting nanoribbon, but is linked to the valley degree of freedom. Though we study these effects in the simplest contexts, they can be expected to occur for more complicated structures, and we show results for rings as well. We conclude that experience from electron gas waveguides does not carry over to graphene nanostructures. The interior interfaces causing extra scattering result from the extra effective degrees of freedom of the graphene structure, namely the valley and sublattice pseudospins
Edge effects in graphene nanostructures: II. Semiclassical theory of spectral fluctuations and quantum transport
We investigate the effect of different edge types on the statistical
properties of both the energy spectrum of closed graphene billiards and the
conductance of open graphene cavities in the semiclassical limit. To this end,
we use the semiclassical Green's function for ballistic graphene flakes that we
have derived in Reference 1. First we study the spectral two point correlation
function, or more precisely its Fourier transform the spectral form factor,
starting from the graphene version of Gutzwiller's trace formula for the
oscillating part of the density of states. We calculate the two leading order
contributions to the spectral form factor, paying particular attention to the
influence of the edge characteristics of the system. Then we consider transport
properties of open graphene cavities. We derive generic analytical expressions
for the classical conductance, the weak localization correction, the size of
the universal conductance fluctuations and the shot noise power of a ballistic
graphene cavity. Again we focus on the effects of the edge structure. For both,
the conductance and the spectral form factor, we find that edge induced
pseudospin interference affects the results significantly. In particular
intervalley coupling mediated through scattering from armchair edges is the key
mechanism that governs the coherent quantum interference effects in ballistic
graphene cavities
Weak localization in mesoscopic hole transport: Berry phases and classical correlations
We consider phase-coherent transport through ballistic and diffusive
two-dimensional hole systems based on the Kohn-Luttinger Hamiltonian. We show
that intrinsic heavy-hole light-hole coupling gives rise to clear-cut
signatures of an associated Berry phase in the weak localization which renders
the magneto-conductance profile distinctly different from electron transport.
Non-universal classical correlations determine the strength of these Berry
phase effects and the effective symmetry class, leading even to
antilocalization-type features for circular quantum dots and Aharonov-Bohm
rings in the absence of additional spin-orbit interaction. Our semiclassical
predictions are quantitatively confirmed by numerical transport calculations
Measurement of spin-dependent conductivities in a two-dimensional electron gas
Spin accumulation is generated by injecting an unpolarized charge current
into a channel of GaAs two-dimensional electron gas subject to an in-plane
magnetic field, then measured in a non-local geometry. Unlike previous
measurements that have used spin-polarized nanostructures, here the spin
accumulation arises simply from the difference in bulk conductivities for
spin-up and spin-down carriers. Comparison to a diffusive model that includes
spin subband splitting in magnetic field suggests a significantly enhanced
electron spin susceptibility in the 2D electron gas
Edge effects in graphene nanostructures: I. From multiple reflection expansion to density of states
We study the influence of different edge types on the electronic density of
states of graphene nanostructures. To this end we develop an exact expansion
for the single particle Green's function of ballistic graphene structures in
terms of multiple reflections from the system boundary, that allows for a
natural treatment of edge effects. We first apply this formalism to calculate
the average density of states of graphene billiards. While the leading term in
the corresponding Weyl expansion is proportional to the billiard area, we find
that the contribution that usually scales with the total length of the system
boundary differs significantly from what one finds in semiconductor-based,
Schr\"odinger type billiards: The latter term vanishes for armchair and
infinite mass edges and is proportional to the zigzag edge length, highlighting
the prominent role of zigzag edges in graphene. We then compute analytical
expressions for the density of states oscillations and energy levels within a
trajectory based semiclassical approach. We derive a Dirac version of
Gutzwiller's trace formula for classically chaotic graphene billiards and
further obtain semiclassical trace formulae for the density of states
oscillations in regular graphene cavities. We find that edge dependent
interference of pseudospins in graphene crucially affects the quantum spectrum.Comment: to be published in Phys. Rev.
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