62 research outputs found
Electron wave functions on in a static magnetic field of arbitrary direction
A basis set expansion is performed to find the eigenvalues and wave functions
for an electron on a toroidal surface subject to a constant magnetic
field in an arbitrary direction. The evolution of several low-lying states as a
function of field strength and field orientation is reported, and a procedure
to extend the results to include two-body Coulomb matrix elements on is
presented.Comment: 18 pages, 6 figure
Hall Conductance of a Two-Dimensional Electron Gas in Periodic Lattice with Triangular Antidots
The topic of this contribution is the investigation of quantum states and
quantum Hall effect in electron gas subjected to a periodic potential of the
lateral lattice. The potential is formed by triangular quantum antidos located
on the sites of the square lattice. In a such system the inversion center and
the four-fold rotation symmetry are absent. The topological invariants which
characterize different magnetic subbands and their Hall conductances are
calculated. It is shown that the details of the antidot geometry are crucial
for the Hall conductance quantization rule. The critical values of lattice
parameters defining the shape of triangular antidots at which the Hall
conductance is changed drastically are determined. We demonstrate that the
quantum states and Hall conductance quantization law for the triangular antidot
lattice differ from the case of the square lattice with cylindrical antidots.
As an example, the Hall conductances of magnetic subbands for different antidot
geometries are calculated for the case when the number of magnetic flux quanta
per unit cell is equal to three.Comment: 6 pages, 5 figure
Curvature effects on surface electron states in ballistic nanostructures
The curvature effect on the electronic states of a deformed cylindrical
conducting surface of variable diameter is theoretically investigated. The
quantum confinement of electrons normal to the curved surface results in an
effective potential energy that affects the electronic structures of the system
at low energies. This suggests the possibility that ballistic transport of
electrons in low-dimensional nanostructures can be controlled by inducing a
local geometric deformation.Comment: 11 pages, 3 figure
Self-consistent potential correction for charged periodic systems
Supercell models are often used to calculate the electronic structure of
local perturbations from the ideal periodicity in the bulk or on the surface of
a crystal or in wires. When the defect or adsorbent is charged, a jellium
counter charge is applied to maintain overall neutrality, but the interaction
of the artificially repeated charges has to be corrected, both in the total
energy and in the one-electron eigenvalues and eigenstates. This becomes
paramount in slab or wire calculations, where the jellium counter charge may
induce spurious states in the vacuum. We present here a self-consistent
potential correction scheme and provide successful tests of it for bulk and
slab calculations
Low-Temperature Resistivity Anomalies in Periodic Curved Surfaces
Effects of periodic curvature on the the electrical resistivity of corrugated
semiconductor films are theoretically considered. The presence of a
curvature-induced potential affects the motion of electrons confined to the
thin curved film, resulting in a significant resistivity enhancement at
specific values of two geometric parameters: the amplitude and period of the
surface corrugation. The maximal values of the two parameters in order to
observe the corrugation-induced resistivity enhancement in actual experiments
are quantified by employing existing material constants.Comment: 4 pages, 5 figure
Spectral properties on a circle with a singularity
We investigate the spectral and symmetry properties of a quantum particle
moving on a circle with a pointlike singularity (or point interaction). We find
that, within the U(2) family of the quantum mechanically allowed distinct
singularities, a U(1) equivalence (of duality-type) exists, and accordingly the
space of distinct spectra is U(1) x [SU(2)/U(1)], topologically a filled torus.
We explore the relationship of special subfamilies of the U(2) family to
corresponding symmetries, and identify the singularities that admit an N = 2
supersymmetry. Subfamilies that are distinguished in the spectral properties or
the WKB exactness are also pointed out. The spectral and symmetry properties
are also studied in the context of the circle with two singularities, which
provides a useful scheme to discuss the symmetry properties on a general basis.Comment: TeX, 26 pages. v2: one reference added and two update
Renormalization approach for quantum-dot structures under strong alternating fields
We develop a renormalization method for calculating the electronic structure
of single and double quantum dots under intense ac fields. The nanostructures
are emulated by lattice models with a clear continuum limit of the
effective-mass and single-particle approximations. The coupling to the ac field
is treated non-perturbatively by means of the Floquet Hamiltonian. The
renormalization approach allows the study of dressed states of the nanoscopic
system with realistic geometries as well arbitrary strong ac fields. We give
examples of a single quantum dot, emphasizing the analysis of the
effective-mass limit for lattice models, and double-dot structures, where we
discuss the limit of the well used two-level approximation.Comment: 6 pages, 7 figure
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