7,030 research outputs found
Snake states in graphene quantum dots in the presence of a p-n junction
We investigate the magnetic interface states of graphene quantum dots that
contain p-n junctions. Within a tight-binding approach, we consider rectangular
quantum dots in the presence of a perpendicular magnetic field containing p-n,
as well as p-n-p and n-p-n junctions. The results show the interplay between
the edge states associated with the zigzag terminations of the sample and the
snake states that arise at the p-n junction, due to the overlap between
electron and hole states at the potential interface. Remarkable localized
states are found at the crossing of the p-n junction with the zigzag edge
having a dumb-bell shaped electron distribution. The results are presented as
function of the junction parameters and the applied magnetic flux.Comment: 13 pages, 23 figures, to be appeared in Phys. Rev.
Life and death of a hero - Lessons learned from modeling the dwarf spheroidal Hercules: an incorrect orbit?
Hercules is a dwarf spheroidal satellite of the Milky Way, found at a
distance of about 138 kpc, and showing evidence of tidal disruption. It is very
elongated and exhibits a velocity gradient of 16 +/- 3 km/s/kpc. Using this
data a possible orbit of Hercules has previously been deduced in the
literature. In this study we make use of a novel approach to find a best fit
model that follows the published orbit. Instead of using trial and error, we
use a systematic approach in order to find a model that fits multiple
observables simultaneously. As such, we investigate a much wider parameter
range of initial conditions and ensure we have found the best match possible.
Using a dark matter free progenitor that undergoes tidal disruption, our
best-fit model can simultaneously match the observed luminosity, central
surface brightness, effective radius, velocity dispersion, and velocity
gradient of Hercules. However, we find it is impossible to reproduce the
observed elongation and the position angle of Hercules at the same time in our
models. This failure persists even when we vary the duration of the simulation
significantly, and consider a more cuspy density distribution for the
progenitor. We discuss how this suggests that the published orbit of Hercules
is very likely to be incorrect.Comment: accepted by MNRAS; 19 pages, 19 figures, 2 table
Weakly holomorphic modular forms in prime power levels of genus zero
Let be the space of weight , level weakly holomorphic
modular forms with poles only at the cusp at . We explicitly construct
a canonical basis for for , and show that
many of the Fourier coefficients of the basis elements in are
divisible by high powers of the prime dividing the level . Additionally, we
show that these basis elements satisfy a Zagier duality property, and extend
Griffin's results on congruences in level 1 to levels 2, 3, 4, 5, 7, 8, 9, 16,
and 25
The split-operator technique for the study of spinorial wavepacket dynamics
The split-operator technique for wave packet propagation in quantum systems
is expanded here to the case of propagating wave functions describing
Schr\"odinger particles, namely, charge carriers in semiconductor
nanostructures within the effective mass approximation, in the presence of
Zeeman effect, as well as of Rashba and Dresselhaus spin-orbit interactions. We
also demonstrate that simple modifications to the expanded technique allow us
to calculate the time evolution of wave packets describing Dirac particles,
which are relevant for the study of transport properties in graphene.Comment: 19 pages, 4 figure
Simplified model for the energy levels of quantum rings in single layer and bilayer graphene
Within a minimal model, we present analytical expressions for the eigenstates
and eigenvalues of carriers confined in quantum rings in monolayer and bilayer
graphene. The calculations were performed in the context of the continuum
model, by solving the Dirac equation for a zero width ring geometry, i.e. by
freezing out the carrier radial motion. We include the effect of an external
magnetic field and show the appearance of Aharonov-Bohm oscillations and of a
non-zero gap in the spectrum. Our minimal model gives insight in the energy
spectrum of graphene-based quantum rings and models different aspects of finite
width rings.Comment: To appear in Phys. Rev.
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