7,112 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.
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
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