41,628 research outputs found
Correctors for the Neumann problem in thin domains with locally periodic oscillatory structure
In this paper we are concerned with convergence of solutions of the Poisson
equation with Neumann boundary conditions in a two-dimensional thin domain
exhibiting highly oscillatory behavior in part of its boundary. We deal with
the resonant case in which the height, amplitude and period of the oscillations
are all of the same order which is given by a small parameter .
Applying an appropriate corrector approach we get strong convergence when we
replace the original solutions by a kind of first-order expansion through the
Multiple-Scale Method.Comment: to appear in Quarterly of Applied Mathematic
Valley polarization effects on the localization in graphene Landau levels
Effects of disorder and valley polarization in graphene are investigated in
the quantum Hall regime. We find anomalous localization properties for the
lowest Landau level (LL), where disorder can induce wavefunction delocalization
(instead of localization), both for white-noise and gaussian-correlated
disorder. We quantitatively identify the contribution of each sublattice to
wavefunction amplitudes. Following the valley (sublattice) polarization of
states within LLs for increasing disorder we show: (i) valley mixing in the
lowest LL is the main effect behind the observed anomalous localization
properties, (ii) the polarization suppression with increasing disorder depends
on the localization for the white-noise model, while, (iii) the disorder
induces a partial polarization in the higher Landau levels for both disorder
models.Comment: 5 pages, 6 figures, extended version, with 2 new figures adde
Adittional levels between Landau bands due to vacancies in graphene: towards a defect engineering
We describe the effects of vacancies on the electronic properties of a
graphene sheet in the presence of a perpendicular magnetic field: from a single
defect to an organized vacancy lattice. An isolated vacancy is the minimal
possible inner edge, showing an antidotlike behaviour, which results in an
extra level between consecutive Landau levels. Two close vacancies may couple
to each other, forming a vacancy molecule tuned by the magnetic field. We show
that a vacancy lattice introduce an extra band in between Landau levels with
localization properties that could lead to extra Hall resistance plateaus.Comment: 6 pages, 4 figures, few comments added after referees - accepted to
publication in Phys. Rev.
Inner and outer edge states in graphene rings: A numerical investigation
We numerically investigate quantum rings in graphene and find that their
electronic properties may be strongly influenced by the geometry, the edge
symmetries and the structure of the corners. Energy spectra are calculated for
different geometries (triangular, hexagonal and rhombus-shaped graphene rings)
and edge terminations (zigzag, armchair, as well as the disordered edge of a
round geometry). The states localized at the inner edges of the graphene rings
describe different evolution as a function of magnetic field when compared to
those localized at the outer edges. We show that these different evolutions are
the reason for the formation of sub-bands of edge states energy levels,
separated by gaps (anticrossings). It is evident from mapping the charge
densities that the anticrossings occur due to the coupling between inner and
outer edge states.Comment: 8 pages, 7 figures. Figures in low resolution due to size
requirements - higher quality figures on reques
Resonant tunneling through protected quantum dots at phosphorene edges
We theoretically investigate phosphorene zigzag nanorribons as a platform for
constriction engineering. In the presence of a constriction at the upper edge,
quantum confinement of edge protected states reveals resonant tunnelling
Breit-Wigner transmission peaks, if the upper edge is uncoupled to the lower
edge. Coupling between edges in thin constrictions gives rise to Fano-like and
anti-resonances in the transmission spectrum of the system.Comment: 8 pages,7 figure
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