247 research outputs found
Tunable quantum dots in bilayer graphene
We demonstrate theoretically that quantum dots in bilayers of graphene can be
realized. A position-dependent doping breaks the equivalence between the upper
and lower layer and lifts the degeneracy of the positive and negative momentum
states of the dot. Numerical results show the simultaneous presence of electron
and hole confined states for certain doping profiles and a remarkable angular
momentum dependence of the quantum dot spectrum which is in sharp contrast with
that for conventional semiconductor quantum dots. We predict that the optical
spectrum will consist of a series of non-equidistant peaks.Comment: 5 pages, to appear in Nano Letter
Landau levels and oscillator strength in a biased bilayer of graphene
We obtain analytical expressions for the eigenstates and the Landau level
spectrum of biased graphene bilayers in a magnetic field. The calculations are
performed in the context of a four-band continuum model and generalize previous
approximate results. Solutions are presented for the spectrum as a function of
interlayer coupling, the potential difference between the layers and the
magnetic field. The explicit expressions allow us to calculate the oscillator
strength and the selection rules for electric dipole transitions between the
Landau states. Some transitions are significantly shifted in energy relative to
those in an unbiased bialyer and exhibit a very different magnetic field
dependence.Comment: To appear in Phys. Rev.
Confined states and direction-dependent transmission in graphene quantum wells
We report the existence of confined massless fermion states in a graphene
quantum well (QW) by means of analytical and numerical calculations. These
states show an unusual quasi-linear dependence on the momentum parallel to the
QW: their number depends on the wavevector and is constrained by electron-hole
conversion in the barrier regions. An essential difference with
non-relativistic electron states is a mixing between free and confined states
at the edges of the free-particle continua, demonstrated by the
direction-dependent resonant transmission across a potential well.Comment: Submitted to PR
Dirac and Klein-Gordon particles in one-dimensional periodic potentials
We evaluate the dispersion relation for massless fermions, described by the
Dirac equation, and for zero-spin bosons, described by the Klein-Gordon
equation, moving in two dimensions and in the presence of a one-dimensional
periodic potential. For massless fermions the dispersion relation shows a zero
gap for carriers with zero momentum in the direction parallel to the barriers
in agreement with the well-known "Klein paradox". Numerical results for the
energy spectrum and the density of states are presented. Those for fermions are
appropriate to graphene in which carriers behave relativistically with the
"light speed" replaced by the Fermi velocity. In addition, we evaluate the
transmission through a finite number of barriers for fermions and zero-spin
bosons and relate it with that through a superlattice.Comment: 9 pages, 12 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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