27 research outputs found
Dirac Spectrum in Piecewise Constant One-Dimensional Potentials
We study the electronic states of graphene in piecewise constant potentials
using the continuum Dirac equation appropriate at low energies, and a transfer
matrix method. For superlattice potentials, we identify patterns of induced
Dirac points which are present throughout the band structure, and verify for
the special case of a particle-hole symmetric potential their presence at zero
energy. We also consider the cases of a single trench and a p-n junction
embedded in neutral graphene, which are shown to support confined states. An
analysis of conductance across these structures demonstrates that these
confined states create quantum interference effects which evidence their
presence.Comment: 10 pages, 12 figures, additional references adde
Unexpected features of branched flow through high-mobility two-dimensional electron gases
GaAs-based two-dimensional electron gases (2DEGs) show a wealth of remarkable
electronic states, and serve as the basis for fast transistors, research on
electrons in nanostructures, and prototypes of quantum-computing schemes. All
these uses depend on the extremely low levels of disorder in GaAs 2DEGs, with
low-temperature mean free paths ranging from microns to hundreds of microns.
Here we study how disorder affects the spatial structure of electron transport
by imaging electron flow in three different GaAs/AlGaAs 2DEGs, whose mobilities
range over an order of magnitude. As expected, electrons flow along narrow
branches that we find remain straight over a distance roughly proportional to
the mean free path. We also observe two unanticipated phenomena in
high-mobility samples. In our highest-mobility sample we observe an almost
complete absence of sharp impurity or defect scattering, indicated by the
complete suppression of quantum coherent interference fringes. Also, branched
flow through the chaotic potential of a high-mobility sample remains stable to
significant changes to the initial conditions of injected electrons.Comment: 22 pages, 4 figures, 1 tabl