61 research outputs found
Path distributions for describing eigenstates of the harmonic oscillator and other 1-dimensional problems
The manner in which probability amplitudes of paths sum up to form wave
functions of a harmonic oscillator, as well as other, simple 1-dimensional
problems, is described. Using known, closed-form, path-based propagators for
each problem, an integral expression is written that describes the wave
function. This expression conventionally takes the form of an integral over
initial locations of a particle, but it is re-expressed here in terms of a
characteristic momentum associated with motion between the endpoints of a path.
In this manner, the resulting expression can be analyzed using a generalization
of stationary-phase analysis, leading to distributions of paths that exactly
describe each eigenstate. These distributions are valid for all travel times,
but when evaluated for long times they turn out to be real, non-negative
functions of the characteristic momentum. For the harmonic oscillator in
particular, a somewhat broad distribution is found, peaked at value of momentum
that corresponds to a classical energy which in turn equals the energy
eigenvalue for the state being described.Comment: 26 page, 10 figures; in v2, added refs. 43 and 44 along with a brief
description of the latter, and made a few minor typographical correction
SymFET: A Proposed Symmetric Graphene Tunneling Field Effect Transistor
In this work, an analytical model to calculate the channel potential and
current-voltage characteristics in a Symmetric tunneling
Field-Effect-Transistor (SymFET) is presented. The current in a SymFET flows by
tunneling from an n-type graphene layer to a p-type graphene layer. A large
current peak occurs when the Dirac points are aligned at a particular drain-to-
source bias VDS . Our model shows that the current of the SymFET is very weakly
dependent on temperature. The resonant current peak is controlled by chemical
doping and applied gate bias. The on/off ratio increases with graphene
coherence length and doping. The symmetric resonant peak is a good candidate
for high-speed analog applications, and can enable digital logic similar to the
BiSFET. Our analytical model also offers the benefit of permitting simple
analysis of features such as the full-width-at-half-maximum (FWHM) of the
resonant peak and higher order harmonics of the nonlinear current. The SymFET
takes advantage of the perfect symmetry of the bandstructure of 2D graphene, a
feature that is not present in conventional semiconductors
Photo-physics and electronic structure of lateral graphene/MoS2 and metal/MoS2 junctions
Integration of semiconducting transition metal dichalcogenides (TMDs) into
functional optoelectronic circuitries requires an understanding of the charge
transfer across the interface between the TMD and the contacting material.
Here, we use spatially resolved photocurrent microscopy to demonstrate
electronic uniformity at the epitaxial graphene/molybdenum disulfide (EG/MoS2)
interface. A 10x larger photocurrent is extracted at the EG/MoS2 interface when
compared to metal (Ti/Au) /MoS2 interface. This is supported by semi-local
density-functional theory (DFT), which predicts the Schottky barrier at the
EG/MoS2 interface to be ~2x lower than Ti/MoS2. We provide a direct
visualization of a 2D material Schottky barrier through combination of angle
resolved photoemission spectroscopy with spatial resolution selected to be ~300
nm (nano-ARPES) and DFT calculations. A bending of ~500 meV over a length scale
of ~2-3 micrometer in the valence band maximum of MoS2 is observed via
nano-ARPES. We explicate a correlation between experimental demonstration and
theoretical predictions of barriers at graphene/TMD interfaces. Spatially
resolved photocurrent mapping allows for directly visualizing the uniformity of
built-in electric fields at heterostructure interfaces, providing a guide for
microscopic engineering of charge transport across heterointerfaces. This
simple probe-based technique also speaks directly to the 2D synthesis community
to elucidate electronic uniformity at domain boundaries alongside morphological
uniformity over large areas
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