426 research outputs found
Diffraction catastrophes and semiclassical quantum mechanics for Veselago lensing in graphene
We study the effect of trigonal warping on the focussing of electrons by n-p
junctions in graphene. We find that perfect focussing, which was predicted for
massless Dirac fermions, is only preserved for one specific sample orientation.
In the general case, trigonal warping leads to the formation of cusp caustics,
with a different position of the focus for graphene's two valleys. We develop a
semiclassical theory to compute these positions and find very good agreement
with tight-binding simulations. Considering the transmission as a function of
potential strength, we find that trigonal warping splits the single Dirac peak
into two distinct peaks, leading to valley polarization. We obtain the
transmission curves from tight-binding simulations and find that they are in
very good agreement with the results of a billiard model that incorporates
trigonal warping. Furthermore, the positions of the transmission maxima and the
scaling of the peak width are accurately predicted by our semiclassical theory.
Our semiclassical analysis can easily be carried over to other Dirac materials,
which generally have different Fermi surface distortions.Comment: 6 pages, 4 figures, plus supplemental material. Important reference
added and text update
Modeling Klein tunneling and caustics of electron waves in graphene
We employ the tight-binding propagation method to study Klein tunneling and
quantum interference in large graphene systems. With this efficient numerical
scheme, we model the propagation of a wave packet through a potential barrier
and determine the tunneling probability for different incidence angles. We
consider both sharp and smooth potential barriers in n-p-n and n-n' junctions
and find good agreement with analytical and semiclassical predictions. When we
go outside the Dirac regime, we observe that sharp n-p junctions no longer show
Klein tunneling because of intervalley scattering. However, this effect can be
suppressed by considering a smooth potential. Klein tunneling holds for
potentials changing on the scale much larger than the interatomic distance.
When the energies of both the electrons and holes are above the Van Hove
singularity, we observe total reflection for both sharp and smooth potential
barriers. Furthermore, we consider caustic formation by a two-dimensional
Gaussian potential. For sufficiently broad potentials we find a good agreement
between the simulated wave density and the classical electron trajectories.Comment: 14 pages, 12 figure
Electronic optics in graphene in the semiclassical approximation
We study above-barrier scattering of Dirac electrons by a smooth
electrostatic potential combined with a coordinate-dependent mass in graphene.
We assume that the potential and mass are sufficiently smooth, so that we can
define a small dimensionless semiclassical parameter . This electronic
optics setup naturally leads to focusing and the formation of caustics, which
are singularities in the density of trajectories. We construct a semiclassical
approximation for the wavefunction in all points, placing particular emphasis
on the region near the caustic, where the maximum of the intensity lies.
Because of the matrix character of the Dirac equation, this wavefunction
contains a nontrivial semiclassical phase, which is absent for a scalar wave
equation and which influences the focusing. We carefully discuss the three
steps in our semiclassical approach: the adiabatic reduction of the matrix
equation to an effective scalar equation, the construction of the wavefunction
using the Maslov canonical operator and the application of the uniform
approximation to the integral expression for the wavefunction in the vicinity
of a caustic. We consider several numerical examples and show that our
semiclassical results are in very good agreement with the results of
tight-binding calculations. In particular, we show that the semiclassical phase
can have a pronounced effect on the position of the focus and its intensity.Comment: 103 pages, 11 figure
Semiclassical theory for plasmons in two-dimensional inhomogeneous media
The progress in two-dimensional materials has led to rapid experimental
developments in quantum plasmonics, where light is manipulated using plasmons.
Although numerical methods can be used to quantitatively describe plasmons in
spatially inhomogeneous systems, they are limited to relatively small setups.
Here, we present a novel semi-analytical method to describe plasmons in
two-dimensional inhomogeneous media within the framework of the Random Phase
Approximation (RPA). Our approach is based on the semiclassical approximation,
which is formally applicable when the length scale of the inhomogeneity is much
larger than the plasmon wavelength. We obtain an effective classical
Hamiltonian for quantum plasmons by first separating the in-plane and
out-of-plane degrees of freedom and subsequently employing the semiclassical
Ansatz for the electrostatic plasmon potential. We illustrate this general
theory by considering scattering of plasmons by radially symmetric
inhomogeneities. We derive a semiclassical expression for the differential
scattering cross section and compute its numerical values for a specific model
of the inhomogeneity.Comment: 27 pages, 9 figure
Pinning and collective modes of a vortex lattice in a Bose-Einstein condensate
We consider the ground state of vortices in a rotating Bose-Einstein
condensate that is loaded in a corotating two-dimensional optical lattice. Due
to the competition between vortex interactions and their potential energy, the
vortices arrange themselves in various patterns, depending on the strength of
the optical potential and the vortex density. We outline a method to determine
the phase diagram for arbitrary vortex filling factor. Using this method, we
discuss several filling factors explicitly. For increasing strength of the
optical lattice, the system exhibits a transition from the unpinned hexagonal
lattice to a lattice structure where all the vortices are pinned by the optical
lattice. The geometry of this fully pinned vortex lattice depends on the
filling factor and is either square or triangular. For some filling factors
there is an intermediate half-pinned phase where only half of the vortices is
pinned. We also consider the case of a two-component Bose-Einstein condensate,
where the possible coexistence of the above-mentioned phases further enriches
the phase diagram. In addition, we calculate the dispersion of the low-lying
collective modes of the vortex lattice and find that, depending on the
structure of the ground state, they can be gapped or gapless. Moreover, in the
half-pinned and fully pinned phases, the collective mode dispersion is
anisotropic. Possible experiments to probe the collective mode spectrum, and in
particular the gap, are suggested.Comment: 29 pages, 4 figures, changes in section
Optical investigation of thermoelectric topological crystalline insulator PbSnSe
PbSnSe is a novel alloy of two promising thermoelectric
materials PbSe and SnSe that exhibits a temperature dependent band inversion
below 300 K. Recent work has shown that this band inversion also coincides with
a trivial to nontrivial topological phase transition. To understand how the
properties critical to thermoelectric efficiency are affected by the band
inversion, we measured the broadband optical response of
PbSnSe as a function of temperature. We find clear optical
evidence of the band inversion at K, and use the extended Drude
model to accurately determine a dependence of the bulk carrier
lifetime, associated with electron-acoustic phonon scattering. Due to the high
bulk carrier doping level, no discriminating signatures of the topological
surface states are found, although their presence cannot be excluded from our
data.Comment: 11 pages, 6 figure
Measurement of the temperature of an ultracold ion source using time-dependent electric fields
We report on a measurement of the characteristic temperature of an ultracold
rubidium ion source, in which a cloud of laser-cooled atoms is converted to
ions by photo-ionization. Extracted ion pulses are focused on a detector with a
pulsed-field technique. The resulting experimental spot sizes are compared to
particle-tracking simulations, from which a source temperature
mK and the corresponding transversal reduced emittance m rad are determined. We find that this result is
likely limited by space charge forces even though the average number of ions
per bunch is 0.022.Comment: 8 pages, 11 figure
Chiral tunneling in single and bilayer graphene
We review chiral (Klein) tunneling in single-layer and bilayer graphene and
present its semiclassical theory, including the Berry phase and the Maslov
index. Peculiarities of the chiral tunneling are naturally explained in terms
of classical phase space. In a one-dimensional geometry we reduced the original
Dirac equation, describing the dynamics of charge carriers in the single layer
graphene, to an effective Schr\"odinger equation with a complex potential. This
allowed us to study tunneling in details and obtain analytic formulas. Our
predictions are compared with numerical results. We have also demonstrated
that, for the case of asymmetric n-p-n junction in single layer graphene, there
is total transmission for normal incidence only, side resonances are
suppressed.Comment: submitted to Proceedings of Nobel Symposium on graphene, May 201
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