43 research outputs found
On the theory of cavities with point-like perturbations. Part II: Rectangular cavities
We consider an application of a general theory for cavities with point-like
perturbations for a rectangular shape. Hereby we concentrate on experimental
wave patterns obtained for nearly degenerate states. The nodal lines in these
patterns may be broken, which is an effect coming only from the experimental
determination of the patterns. These findings are explained within a framework
of the developed theory.Comment: 14 pages, 3 figure
Peculiarities of dynamics of Dirac fermions associated with zero-mass lines
Zero-mass lines result in appearance of linear dispersion modes for Dirac
fermions. These modes play an important role in various physical systems.
However, a Dirac fermion may not precisely follow a single zero-mass line, due
to either tunneling between different lines or centrifugal forces. Being
shifted from a zero-mass line the Dirac fermion acquires mass which can
substantially influence its expected "massless" behavior. In the paper we
calculate the energy gap caused by the tunneling between two zero-mass lines
and show that its opening leads to the delocalization of linear dispersion
modes. The adiabatic bending of a zero-mass line gives rise to geometric
phases. These are the Berry phase, locally associated with a curvature, and a
new phase resulting from the mass square asymmetry in the vicinity of a
zero-mass line.Comment: 6 pages, 4 figures. In the second version some references were added
and minor changes were made in the introductio
Inter-valley plasmons in graphene
The spectrum of two-dimensional (2D) plasma waves in graphene has been
recently studied in the Dirac fermion model. We take into account the whole
dispersion relation for graphene electrons in the tight binding approximation
and the local field effects in the electrodynamic response. Near the
wavevectors close to the corners of the hexagon-shaped Brillouin zone we found
new low-frequency 2D plasmon modes with a linear spectrum. These "inter-valley"
plasmon modes are related to the transitions between the two nearest Dirac
cones.Comment: 4 pages, 2 figures; submitted in PR
Theory of Coulomb drag for massless Dirac fermions
Coulomb drag between two unhybridized graphene sheets separated by a
dielectric spacer has recently attracted considerable theoretical interest. We
first review, for the sake of completeness, the main analytical results which
have been obtained by other authors. We then illustrate pedagogically the
minimal theory of Coulomb drag between two spatially-separated two-dimensional
systems of massless Dirac fermions which are both away from the
charge-neutrality point. This relies on second-order perturbation theory in the
screened interlayer interaction and on Boltzmann transport theory. In this
theoretical framework and in the low-temperature limit, we demonstrate that, to
leading (i.e. quadratic) order in temperature, the drag transresistivity is
completely insensitive to the precise intralayer momentum-relaxation mechanism
(i.e. to the functional dependence of the scattering time on energy). We also
provide analytical results for the low-temperature drag transresistivity for
both cases of "thick" and "thin" spacers and for arbitrary values of the
dielectric constants of the media surrounding the two Dirac-fermion layers.
Finally, we present numerical results for the low-temperature drag
transresistivity in the case in which one of the media surrounding the
Dirac-fermion layers has a frequency-dependent dielectric constant. We conclude
by suggesting an experiment that can potentially allow for the observation of
departures from the canonical Fermi-liquid quadratic-in-temperature behavior of
the transresistivity.Comment: 20 pages, 4 figure
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
A new electromagnetic mode in graphene
A new, weakly damped, {\em transverse} electromagnetic mode is predicted in
graphene. The mode frequency lies in the window
, where is the chemical potential, and can be
tuned from radiowaves to the infrared by changing the density of charge
carriers through a gate voltage.Comment: 5 pages, 4 figure
Dirac Point and Edge States in a Microwave Realization of Tight-Binding Graphene-like Structures
We present a microwave realization of finite tight-binding graphene-like
structures. The structures are realized using discs with a high index of
refraction. The discs are placed on a metallic surface while a second surface
is adjusted atop the discs, such that the waves coupling the discs in the air
are evanescent, leading to the tight-binding behavior. In reflection
measurements the Dirac point and a linear increase close to the Dirac point is
observed, if the measurement is performed inside the sample. Resonances due to
edge states are found close to the Dirac point if the measurements are
performed at the zigzag-edge or at the corner in case of a broken benzene ring.Comment: 4 pages, 6 figure
On the eigenvalue spacing distribution for a point scatterer on the flat torus
We study the level spacing distribution for the spectrum of a point scatterer
on a flat torus. In the 2-dimensional case, we show that in the weak coupling
regime the eigenvalue spacing distribution coincides with that of the spectrum
of the Laplacian (ignoring multiplicties), by showing that the perturbed
eigenvalues generically clump with the unperturbed ones on the scale of the
mean level spacing. We also study the three dimensional case, where the
situation is very different.Comment: 25 page
Semiclassical theory of potential scattering for massless Dirac fermions
In this paper we study scattering of two-dimensional massless Dirac fermions
by a potential that depends on a single Cartesian variable. Depending on the
energy of the incoming particle and its angle of incidence, there are three
different regimes of scattering. To find the reflection and transmission
coefficients in these regimes, we apply the Wentzel-Kramers-Brillouin (WKB),
also called semiclassical, approximation. We use the method of comparison
equations to extend our prediction to nearly normal incidence, where the
conventional WKB method should be modified due to the degeneracy of turning
points. We compare our results to numerical calculations and find good
agreement.Comment: Minor revision; several references have been adde