252 research outputs found
Four-Particle Anyon Exciton: Boson Approximation
A theory of anyon excitons consisting of a valence hole and three
quasielectrons with electric charges is presented. A full symmetry
classification of the states is given, where is the exciton momentum.
The energy levels of these states are expressed by quadratures of confluent
hypergeometric functions. It is shown that the angular momentum of the
exciton ground state depends on the distance between electron and hole
confinement planes and takes the values , where is an integer. With
increasing the electron density shows a spectacular splitting on bundles.
At first a single anyon splits off of the two-anyon core, and finally all
anyons become separated.Comment: Revtex 13 pages + 6 uuencoded postscript figure
Localization of massless Dirac particles via spatial modulations of the Fermi velocity
The electrons found in Dirac materials are notorious for being difficult to
manipulate due to the Klein phenomenon and absence of backscattering. Here we
investigate how spatial modulations of the Fermi velocity in two-dimensional
Dirac materials can give rise to localization effects, with either full
(zero-dimensional) confinement or partial (one-dimensional) confinement
possible depending on the geometry of the velocity modulation. We present
several exactly solvable models illustrating the nature of the bound states
which arise, revealing how the gradient of the Fermi velocity is crucial for
determining fundamental properties of the bound states such as the zero-point
energy. We discuss the implications for guiding electronic waves in few-mode
waveguides formed by Fermi velocity modulation.Comment: 9 pages, 6 figure
Excitonic Mott transition in double quantum wells
We consider an electron-hole system in double quantum wells theoretically. We
demonstrate that there is a temperature interval over which an abrupt jump in
the value of the ionization degree occurs with an increase of the carrier
density or temperature. The opposite effect - the collapse of the ionized
electron-hole plasma into an insulating exciton system - should occur at lower
densities. In addition, we predict that under certain conditions there will be
a sharp decrease of the ionization degree with increasing temperature - the
anomalous Mott transition. We discuss how these effects could be observed
experimentally.Comment: 6 pages, 4 figure
One-dimensional Coulomb problem in Dirac materials
We investigate the one-dimensional Coulomb potential with application to a
class of quasirelativistic systems, so-called Dirac-Weyl materials, described
by matrix Hamiltonians. We obtain the exact solution of the shifted and
truncated Coulomb problems, with the wavefunctions expressed in terms of
special functions (namely Whittaker functions), whilst the energy spectrum must
be determined via solutions to transcendental equations. Most notably, there
are critical bandgaps below which certain low-lying quantum states are missing
in a manifestation of atomic collapse.Comment: 7 pages, 5 figure
Bielectron vortices in two-dimensional Dirac semimetals
Searching for new states of matter and unusual quasiparticles in emerging
materials and especially low-dimensional systems is one of the major trends in
contemporary condensed matter physics. Dirac materials, which host
quasiparticles which are described by ultrarelativistic Dirac-like equations,
are of a significant current interest from both a fundamental and applied
physics perspective. Here we show that a pair of two-dimensional massless
Dirac-Weyl fermions can form a bound state independently of the sign of the
inter-particle interaction potential, as long as this potential decays at large
distances faster than Kepler's inverse distance law. This leads to the
emergence of a new type of energetically-favourable quasiparticle: bielectron
vortices, which are double-charged and reside at zero-energy. Their bosonic
nature allows for condensation and may give rise to Majorana physics without
invoking a superconductor. These novel quasiparticles arguably explain a range
of poorly understood experiments in gated graphene structures at low doping.Comment: 9 pages, 2 figure
Massless Dirac fermions in two dimensions: Confinement in nonuniform magnetic fields
We show how it is possible to trap two-dimensional massless Dirac fermions in
spatially inhomogeneous magnetic fields, as long as the formed magnetic quantum
dot (or ring) is of a slowly decaying nature. It is found that a modulation of
the depth of the magnetic quantum dot leads to successive
confinement-deconfinement transitions of vortexlike states with a certain
angular momentum, until a regime is reached where only states with one sign of
angular momentum are supported. We illustrate these characteristics with both
exact solutions and a hitherto unknown quasi-exactly solvable model utilizing
confluent Heun functions.Comment: 7 pages, 3 figure
Exactly-solvable problems for two-dimensional excitons
Several problems in mathematical physics relating to excitons in two
dimensions are considered. First, a fascinating numerical result from a
theoretical treatment of screened excitons stimulates a re-evaluation of the
familiar two-dimensional hydrogen atom. Formulating the latter problem in
momentum space leads to a new integral relation in terms of special functions,
and fresh insights into the dynamical symmetry of the system are also obtained.
A discussion of an alternative potential to model screened excitons is given,
and the variable phase method is used to compare bound-state energies and
scattering phase shifts for this potential with those obtained using the
two-dimensional analogue of the Yukawa potential. The second problem relates to
excitons in a quantising magnetic field in the fractional quantum Hall regime.
An exciton against the background of an incompressible quantum liquid is
modelled as a few-particle neutral composite consisting of a positively-charged
hole and several quasielectrons with fractional negative charge. A complete set
of exciton basis functions is derived, and these functions are classified using
a result from the theory of partitions. Some exact results are obtained for
this complex few-particle problem.Comment: 66 pages, 9 figure
Momentum alignment and the optical valley Hall effect in low-dimensional Dirac materials
We study the momentum alignment phenomenon and the optical control of valley
population in gapless and gapped graphene-like materials. We show that the
trigonal warping effect allows for the spatial separation of carriers belonging
to different valleys via the application of linearly polarized light. Valley
separation in gapped materials can be detected by measuring the degree of
circular polarization of band-edge photoluminescence at different sides of the
sample or light spot (optical valley Hall effect). We also show that the
momentum alignment phenomenon leads to the giant enhancement of near-band-edge
interband optical transitions in narrow-gap carbon nanotubes and graphene
nanoribbons independent of the mechanism of the gap formation. A detection
scheme to observe these giant interband transitions is proposed which opens a
route for creating novel terahertz radiation emitters.Comment: 28 pages, 9 figure
Photon emission induced by elastic exciton--carrier scattering in semiconductor quantum wells
We present a study of the elastic exciton--electron () and
exciton--hole () scattering processes in semiconductor quantum wells,
including fermion exchange effects. The balance between the exciton and the
free carrier populations within the electron-hole plasma is discussed in terms
of ionization degree in the nondegenerate regime. Assuming a two-dimensional
Coulomb potential statically screened by the free carrier gas, we apply the
variable phase method to obtain the excitonic wavefunctions, which we use to
calculate the 1 exciton--free carrier matrix elements that describe the
scattering of excitons into the light cone where they can radiatively
recombine. The photon emission rates due to the carrier-assisted exciton
recombination in semiconductor quantum-wells (QWs) at room temperature and in a
low density regime are obtained from Fermi's golden rule, and studied for
mid-gap and wide-gap materials. The quantitative comparison of the direct and
exchange terms of the scattering matrix elements shows that fermion exchange is
the dominant mechanism of the exciton--carrier scattering process. This is
confirmed by our analysis of the rates of photon emission induced by
electron-assisted and hole-assisted exciton recombinations.Comment: Thoroughly revised version of previous work. Weak and incorrect
assumptions have been removed from the paper, and its scope has evolved: see
abstract. This is the final version, i.e. as accepted for publication in the
European Physical Journal
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