208 research outputs found
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
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Zero-energy states in graphene quantum dots and rings
We present exact analytical zero-energy solutions for a class of smooth
decaying potentials, showing that the full confinement of charge carriers in
electrostatic potentials in graphene quantum dots and rings is indeed possible
without recourse to magnetic fields. These exact solutions allow us to draw
conclusions on the general requirements for the potential to support fully
confined states, including a critical value of the potential strength and
spatial extent.Comment: 8 pages, 3 figures, references added, typos corrected, discussion
section expande
The two-dimensional hydrogen atom revisited
The bound state energy eigenvalues for the two-dimensional Kepler problem are
found to be degenerate. This "accidental" degeneracy is due to the existence of
a two-dimensional analogue of the quantum-mechanical Runge-Lenz vector.
Reformulating the problem in momentum space leads to an integral form of the
Schroedinger equation. This equation is solved by projecting the
two-dimensional momentum space onto the surface of a three-dimensional sphere.
The eigenfunctions are then expanded in terms of spherical harmonics, and this
leads to an integral relation in terms of special functions which has not
previously been tabulated. The dynamical symmetry of the problem is also
considered, and it is shown that the two components of the Runge-Lenz vector in
real space correspond to the generators of infinitesimal rotations about the
respective coordinate axes in momentum space.Comment: 10 pages, no figures, RevTex
Excitons in narrow-gap carbon nanotubes
We calculate the exciton binding energy in single-walled carbon nanotubes
with narrow band gaps, accounting for the quasi-relativistic dispersion of
electrons and holes. Exact analytical solutions of the quantum relativistic
two-body problem are obtain for several limiting cases. We show that the
binding energy scales with the band gap, and conclude on the basis of the data
available for semiconductor nanotubes that there is no transition to an
excitonic insulator in quasi-metallic nanotubes and that their THz applications
are feasible.Comment: 11 pages, 3 figures. Several references and an additional appendix
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Superlattice properties of carbon nanotubes in a transverse electric field
Electron motion in a (n,1) carbon nanotube is shown to correspond to a de
Broglie wave propagating along a helical line on the nanotube wall. This
helical motion leads to periodicity of the electron potential energy in the
presence of an electric field normal to the nanotube axis. The period of this
potential is proportional to the nanotube radius and is greater than the
interatomic distance in the nanotube. As a result, the behavior of an electron
in a (n,1) nanotube subject to a transverse electric field is similar to that
in a semiconductor superlattice. In particular, Bragg scattering of electrons
from the long-range periodic potential results in the opening of gaps in the
energy spectrum of the nanotube. Modification of the bandstructure is shown to
be significant for experimentally attainable electric fields, which raises the
possibility of applying this effect to novel nanoelectronic devices.Comment: 7 pages, 3 figure
Ionization degree of the electron-hole plasma in semiconductor quantum wells
The degree of ionization of a nondegenerate two-dimensional electron-hole
plasma is calculated using the modified law of mass action, which takes into
account all bound and unbound states in a screened Coulomb potential.
Application of the variable phase method to this potential allows us to treat
scattering and bound states on the same footing. Inclusion of the scattering
states leads to a strong deviation from the standard law of mass action. A
qualitative difference between mid- and wide-gap semiconductors is
demonstrated. For wide-gap semiconductors at room temperature, when the bare
exciton binding energy is of the order of T, the equilibrium consists of an
almost equal mixture of correlated electron-hole pairs and uncorrelated free
carriers.Comment: 22 pages, 6 figure
Quasi-exact solution to the Dirac equation for the hyperbolic-secant potential
Copyright © 2014 American Physical SocietyWe analyze bound modes of two-dimensional massless Dirac fermions confined within a hyperbolic secant potential, which provides a good fit for potential profiles of existing top-gated graphene structures. We show that bound states of both positive and negative energies exist in the energy spectrum and that there is a threshold value of the characteristic potential strength for which the first mode appears. Analytical solutions are presented in several limited cases and supercriticality is discussed.URCOEU FP7 ITN NOTEDEVFP7 IRSES project SPINMETFP7 IRSES project QOCaNFP7 IRSES project InterNo
Widely tunable gain-switched operation of external cavity grating-coupled surface emitting laser
Widely tunable gain switching of a grating-coupled surface-emitting laser (GCSEL) has been demonstrated in a simple external cavity configuration for the first time. Pulse duration in range of 40-100ps and wavelength tuning over 100nm have been achieved. High power, tail-free optical pulses have been observed at 980nm
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