Anyon exciton revisited: Exact solutions for a few-particle system

Copyright © 2003 The American Physical SocietyThe anyon exciton model is generalized to the case of a neutral exciton consisting of a valence hole and an arbitrary number N of fractionally charged quasielectrons (anyons). A complete set of exciton basis functions is obtained and these functions are classified using a result from the theory of partitions. Expressions are derived for the interparticle interaction matrix elements of a six-particle system (N=5), which describes an exciton against the background of an incompressible quantum liquid with filling factor ν=2/5. Several exact results are obtained in a boson approximation, including the binding energy of a (N+1)-particle exciton with zero in-plane momentum and zero internal angular momentum

Anyon exciton revisited

15th International Conference on High Magnetic Fields in Semiconductor Physics, Oxford, UK, 5 - 9 August 2002We review the main results of the anyon exciton model in light of recent criticism by Wojs and Quinn. We show that the appearance of fractionally charged anyon ions at the bottom of their numerically calculated excitation spectra is an artefact caused by finite-size effects in a spherical geometry

Exactly-solvable problems for two-dimensional excitons

Mathematical Physics Frontiers (editor: Charles V. Benton)Copyright © 2004 Nova Science PublishersSeveral 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 quantizing 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 quasi-electrons 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

Spin-orbit terms in multi-subband electron systems: A bridge between bulk and two-dimensional Hamiltonians

This a preprint of the materials accepted for publication in Semiconductors Copyright © 2008 SP MAIK Nauka/Interperiodica / SpringerWe analyze the spin-orbit terms in multi-subband quasi-two-dimensional electron systems, and how they descend from the bulk Hamiltonian of the conduction band. Measurements of spin-orbit terms in one subband alone are shown to give incomplete information on the spin-orbit Hamiltonian of the system. They should be complemented by measurements of inter-subband spin-orbit matrix elements. Tuning electron energy levels with a quantizing magnetic field is proposed as an experimental approach to this problem

Variable-phase method and Levinson's theorem in two dimensions: Application to a screened Coulomb potential

Copyright © 1997 Elsevier. NOTICE: this is the pre-print version of a work that was accepted for publication in Solid State Communications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Solid State Communications Volume 103, Issue 6, pp. 325–329 (1997). DOI: 10.1016/S0038-1098(97)00203-2The variable-phase approach is applied to scattering and bound states in an attractive Coulomb potential, statically screened by a two-dimensional (2D) electron gas. A 2D formulation of Levinson's theorem is used for bound-state counting and a hitherto undiscovered, simple relationship between the screening length and the number of bound states is found. As the screening length is increased, sets of bound states with differing quantum numbers appear degenerately. (C) 1997 Elsevier Science Ltd

Use of the Faraday optical transformer for ultrafast magnetization reversal of nanomagnets

Copyright 2007 Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.We propose a new strategy for ultrafast magnetization reversal of nanomagnets. Due to the Inverse Faraday Effect, circularly polarized optical pulses induce a pulsed magnetic flux in materials with large magneto-optical susceptibility. Alternatively, intense optical pulses can induce a pulsed magnetic flux by means of ultrafast demagnetization of a metallic thin film or multilayer with a perpendicular magnetic anisotropy. The time varying magnetic flux induces a transient electro-motive force and electric current in a conducting loop on the surface of the illuminated material, and hence a transient magnetic field. The magnetic field pulses due to the transient current appear to be too short for use in the magnetic field or spin-current induced precessional switching of magnetization. However, our calculations suggest that the magnetic field could lead to ultrafast switching of a nanomagnet overlaid on the surface of the conductor and demagnetized by the same optical pulse. In the case of magnetic pulses due to the Inverse Faraday Effect, the switching direction could be controlled by the helicity of the optical pulse

Probing two-subband systems in a quantizing magnetic field with non-equilibrium phonons

ICPS-26: 26th International Conferences on Physics of Semiconductors, Edinburgh, Scotland, 29 July - 2 August 2002We propose to use phonon absorption spectroscopy to study many-body gaps and phases of two-subband heterostructures in the quantum Hall regime. Implications of the spin-orbit interaction for phonon absorption in this system are considered

Momentum alignment and spin orientation of photoexcited electrons in quantum wells

PublishedThe momentum and spin distribution functions for electrons excited by polarized light incident normally to the heterostructure plane are determined for a quantum well with infinitely high walls. It is shown that for a low ratio of the light and heavy hole masses, an anomalously rapid growth of momentum alignment and a decrease of electron spin orientation occur with increase of their energy of motion in the plane of the well. The dependences on the exciting photon energy of the plane and circular polarizations of the hot luminescence in the pumping direction at it shortwave edge are found

Searching for confined modes in graphene channels: The variable phase method

Copyright © 2012 American Physical SocietyUsing the variable phase method, we reformulate the Dirac equation governing the charge carriers in graphene into a nonlinear first-order differential equation from which we can treat both confined-state problems in electron waveguides and above-barrier scattering problems for arbitrary-shaped potential barriers and wells, decaying at large distances. We show that this method agrees with a known analytic result for a hyperbolic secant potential and go on to investigate the nature of more experimentally realizable electron waveguides, showing that when the Fermi energy is set at the Dirac point, truly confined states are supported in pristine graphene. In contrast to exponentially decaying potentials, we discover that the threshold potential strength at which the first confined state appears is vanishingly small for potentials decaying at large distances as a power law; but nonetheless, further confined states are formed when the strength and spread of the potential reach a certain threshold.Millhayes Foundation (DAS)Engineering and Physical Sciences Research Council: EPSRC (CAD)EU FP7 ITN SpinoptronicsFP7 IRSES project SPINMETFP7 IRSES project TerACaNFP7 IRSES project ROBOCO

Smooth electron waveguides in graphene

Copyright © 2010 American Physical SocietyWe present exact analytical solutions for the zero-energy modes of two-dimensional massless Dirac fermions fully confined within a smooth one-dimensional potential V(x)=−α/cosh(βx), which provides a good fit for potential profiles of existing top-gated graphene structures. We show that there is a threshold value of the characteristic potential strength α/β for which the first mode appears, in striking contrast to the nonrelativistic case. A simple relationship between the characteristic strength and the number of modes within the potential is found. An experimental setup is proposed for the observation of these modes. The proposed geometry could be utilized in future graphene-based devices with high on/off current ratios