Magnetic field effects on quantum ring excitons

Abstract

We study the effect of magnetic field and geometric confinement on excitons confined to a quantum ring. We use analytical matrix elements of the Coulomb interaction and diagonalize numerically the effective-mass Hamiltonian of the problem. To explore the role of different boundary conditions, we investigate the quantum ring structure with a parabolic confinement potential, which allows the wavefunctions to be expressed in terms of center of mass and relative degrees of freedom of the exciton. On the other hand, wavefunctions expressed in terms of Bessel functions for electron and hole are used for a hard-wall confinement potential. The binding energy and electron-hole separation of the exciton are calculated as function of the width of the ring and the strength of a external magnetic field. The linear optical susceptibility as a function of magnetic fields is also discussed. We explore the Coulomb electron-hole correlation and magnetic confinement for several ring width and size combinations. The Aharanov-Bohm oscillations of exciton characteristics predicted for one-dimensional rings are found to not be present in these 1 finite-width systems.

Electric and magnetic field effects on the excitonic properties of elliptic core–multishell quantum wires

“…As a matter of fact, these more accurate procedures were used in the literature mostly for circularly symmetric problems, where one can take advantage of the system symmetry to reduce the number of coordinates, or to (semi-)analytically solve for the single-particle eigenstates. [16,31] Conversely, our case requires Cartesian coordinates, which allows us to investigate elliptic shells, in-plane electric fields, and systems with arbitrary shell geometry, by paying the price of having more coordinates to deal with. Thus, the main idea of the present model is to circumvent this problem by using a much simpler approach, which, in summary, consists in (i) assuming, as an approximation, that one can separate the variables, (ii) solving for the single-particles separately, and then (iii) minimizing the exciton energy as a whole by a variational procedure.…”

“…[15] As the exciton has neutral net charge, it is not supposed to be affected by electric/magnetic fields a priori. [16] However, electric fields naturally separate electrons and holes wavefunctions, due to their opposite charges, creating regions of non-neutral net charge and affecting the exciton binding energy, [17] through the so-called quantum confined Stark effect (QCSE). Our results show how the carriers energy spectra and exciton binding energy are affected by an applied electric field perpendicular to the wire axis, considering different in-plane directions, which can be used to obtain information about the eccentricity of the wire and its direction of distortion.…”

Donor-bound electrons in quantum rings under magnetic fields

“…Parabolic confining potentials are amenable of analytical calculations since the center-ofmass motion of excitons can be separated from the relative electron-hole motion. 5,6 In contrast, band-edge offsets give rise to the confining potential in QRs based on semiconductor heterostructures. 7 In this case, calculation of the effects of the Coulomb interaction is more complex.…”

Excitons in quantum-ring structures in a magnetic field: optical properties and persistent currents

“…The growth of ring-shaped semiconductor quantum dots with nm-scale radii has triggered much interest in the theoretical and experimental investigation of their electronic and optical properties [1][2][3][4][5]. Here we consider the effect of static high magnetic fields on the optical spectra of excitons confined in semiconductor quantum rings.…”

“…This Aharonov-Bohm (AB) effect for a neutral exciton occurs due to electron-to-hole tunneling around the ring [3]. However, the amplitude of the predicted AB oscillations in the exciton binding energy is very sensitive to a finite width of a quantum ring [4] and includes an exponentially-small tunneling amplitude. Here, we describe a different magnetic interference effect, which relates to the polarized exciton in a quantum ring with a finite width and does not include an exponentially-small tunneling factor.…”