Electronic structure of three‐dimensional triangular torus‐shaped quantum rings under external magnetic fields

Abstract

In this paper, we calculate the electron -hole energy states and the magnetization for InAs/GaAs triangular torus-shaped (TTS) quantum rings in a magnetic field. Our three-dimensional (3D) model considers (i) the effective one-band Hamiltonian approximation, (ii) the position-and energy-dependent quasi-particle effective mass approximation, (iii) the finite hard wall confinement potential, and (iv) the Ben DanielDuke boundary conditions. This model is solved numerically with the nonlinear iterative method to obtain the "self-consistent" solutions. We investigate the electron-hole energy spectra versus magnetic field for two different ring widths: R 0 = 20 and 50 nm, and find that they strongly depend on the ring shape and size. Since the magnetic field penetrates into the inside region of the nonsimply connected ring, the electron (hole) transition energy between the lowest states versus magnetic field oscillates nonperiodically and is different from that of quantum dots. We find the magnetization at zero temperature is a negative function, saturates, and oscillates nonperiodically when the magnetic field increases.1 Introduction Based on the advanced semiconductor technology, nanoscale systems including quantum rings can be fabricated with a wide range of geometries. The ring shape can be viewed as a triangular cross section with the typical ring widths: 20 and 50 nm. The TTS ring height is about 2 nm and inner radius varies in the 10 nm regime, respectively (see [1] and references therein). For semiconductor nanoscale rings, it is necessary to explore their magnetic properties for device and spintronics applications [2]. Various models for studying electronic structures of rings have been proposed; unfortunately, these models did not systematically consider the ring (inner and outer) radius effect, the finite hard wall confinement potential, and nonparabolic band approximation for electron effective mass. To the best of our knowledge, the study of magnetization for 3D nanoscale rings has never been done yet.In this paper, we study the electron and hole energy states and magnetization for 3D nanoscale quantum rings. Figure 1 shows the studied TTS ring that is from an experimental formation of quantum rings [1]. The calculations are performed for 3D models of InAs/GaAs quantum rings with the finite hard wall confinement potential. We use the effective 3D one-band Hamiltonian, the energy-(non-parabolic approximation) and position-dependent quasi-particle effective mass approximation, and the Ben DanielDuke boundary conditions. The simulation of the above 3D model applies the nonlinear iterative method [3] to compute the self-consistent solutions. In the 1D approach, varying the magnetic field strength B only changes the phase of the electronic wave function, resulting in periodic oscillations in the magnetization (the Aharonov-Bohm effect). In the 2D confinement parabolic potential approach, the effects of

Aharonov-Bohm Effect in Quantum Nanocups

“…In the last years the Aharonov-Bohm (AB) effect had been studied theoretical [1,2,3] and experimentally [4,5,6] in single and double quantum ring, and type II quantum dots. Theoretical reports [1,2] show that the electron energy levels in a nonuniform quantum ring have a different structure than an uniform with applied magnetic field.…”