Time dependent simulations of electron transport through a quantum ring: effect of the Lorentz force

TL;DR

This paper investigates how the Lorentz force influences electron transport and Aharonov-Bohm oscillations in a quantum ring under a magnetic field, revealing effects on oscillation amplitude and phase shifts due to scattering and cavity tuning.

Contribution

It provides a detailed time-dependent simulation of electron behavior in quantum rings, highlighting the Lorentz force's role in modifying interference patterns and transport properties.

Findings

Lorentz force decreases oscillation amplitude when the ring is transparent at zero field.

Lorentz force can enhance transport in backscattering regimes, increasing oscillation amplitude.

Elastic scattering with a cavity can induce a π phase shift or half-flux quantum oscillations.

Abstract

The time dependent Schr\"odinger equation for an electron passing through a semiconductor quantum ring of nonzero width is solved in the presence of a perpendicular homogenous magnetic field. We study the effects of the Lorentz force on the Aharonov-Bohm oscillations. Within the range of incident momentum for which the ring is transparent at zero magnetic field, the Lorentz force leads to a decrease of the oscillation amplitude, due to the asymmetry in the electron injection in the two arms of the ring. For structures in which the fast electrons are predominantly backscattered, the Lorentz force assists in the transport producing an initial increase of the corresponding oscillation amplitude. Furthermore, we discuss the effect of elastic scattering on a potential cavity within one of the arms of the ring. For the cavity tuned to shift maximally the phase of the maximum of the wave packet we observe a $\pi$ shift of the Aharonov-Bohm oscillations. For other cavity depths the oscillations with a period of half of the flux quantum are observed.