Controllable Goos-H\"{a}nchen shifts and spin beam splitter for ballistic electrons in a parabolic quantum well under a uniform magnetic field

TL;DR

This paper explores how ballistic electrons in a parabolic quantum well under a magnetic field exhibit controllable Goos-H"anchen shifts, enabling a novel spin beam splitter for spintronic applications.

Contribution

It demonstrates the controllability of electron beam shifts via magnetic field and energy parameters, proposing a new spin beam splitter device based on these effects.

Findings

Goos-H"anchen shift can be positive, negative, or zero at resonances.

Shift depends on energy, incident angle, magnetic field, and Landau level.

Proposes a spintronic device utilizing these shifts for spin separation.

Abstract

The quantum Goos-H\"{a}nchen shift for ballistic electrons is investigated in a parabolic potential well under a uniform vertical magnetic field. It is found that the Goos-H\"{a}nchen shift can be negative as well as positive, and becomes zero at transmission resonances. The beam shift depends not only on the incident energy and incidence angle, but also on the magnetic field and Landau quantum number. Based on these phenomena, we propose an alternative way to realize the spin beam splitter in the proposed spintronic device, which can completely separate spin-up and spin-down electron beams by negative and positive Goos-H\"{a}nchen shifts.