An exactly solvable model for a strongly spin-orbit-coupled nanowire quantum dot

TL;DR

This paper introduces an analytical method to exactly solve a one-dimensional quantum dot model with strong spin-orbit coupling and magnetic field, revealing unique effects like g-factor anisotropy and tunability.

Contribution

The authors develop an exact analytical solution for a strongly spin-orbit-coupled quantum dot, enabling precise analysis of its eigenenergies and eigenstates.

Findings

Demonstration of anisotropic electron g-factor

Tunability of g-factor with magnetic field

Exact eigenstates and eigenenergies obtained

Abstract

In the presence of spin-orbit coupling, quantum models for semiconductor materials are generally not exactly solvable. As a result, understanding of the strong spin-orbit coupling effects in these systems remains poor. Here we develop an analytical method to solve the one-dimensional hard-wall quantum dot problem in the presence of strong spin-orbit coupling and magnetic field, which allows us to obtain exact eigenenergies and eigenstates of a single electron. With the help of the exact solution, we demonstrate some unique effects from the strong spin-orbit coupling in a semiconductor quantum dot, in particular the anisotropy of the electron g-factor and its tunability.