Multi-band energy spectra of spin-1/2 electrons with two-dimensional magnetic modulations

TL;DR

This paper calculates the energy spectra of spin-1/2 electrons in two-dimensional magnetic modulations, revealing unique features such as a stable zero-energy level and spin degeneracy, differing from electric modulation spectra.

Contribution

It extends previous models by analyzing the spectra beyond the one-band approximation for arbitrary magnetic field distributions with rectangular lattice symmetry.

Findings

Zero-energy level remains unaffected by modulation for g factor equal to two.

All positive energy states exhibit two-fold spin degeneracy.

Spectra differ qualitatively from electric modulation counterparts.

Abstract

The energy spectra of spin-1/2 electrons under two-dimensional magnetic field modulations are calculated beyond the one-band approximation. Our formulation is generally applicable to a modulation field with a rectangular lattice symmetry. The field distribution within a plaquette is otherwise arbitrary. The spectra being obtained are qualitatively different from their electric modulated counterparts. Peculiar features of the spectra are that, for an electron with a g factor precisely being equal to two, no matter how strong the modulation is, the zero-energy level seems to be unaffected by the modulation and is separated from higher energy levels with a nonzero energy gap. Moreover, there is a two-fold degenerancy for all states with positive energies with respect to spin flip. These features agree with earlier analytical studies of the periodically magnetic modulated systems.