Energy Spectrum of Bloch Electrons Under Checkerboard Field Modulations

TL;DR

This paper explores how checkerboard electric and magnetic modulations affect the energy spectrum of 2D Bloch electrons in a magnetic field, revealing new symmetries and an electric-modulation induced energy gap.

Contribution

It provides a comprehensive analysis of the new spectral symmetries and discovers an electric-modulation induced energy gap independent of field strengths.

Findings

Discovery of additional spectral symmetries due to modulations

Identification of an electric-modulation induced energy gap

Relevance to experimental systems and frustrated antiferromagnetism

Abstract

Two-dimensional Bloch electrons in a uniform magnetic field exhibit complex energy spectrum. When static electric and magnetic modulations with a checkerboard pattern are superimposed on the uniform magnetic field, more structures and symmetries of the spectra are found, due to the additional adjustable parameters from the modulations. We give a comprehensive report on these new symmetries. We have also found an electric-modulation induced energy gap, whose magnitude is independent of the strength of either the uniform or the modulated magnetic field. This study is applicable to experimentally accessible systems and is related to the investigations on frustrated antiferromagnetism.