Counting Pseudo Landau Levels in Spatially Modulated Dirac Systems

TL;DR

This paper derives a simple formula to count pseudo Landau levels in Dirac systems with spatial modulation, revealing advantages of anisotropic cones and proposing experimental setups using material composition modulation.

Contribution

It provides a concise formula for counting pseudo Landau levels and demonstrates how anisotropic Dirac cones enhance their formation, with practical estimation in real materials.

Findings

Derived a simple formula for pseudo Landau level counting

Anisotropic Dirac cones favor pseudo Landau level formation

Estimated pseudo magnetic field in an antiperovskite material

Abstract

In a system with Dirac cones, spatial modulation in material parameters induces a pseudo magnetic field, which acts like an external magnetic field. Here, we derive a concise formula to count the pseudo Landau levels in the simplest setup for having a pseudo magnetic field. The formula is so concise that it is helpful in seeing the essence of the phenomenon, and in considering the experimental design for the pseudo magnetic field. Furthermore, it is revealed that anisotropic Dirac cones are advantageous in pseudo Landau level formation in general. The proposed setup is relatively easy to be realized by spatial modulation in the chemical composition, and we perform an estimation of the pseudo magnetic field in an existing material (an antiperovskite material), by following the composition dependence with the help of the ab-initio method.