Landau level collapse in graphene in the presence of in-plane radial electric and perpendicular magnetic fields

TL;DR

This paper investigates the collapse of Landau levels in graphene under a radial in-plane electric field and perpendicular magnetic field, revealing how the phenomenon depends on angular momentum and the presence of a gap.

Contribution

It introduces a study of Landau level collapse in graphene with a radial electric field, using numerical methods due to the lack of analytical solutions, and compares gapped and gapless cases.

Findings

Landau levels collapse at specific electric field values depending on angular momentum.

Collapse occurs for positive angular momentum quantum numbers.

Gapped graphene shows distinctive features compared to gapless graphene.

Abstract

It is known that in two-dimensional relativistic Dirac systems placed in orthogonal uniform magnetic and electric fields, the Landau levels collapse as the applied in-plane electric field reaches a critical value $\pm E_c$. We study this phenomenon for a distinct field configuration with in-plane constant radial electric field. The Dirac equation for this configuration does not allow analytical solutions in terms of known special functions. The results are obtained by using both the WKB approximation and the exact diagonalization and shooting methods. It is shown that the collapse occurs for positive values of the total angular momentum quantum number, the hole (electron)-like Landau levels collapse as the electric field reaches the value $ +(-) E_c/2$. The investigation of the Landau level collapse in the case of gapped graphene shows a number of distinctive features in comparison with the gapless case.