Relativistic collapse of Landau levels of Kane fermions in crossed electric and magnetic fields

TL;DR

This paper reveals that Kane fermions in HgCdTe crystals are composed of two nested Dirac particles, and their Landau levels undergo relativistic collapse in crossed electric and magnetic fields, providing new insights into semi-relativistic effects.

Contribution

The study demonstrates that Kane fermions are two nested Dirac particles and applies Lorentz transformations to analyze their relativistic behavior in crossed fields.

Findings

Kane fermions are two nested Dirac particles.

Landau levels collapse under increasing electric field.

Relativistic decay into independent Dirac particles observed.

Abstract

Using an elegant model involving only $\Gamma_{6c}$ and $\Gamma_{8v}$ bands, massless Kane fermions were defined as the particles associated with the peculiar band structure of gapless HgCdTe crystals. Although their dispersion relation resembles that of a pseudo-spin-1 Dirac semimetal, these particles were originally considered to be hybrids of pseudospin-1 and -1/2 fermions. Here we unequivocally find that by considering an additional $\Gamma_{7c}$ conduction band inherent in HgCdTe crystals, the Kane fermions are ultimately two nested Dirac particles. This observation allows the direct application of Lorentz transformations to describe the relativistic behavior of these particles in crossed electric and magnetic fields. By studying the relativistic collapse of their Landau levels at different orientations between the crossed fields and the main crystallographic axes, we demonstrate that the Kane fermions strikingly decay into two independent Dirac particles with increasing of electric field. Our results provide new insight into semi-relativistic effects in narrow-gap semiconductors in crossed electric and magnetic fields.