Quasi-Dirac points in electron-energy spectra of crystals

TL;DR

This paper demonstrates that properties associated with Dirac points in electron spectra can also occur in materials with gapped spectra, provided a two-band model with strong spin-orbit interaction describes the vicinity of quasi-Dirac points.

Contribution

It introduces the concept of quasi-Dirac points, showing that Dirac-like properties can exist without band degeneracy, expanding the class of materials exhibiting these features.

Findings

ZrTe$_5$ spectrum contains a quasi-Dirac point similar to bismuth.

Dirac properties can occur with a noticeable gap in the spectrum.

A two-band model with strong spin-orbit interaction describes quasi-Dirac points.

Abstract

Specific properties, such as surface Fermi arcs, features of quantum oscillations and of various responses to a magnetic field, distinguish Dirac semimetals from ordinary materials. These properties are determined by Dirac points at which a contact of two electron-energy bands occurs and in the vicinity of which these bands disperse linearly in the quasimomentum. This work shows that almost the same properties are inherent in a wider class of materials in which the Dirac spectrum can have a noticeable gap comparable with the Fermi energy. In other words, the degeneracy of the bands at the point and their linear dispersion are not necessary for the existence of these properties. The only sufficient condition is the following: In the vicinity of such a quasi-Dirac point, the two close bands are well described by a two-band model that takes into account the strong spin-orbit interaction. To illustrate the results, the spectrum of ZrTe$_5$ is considered. This spectrum contains a special quasi-Dirac point, similar to that in bismuth.