Quasi-Dirac points in electron-energy spectra of crystals

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 ZrTe5 is considered. This spectrum contains a special quasi-Dirac point, similar to that in bismuth. Dirac semimetals are 3D materials where the conduction and valence bands meet at what are called Dirac points. The author shows that almost all the properties inherent in the Dirac semimetals are exhibited by a wider class of materials that need not have the gapless Dirac points.