Abstract
New semimetal systems along with Dirac and Weyl semimetals contain compounds, in which the energy of electron excitations vanishes not at nodes but on lines. A higher dimension of the degeneracy space changes many physical properties. We consider a chain of loops consisting of Dirac spectrum nodes in nonsymmorphic crystalline compounds placed in external mutually perpendicular magnetic and electric fields. An exact solution for the spectrum is obtained under the assumption of particle-hole symmetry. An analysis of this spectrum shows the existence of a line of critical values of the magnetic and electric fields, at which a quantum phase transition to a gapless state occurs. The use of the obtained spectrum allows also predicting a number of new oscillation and resonance effects in the field of magneto-optical phenomena.
Highlights
We consider a chain of loops consisting of Dirac spectrum nodes in nonsymmorphic crystalline compounds placed in external mutually perpendicular magnetic and electric fields
The degeneracy spaces of the electron energy spectrum in crystals, in which the valence band touches the conduction band, can be points [1,2] or lines and, in some high-dimensional cases, surfaces [3]
Since discovery of Dirac electron spectrum in graphene, and in topological insulators, where the degeneracy space consists the nodes, the study of new electron phase states focuses on the three-dimensional case in Dirac and Weyl semimetals
Summary
The degeneracy spaces of the electron energy spectrum in crystals, in which the valence band touches the conduction band, can be points [1,2] or lines and, in some high-dimensional cases, surfaces [3]. Since discovery of Dirac electron spectrum in graphene, and in topological insulators, where the degeneracy space consists the nodes, the study of new electron phase states focuses on the three-dimensional case in Dirac and Weyl semimetals. In the case of nonsymmorphic symmetry [20,21,22,24,25,27,28,29,30], the lines of nodes occur in different mutually perpendicular highly symmetric planes These lines touch each other at points of highly symmetric axes and form a chain of double-degenerate states spreading across the entire Brillouin zone (see Fig. 1). We will examine the case of mutually perpendicular magnetic and electric fields
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