Chain of Dirac spectrum loops of nodes in crossed magnetic and electric fields

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.

Figure 1

A chain of Dirac nodes and its location in the Brillouin zone. The lines on the planes show different orientations of the nodal lines. Joining the points A(A) and B(B) by the nodal lines in a chiral-symmetric model forms a nodal net.

Figure 2

Landau damping regions for left-hand polarized waves in the case of four occupied Landau levels and $\mathrm{\Omega }\simeq 2{\mathcal{E}}_F=4.2,q\simeq 2k_F=4.2,w/E_0=0.2$.