Influence of electric field on the quantum oscillations in the Weyl semimetals

Investigation of Weyl semimetals (WSMs) is one of the most important and hot topics of modern condensed matter physics. In this paper, we investigated the Landau band and quantum oscillations in the WSMs under crossed magnetic and electric fields (CMEFs). We obtained an expression for the energy spectrum of such system using an algebraic and quasi-classical approaches. We have shown that the electric field leads to a cardinal change the Landau bands. When an electric field is equal to u(F)H/c, the collapse of the Landau levels occurs, and the motion becomes completely linear. It will lead to fundamental change of the character of the surface states, called the Fermi arcs. The electric field influences on the character of the quantum oscillations. The density of states has a singularity at E = u(F)H/c. We have shown that such a result is due to the continuous model. In the lattice model this singularity disappears. Finally, we investigated the density of states of tilted WSMs. We shown that the phase transition between I and II phases of WSM can be induced by electric field.