Relativistic Wigner functions in transition metal dichalcogenides

Abstract

The Wigner function has been proven useful in many studies of transport as well as quantum coherence in experimental situations. When we deal with Dirac bands, this function becomes a matrix function. Here, we study the Wigner matrix for a situation in a transition metal dichacogenides with a dominant spin–orbit interaction. Here, we discuss $$\hbox {WS}_{2}$$ , where the bands can be described with the Dirac equation, and a unique spin-valley coupling arises. This leads to a 2X2 Wigner matrix for either the conduction band or the valence band. The off-diagonal elements display interference phenomena from the two diagonal components.