Monte-Carlo study of Dirac semimetals phase diagram

TL;DR

This study uses lattice Monte-Carlo simulations to explore the phase diagram of Dirac semimetals, focusing on the transition caused by chiral symmetry breaking and how anisotropy affects the critical coupling for this transition.

Contribution

It provides the first numerical determination of the critical coupling constants for Dirac semimetals with varying Fermi velocity anisotropy, proposing a tentative phase diagram.

Findings

Na3Bi and Cd3As2 are predicted to be in the insulating region of the phase diagram.

Screening effects likely play a significant role in real materials, similar to graphene.

The phase diagram indicates a strong dependence on anisotropy and Coulomb interaction.

Abstract

In this paper the phase diagram of Dirac semimetals is studied within lattice Monte-Carlo simulation. In particular, we concentrate on the dynamical chiral symmetry breaking which results in semimetal/insulator transition. Using numerical simulation we determined the values of the critical coupling constant of the semimetal/insulator transition for different values of the anisotropy of the Fermi velocity. This measurement allowed us to draw tentative phase diagram for Dirac semimetals. It turns out that within the Dirac model with Coulomb interaction both Na$_3$Bi and Cd$_3$As$_2$ known experimentally to be Dirac semimetals would lie deeply in the insulating region of the phase diagram. It probably shows a decisive role of screening of the interelectron interaction in real materials, similar to the situation in graphene.