$PT$ Symmetric Real Dirac Fermions and Semimetals

TL;DR

This paper introduces a theory of real Dirac points in momentum space, generalizing Weyl fermions through $PT$ symmetry, and explores their topological features and potential realizations in quantum materials and cold atom experiments.

Contribution

It develops a framework for real Dirac semimetals as real monopoles, extending topological concepts from Weyl semimetals to $PT$ symmetric systems.

Findings

Real Dirac points act as real monopoles in momentum space.

Topological features of Weyl semimetals are generalized to $PT$ symmetric Dirac semimetals.

A minimal model based on cold atom experiments and quantum materials is constructed.

Abstract

Recently Weyl fermions have attracted increasing interest in condensed matter physics due to their rich phenomenology originated from their nontrivial monopole charges. Here we present a theory of real Dirac points that can be understood as real monopoles in momentum space, serving as a real generalization of Weyl fermions with the reality being endowed by the $PT$ symmetry. The real counterparts of topological features of Weyl semimetals, such as Nielsen-Ninomiya no-go theorem, $2$D sub topological insulators and Fermi arcs, are studied in the $PT$ symmetric Dirac semimetals, and the underlying reality-dependent topological structures are discussed. In particular, we construct a minimal model of the real Dirac semimetals based on recently proposed cold atom experiments and quantum materials about $PT$ symmetric Dirac nodal line semimetals.