Minimal models for topological Weyl semimetals

Abstract

Topological Weyl semimetals (TWS) can be classified as type I TWS, in which the density of states vanishes at the Weyl nodes, and type II TWS, in which an electron pocket and a hole pocket meet at a singular point of momentum space, allowing for distinct topological properties. We consider various minimal lattice models for type II TWS. The simplest time-reversal-breaking band structure, with a pair of Weyl nodes sharing a single electron pocket and a single hole pocket (hydrogen model), exhibits relics of surface Fermi arc states only away from the Fermi energy, with no topological protection. Topologically protected Fermi arcs can be restored by an additional term (hydrogen model) that produces a bulk structure where the electron and hole pockets of each Weyl point are disjoint. In time-reversal-symmetric but inversion-breaking models, we identify nontopological surface track states that arise out of the topological Fermi arc states at the transition from type I to type II and persist in the type II TWS. The distinctions among these minimal models can aid in distinguishing between generic and model-dependent behavior in studies of superconductivity, magnetism, and quantum oscillations of type II Weyl semimetals.