Quantum Anomalous Semimetals

TL;DR

This paper introduces a new class of topological semimetals called quantum anomalous semimetals, characterized by a half-integer topological invariant and hosting unpaired Wilson fermions, expanding the landscape of topological phases.

Contribution

It proposes the concept of quantum anomalous semimetals with half-integer topological invariants and unpaired Wilson fermions, breaking new ground in topological matter research.

Findings

Identification of a new topological phase with half-integer invariant

Realization of unpaired Wilson fermions on a lattice

Potential for exploring fractional topological charges

Abstract

The topological states of matter and topological materials have been attracting extensive interests as one of the frontier topics in condensed matter physics and materials science since the discovery of quantum Hall effect in 1980s. So far all the topological phases such as quantum Hall effect, quantum spin Hall effect and topological insulators and superconductors are characterized by a nonzero integer or Z and Z2 topological invariant. None is a half-integer or fractional. Here we propose a novel type of semimetals which hosts a single cone of Wilson fermions instead of Dirac fermions. The Wilson fermions possess linear dispersion near the energy crossing point, but breaks the chiral or parity symmetry such that an unpaired Dirac cone can be realized on a lattice. They are not prohibited by the Nielsen-Ninomiya theorem and avoid the fermion doubling problem. We find that the system can be classified by the relative homotopy group, and the topological invariant is a half-integer. We term the unexpected and nontrivial quantum phase as "quantum anomalous semimetal". The topological phase is a synergy of topology of band structure in solid and quantum anomaly in quantum field theory. The work opens the door towards exploring novel states of matter with fractional topological charge.