Topological insulating phases from two-dimensional nodal loop semimetals

TL;DR

This paper explores how chiral mass gaps in 2D nodal loop semimetals induce topological insulating phases, analyzing their topological properties, phase transitions, and responses to magnetic fields.

Contribution

It introduces a minimal lattice model for 2D nodal loop semimetals with chiral mass gaps and generalizes an index for topological transitions.

Findings

Chern number equals the phase winding number of the mass gap

Topological phases exhibit distinct edge states in ribbon geometries

Responses to magnetic fields vary between weak and strong regimes

Abstract

Starting from a minimal model for a 2D nodal loop semimetal, we study the effect of chiral mass gap terms. The resulting Dirac loop anomalous Hall insulator's Chern number is the phase winding number of the mass gap terms on the loop. We provide simple lattice models, analyze the topological phases and generalize a previous index characterizing topological transitions. The responses of the Dirac loop anomalous Hall and quantum spin Hall insulators to a magnetic field's vector potential are also studied both in weak and strong field regimes, as well as the edge states in a ribbon geometry.