Spin-Orbit Semimetals in the Layer Groups

TL;DR

This paper develops a general framework for predicting and characterizing spin-orbit coupled nodal semimetals within layer groups, revealing new insights into their properties and relationships to three-dimensional systems.

Contribution

It introduces a unified approach to understanding spin-orbit semimetals in layer groups, expanding predictions to two-dimensional systems built from three-dimensional sites.

Findings

Characterization of allowed semimetallic structures in layer groups.

Connection between layer group semimetals and three-dimensional systems.

Framework applicable to both existing and new nodal materials.

Abstract

Recent interest in point and line node semimetals has led to the proposal and discovery of these phenomena in numerous systems. Frequently, though, these nodal systems are described in terms of individual properties reliant on specific space group intricacies or band-tuning conditions. Restricting ourselves to cases with strong spin-orbit interaction, we develop a general framework which captures existing systems and predicts new examples of nodal materials. In many previously proposed systems, the three-dimensional nature of the space group has obscured key generalities. Therefore, we show how within our framework one can predict and characterize a diverse set of nodal phenomena even in two-dimensional systems constructed of three-dimensional sites, known as the "Layer Groups". Expanding on an existing discussion by Watanabe, Po, Vishwanath, and Zaletel of the relationship between minimal insulating filling, nonsymmorphic symmetries, and compact flat manifolds, we characterize the allowed semimetallic structures in the layer groups and draw connections to related three-dimensional systems.