Triply-degenerate point in three-dimensional spinless systems

TL;DR

This paper explores the existence, symmetry protection, and physical properties of triply-degenerate points in three-dimensional spinless systems, revealing their potential for novel topological phenomena.

Contribution

It provides an exhaustive symmetry-based classification of triply-degenerate points in all 230 space groups and constructs models to describe their properties.

Findings

Triply-degenerate points can exist at high-symmetry points and paths.

Chiral TPs have Chern number ±2 and surface Fermi arcs.

Additional symmetries lead to various types of TPs with distinct dispersions.

Abstract

We study the possibility of triply-degenerate points (TPs) that can be stabilized in spinless crystalline systems. Based on an exhaustive search over all 230 space groups, we find that the spinless TPs can exist at both high-symmetry points and high-symmetry paths, and they may have either linear or quadratic dispersions. For TPs located at high-symmetry points, they all share a common minimal set of symmetries, which is the point group $T$. The TP protected solely by the $T$ group is chiral and has a Chern number of $\pm2$. By incorporating additional symmetries, this TP can evolve into chiral pseudospin-1 point, linear TP without chirality, or quadratic contact TP. For accidental TPs residing on a high-symmetry path, they are not chiral but can have either linear or quadratic dispersions in the plane normal to the path. We further construct effective $k\cdot p$ models and minimal lattice models for characterizing these TPs. Distinguished phenomena for the chiral TPs are discussed, including the extensive surface Fermi arcs and the chiral Landau bands.