Topological hinge modes in Dirac semimetals

TL;DR

This paper explores the boundary and hinge modes in Dirac semimetals, emphasizing the importance of cubic terms in models, and demonstrates their presence in $eta$-CuI through first-principles calculations, including effects of magnetic symmetry breaking.

Contribution

It introduces the necessity of including $k$-cubic terms in effective models to accurately describe boundary modes and demonstrates topological hinge modes in $eta$-CuI with potential experimental implications.

Findings

Cubic terms drive evolution from nodal line to nodal point surface degeneracy.

Hinge modes are clearly exhibited in $eta$-CuI via first-principles calculations.

Breaking time-reversal symmetry can expose hinge modes by gapping surface bands.

Abstract

Dirac semimetals (DSMs) are an important class of topological states of matter. Here, focusing on DSMs of band inversion type, we investigate their boundary modes from the effective model perspective. We show that in order to properly capture the boundary modes, $k$-cubic terms must be included in the effective model, which would drive an evolution of surface degeneracy manifold from a nodal line to a nodal point. Using first-principles calculations, we demonstrate that this feature and the topological hinge modes can be clearly exhibited in $\beta$-CuI. We further extend the discussion to magnetic DSMs and show that the time-reversal symmetry breaking can gap out the surface bands and hence help to expose the hinge modes in the spectrum, which could be beneficial for the experimental detection of hinge modes.