Abundance of second order topology in $C_3$ symmetric two-dimensional insulators

TL;DR

This study screens 71 2D materials with $C_3$ symmetry for second order topological phases, identifying 28 with obstructed atomic limits and potential for fractional corner charges, advancing understanding of 2D topological insulators.

Contribution

The paper introduces a systematic screening method for second order topology in $C_3$ symmetric 2D materials, highlighting 28 promising candidates with obstructed atomic limits.

Findings

28 out of 71 materials exhibit obstructed atomic limits.

Fractional corner charges predicted and verified in MoS$_2$ nanoflakes.

16 materials have vanishing polarization, suitable for experimental tests.

Abstract

We have screened 71 two-dimensional (2D) materials with $C_3$ symmetry for non-trivial second order topological order and find that 28 compounds exhibit an obstructed atomic limit (OAL). In the case of $C_3$ symmetry, the second order topology can be calculated from bulk symmetry indicator invariants, which predict the value of fractional corner charges in symmetry conserving nanoflakes. The procedure is exemplified by MoS$_2$ in the H-phase, which constitutes a generic example of a 2D OAL material and the predicted fractional corner charges is verified by direct calculations of nanoflakes with armchair edges. We also determine the bulk topological polarization, which always lead to gapless states at zigzag edges and thus deteriorates the concept of fractional corner charges in nanoflakes with zigzag edges that are typically more stable that armchair flakes. We then consider the case of TiCl$_2$, which has vanishing polarization as well as an OAL and we verify that the edge states of nanoflakes with zigzag edges may indeed by passivated such that the edges remain insulating and the corner charges are well defined. For the 28 OAL materials we find that 16 have vanishing polarization and these materials thus constitute a promising starting point for experimental verification of second order topology in a 2D material.