Anomalous Crystal Shapes of Topological Crystalline Insulators

TL;DR

This paper reveals that topological crystalline insulators with glide symmetry exhibit unique, orientation-dependent surface energies that influence their crystal shapes, with potential for facet design using symmetry and topology.

Contribution

It demonstrates the singular dependence of surface energy on orientation in glide-symmetric TCIs and links this to unique crystal facets, supported by first-principles calculations.

Findings

Surface energy depends on surface orientation via Miller index parity.

Unique crystal facets emerge due to singular surface energy dependence.

First-principles calculations confirm the realization in KHgSb.

Abstract

Understanding crystal shapes is a fundamental subject in surface science. It is now well studied how chemical bondings determine crystal shapes via dependence of surface energies on surface orientations. Meanwhile, discoveries of topological materials have led us to a new paradigm in surface science, and one can expect that topological surface states may affect surface energies and crystal facets in an unconventional way. Here we show that the surface energy of glide-symmetric topological crystalline insulators (TCI) depends on the surface orientation in a singular way via the parity of the Miller index. This singular surface energy of the TCI affects equilibrium crystal shapes, resulting in emergence of unique crystal facets of the TCI. This singular dependence of the topological surface states is unique to the TCI protected by the glide symmetry in contrast to a TCI protected by a mirror symmetry. In addition, we show that such singular surface states of the TCI protected by the glide symmetries can be realized in KHgSb with first-principles calculations. Our results provide a basis for designs and manipulations of crystal facets by utilizing symmetry and topology.