Anomalous Crystal Shapes of Topological Crystalline Insulators

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 firstprinciples calculations. Our results provide a basis for designs and manipulations of crystal facets by using symmetry and topology.

Automated summary

Understanding crystal shapes is essential in surface science. The discovery of topological materials has revolutionized surface science, as topological surface states can impact surface energies and crystal facets in unconventional ways. This study demonstrates that the surface energy of glide-symmetric topological crystalline insulators depends singularly on the surface orientation, resulting in unique crystal facets. Furthermore, it is shown that such singular surface states can be realized in KHgSb using first-principles calculations. These findings provide a foundation for designing and manipulating crystal facets based on symmetry and topology.