Anomalous crystal shapes of topological crystalline insulators and higher-order topological 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 [1]. This singular surface energy of the TCI affects equilibrium crystal shapes, resulting in emergence of unique crystal facets of the TCI [1]. 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 study crystal shapes of higher-order topological insulators. We show that when a topological insulator transforms into a higher-order topological insulator by adding a magnetic field, the crystal shape changes in a peculiar way.

[1] Y. Tanaka, T. Zhang, M. Uwaha, and S. Murakami, Phys. Rev. Lett. 129, 046802 (2022).