Understanding crystal shapes is a fundamental subject in surface science. It is now well-studied how chemical bondings determine crystal shapes via the 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.

In this talk, 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 the emergence of unique crystal facets of the TCI [1]. Furthermore, we study the equilibrium crystal shapes of a topological insulator (TI), a TCI protected by mirror symmetry, and a second-order topological insulator (SOTI) protected by inversion symmetry. In terms of the calculations of the simple tight-binding model, we show that the various boundary states of the TI, TCI, and SOTI affect the emergence of the specific facets [2].

Reference
[1] Y. Tanaka, T. Zhang, M. Uwaha, and S. Murakami, Phys. Rev. Lett. 129, 046802 (2022).
[2] Y. Tanaka and S. Murakami, Phys. Rev. B 107, 245148 (2023).

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