Anomalous Crystal Shapes of Topological Crystalline Insulators

Speaker

Prof. Shuichi Murakami

Tokyo Institute of Technology, Japan       

Time

10：00am, October 31, 2023

Place

Material Science and Research Building B902

Brief 

Bio of 

the 

Speaker

Professor Shuichi Murakami received his doctoral degree from the University of Tokyo in 1999, and worked as assistant professor there until 2007. He visited Stanford University during 2000-2001. From 2007, he moved to Tokyo Institute of Technology and became a professor there in 2012. He took an important role in the study of topological materials and their exotic transport phenomena. He has finished over 100 papers with more than 15000 citations.

Abstract

A topological crystalline insulator (TCI) is a topological phase characterized by crystallographic symmetries. There exist various TCI phases depending on the crystallographic symmetries, such as mirror- symmetric TCIs and glide-symmetric TCIs [1,2]. In these TCIs, whether or not gapless topological surface states appear depends on the surface orientations. Namely, if the surface orientation is mirror/glide invariant, the corresponding gapless surface states appear. For example, in glide-symmetric TCIs, whether topological gapless surface states appear depends on the parity of the Miller index of the surface.

In this presentation, we discuss relationships between equilibrium crystal shapes and topological phases. When gapless topological surface states appear, the surface energy for the surface orientation will become higher. It makes this surface orientation less favorable, and its area will become smaller. Therefore, we expect that the equilibrium crystal shape will depend on whether the crystal is in a trivial phase or in a topological phase. By model calculation, we show that this is indeed true for various topological phases [3,4].

[1]K. Shiozaki, M. Sato, K. Gomi, Z₂ topology in nonsymmorphic crystalline insulators: Möbius twist in surface states, Phys. Rev. B 91, 155120 (2015).

[2]C. Fang, L. Fu, New classes of three-dimensional topological crystalline insulators: Nonsymmorphic and magnetic, Phys. Rev. B 91, 161105 (2015).

[3] Y. Tanaka, T. Zhang, M. Uwaha, S. Murakami, Anomalous crystal shapes of topological crystalline insulators, Phys. Rev. Lett. 129, 046802 (2022).

[4] Y. Tanaka and S. Murakami, Effects of first- and second-order topological phases on equilibrium crystal shapes, Phys. Rev. B 107, 245148 (2023).