Topological crystalline insulator: from symmetry indicators to material discovery

Topological crystalline insulators (TCIs) are insulating electronic phases of matter in which the nontrivial topology is driven by crystalline symmetries. Recent theoretical advances have proposed new rotational-symmetry-protected TCI states that are expected to show unique topologically protected boundary modes. The surface normal to the rotational axis in these TCIs features ''unpinned'' Dirac surface states whose Dirac points are located at generic k points. Also, due to the ''higher-order'' bulk-boundary correspondence, such a 3D TCI supports 1D helical edge states. However, to date, rotational-symmetry-protected TCIs have remained elusive in real materials. We systematically examine the topological properties of the TCI states in Ca₂As. On both the top and side surfaces, we show the presence of topological surface states protected independently by rotational and mirror symmetries [1]. We also discuss the van der Waals material α-Bi₄Br₄ and the pristine bulk bismuth and show that these materials harbor TCI states protected purely by rotation symmetry [2,3], even though these materials have been long thought to be topologically trivial.

[1] Phys. Rev. B, 98, 241104(R) (2018).
[2] 2D Materials 6, 031004 (2019).
[3] PNAS 116, 13255 (2019).