Purely rotational symmetry-protected topological crystalline insulator α-Bi₄Br₄

Rotational-symmetry-protected topological crystalline insulators (TCIs) are expected to host unique boundary modes, in that the surface normal to the rotational axis can feature surface states with 'unpinned' Dirac points, which are not constrained to lie on high symmetry points or lines, but can lie at any general k point in the Brillouin zone. Also, as a higher order bulk boundary correspondence is involved here, a three-dimensional (3D) TCI can support one-dimensional (1D) helical edge states. Using first-principles band structure calculations, we identify the van der Waals material-Bi₄Br₄ as a purely rotation symmetry protected TCI. We show that the surface of Bi₄Br₄ exhibits a pair of unpinned topological Dirac fermions which are related to the presence of a two-fold rotation axis. These unpinned Dirac fermions possess an exotic spin texture which will be highly favorable for spin transport, and a band structure that consists of van Hove singularities due to a Lifshitz transition. We also identify 1D topological hinge states along the edges of an-Bi₄Br₄ rod. We comment on how the predicted topological features in-Bi₄Br₄ could be accessed experimentally.