Topological phases of nonsymmorphic crystals: Shastry-Sutherland lattice at integer filling

Abstract

Motivated by intertwined crystal symmetries and topological phases, we study the possible realization of topological insulators in nonsymmorphic crystals at integer fillings. In particular, we consider spin-orbit-coupled electronic systems of two-dimensional crystal Shastry-Sutherland lattices at integer filling where the gapless line degeneracy is protected by glide reflection symmetry. Based on a simple tight-binding model, we investigate how the topological insulating phase is stabilized by breaking nonsymmorphic symmetries but in the presence of time reversal symmetry and inversion symmetry. In addition, we also discuss the regime where Dirac semimetal is stabilized, having nontrivial ${Z}_{2}$ invariants even without spin-orbit coupling. Our study can be extended to more general cases where all lattice symmetries are broken and we also discuss possible application to topological Kondo insulators in nonsymmorphic crystals where crystal symmetries can be spontaneously broken as a function of the Kondo coupling.