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

TL;DR

This paper explores how topological insulator phases can emerge in non-symmorphic crystals, specifically in the Shastry-Sutherland lattice, by analyzing symmetry breaking and topological invariants in spin-orbit coupled systems.

Contribution

It demonstrates the stabilization of topological insulator phases through symmetry breaking in a specific lattice model and discusses the potential for topological semimetals and Kondo insulators.

Findings

Topological insulator phases are stabilized by breaking nonsymmorphic symmetries.

Dirac semimetals with non-trivial Z2 invariants can exist without spin-orbit coupling.

Symmetry considerations are crucial for topological phases in non-symmorphic crystals.

Abstract

Motivated by intertwined crystal symmetries and topological phases, we study the possible realization of topological insulator in nonsymmorphic crystals at integer fillings. In particular, we consider spin orbit coupled electronic systems of two-dimensional crystal Shastry-Sutherland lattice 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 non trivial $Z_2$ invariants even without spin orbit coupling (SOC). 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 Kondo coupling.