Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states

TL;DR

This paper introduces a novel Z2 topological phase in nonsymmorphic crystalline insulators that is protected solely by unitary symmetries, featuring surface states with a Mobius twist, expanding the understanding of topological matter.

Contribution

It demonstrates the existence of Z2 topological phases protected by nonsymmorphic symmetries without anti-unitary symmetry, with explicit constructions and surface state analysis.

Findings

Z2 phases exist without anti-unitary symmetry

Surface states exhibit Mobius twist dispersion

Topological phases are constructed across multiple dimensions

Abstract

It has been known that an anti-unitary symmetry such as time-reversal or charge conjugation is needed to realize Z2 topological phases in non-interacting systems. Topological insulators and superconducting nanowires are representative examples of such Z2 topological matters. Here we report the first-known Z2 topological phase protected by only unitary symmetries. We show that the presence of a nonsymmorphic space group symmetry opens a possibility to realize Z2 topological phases without assuming any anti-unitary symmetry. The Z2 topological phases are constructed in various dimensions, which are closely related to each other by Hamiltonian mapping. In two and three dimensions, the Z2 phases have a surface consistent with the nonsymmorphic space group symmetry, and thus they support topological gapless surface states. Remarkably, the surface states have a unique energy dispersion with the Mobius twist, which identifies the Z2 phases experimentally. We also provide the relevant structure in the K-theory.