Spinless Mirror Chern Insulator from Projective Symmetry Algebra

TL;DR

This paper demonstrates that spinless systems can host mirror Chern insulators by leveraging projective symmetry algebras modified through gauge fields, challenging the prior belief that spin-orbital coupling was necessary.

Contribution

It introduces a novel theoretical framework showing how projective symmetry algebra enables spinless MCIs using gauge fields and proposes concrete models for realization.

Findings

Spinless MCIs can be realized with gauge fields and real hopping signs.

Theoretical construction of twisted π-flux blocks for spinless MCIs.

Two explicit models suitable for artificial systems like acoustic crystals.

Abstract

It was commonly believed that a mirror Chern insulator (MCI) must require spin-orbital coupling, since time-reversal symmetry for spinless systems contradicts with the mirror Chern number. So MCI cannot be realized in spinless systems which include the large field of topological artificial crystals. Here, we disprove this common belief. The first point to clarify is that the fundamental constraint is not from spin-orbital coupling but the symmetry algebra of time reversal and mirror operations. Then, our theory is based on the conceptual transformation that the symmetry algebras will be projectively modified under gauge fields. Particularly, we show that the symmetry algebra of mirror reflection and time-reversal required for MCI can be achieved projectively in spinless systems with lattice $\mathbb{Z}_2$ gauge fields, i.e., by allowing real hopping amplitudes to take $\pm$ signs. Moreover, we propose the basic structure, the twisted $\pi$-flux blocks, to fulfill the projective symmetry algebra, and develop a general approach to construct spinless MCIs based on these building blocks. Two concrete spinless MCI models are presented, which can be readily realized in artificial systems such as acoustic crystals.