Brillouin Klein bottle from artificial gauge fields.

ABSTRACT: A Brillouin zone is the unit for the momentum space of a crystal. It is topologically a torus, and distinguishing whether a set of wave functions over the Brillouin torus can be smoothly deformed to another leads to the classification of various topological states of matter. Here, we show that under [Formula: see text] gauge fields, i.e., hopping amplitudes with phases ±1, the fundamental domain of momentum space can assume the topology of a Klein bottle. This drastic change of the Brillouin zone theory is due to the projective symmetry algebra enforced by the gauge field. Remarkably, the non-orientability of the Brillouin Klein bottle corresponds to the topological classification by a [Formula: see text] invariant, in contrast to the Chern number valued in [Formula: see text] for the usua

SUBMITTER: Chen ZY 

PROVIDER: S-EPMC9038716 | biostudies-literature | 2022 Apr

REPOSITORIES: biostudies-literature