Observation of Klein bottle quadrupole topological insulators in electric circuits

TL;DR

This paper reports the experimental realization of Klein bottle quadrupole topological insulators in electric circuits, revealing how nonsymmorphic symmetries influence topological phases and corner states.

Contribution

It demonstrates the first observation of Klein bottle topological insulators in circuit systems, linking theoretical predictions with experimental validation.

Findings

Experimental confirmation of Klein bottle topological phases in circuits

Symmetry properties affect corner state distributions

Practical realization of exotic topological configurations

Abstract

The Klein bottle Benalcazar-Bernevig-Hughes (BBH) insulator phase plays a pivotal role in understanding higher-order topological phases. The insulator phase is characterized by a unique feature: a nonsymmorphic glide symmetry that exists within momentum space, rather than real space. This characteristic transforms the Brillouin zone's fundamental domain into a structure of Klein bottle. Here, we report an observation of a Klein bottle topoelectrical model under gauge fields. To provide a comprehensive understanding of the different corner distributions of odd and even unit cells, we present theoretical calculations and demonstrate that the symmetry properties significantly affect the topological nature. These theoretical predictions are confirmed by experimental results, which demonstrate the practical feasibility of such topological configurations in electronic circuits. Our work establishes a vital connection between the realms of condensed matter physics and circuit systems, thereby paving a pathway for investigating exotic condensed matter physics.