Unveiling Higher-Order Topology via Polarized Topological Charges

TL;DR

This paper introduces polarized topological charges as a new way to characterize higher-order topological phases in momentum space, enabling experimental detection in cold atomic systems and revealing phase transitions through charge dynamics.

Contribution

It proposes a novel polarized topological charge framework for HOTPs, linking topological phases to measurable charges and providing an experimental detection scheme.

Findings

Second- and third-order HOTPs are linked to specific fractions of polarized topological charges.

Topological phase transitions correspond to creation or annihilation of these charges.

The method is experimentally feasible using pseudospin measurements in cold atom systems.

Abstract

Higher-order topological phases (HOTPs) host exotic topological states that go beyond the traditional bulk-boundary correspondence. Up to now, there is still a lack of experimentally measurable momentum-space topological characterization for the HOTPs, which is not conducive to revealing the essential properties of these topological states and also restricts their detection in quantum simulation systems. Here, we propose a concept of polarized topological charges to characterize chiral-symmetric HOTPs in momentum space, which further facilitates a feasible experimental scheme to detect the HOTPs in $^{87}$Rb cold atomic system. Remarkably, our characterization theory not only shows that the second-order (third-order) topological phases are determined by a quarter (negative eighth) of the total polarized topological charges, but also reveals that the higher-order topological phase transitions are identified by the creation or annihilation of polarized topological charges. Particularly, these polarized topological charges can be measured by pseudospin structures of the systems. Due to theoretical simplicity and observational intuitiveness, this work shall advance the broad studies of the HOTPs in both theory and experiment.