Quantized Electric Multipole Insulators

TL;DR

This paper extends the Berry-phase approach to higher electric multipole moments, revealing new topological phases with protected boundary states and fractional charges, supported by nested Wilson loop invariants and feasible experimental implementations.

Contribution

It introduces a novel framework for topological quadrupole and octupole insulators using nested Wilson loops and identifies conditions for their quantization.

Findings

Topological quadrupole and octupole moments are quantized under specific conditions.

Systems exhibit gapped boundaries with lower-dimensional topological phases.

Presence of fractional charge corner states as boundary signatures.

Abstract

In this article we extend the celebrated Berry-phase formulation of electric polarization in crystals to higher electric multipole moments. We determine the necessary conditions under which, and minimal models in which, the quadrupole and octupole moments are topologically quantized electromagnetic observables. Such systems exhibit gapped boundaries that are themselves lower-dimensional topological phases. Furthermore, they manifest topologically protected corner states carrying fractional charge, i.e., fractionalization at the boundary of the boundary. To characterize these new insulating phases of matter, we introduce a new paradigm whereby `nested' Wilson loops give rise to a large number of new topological invariants that have been previously overlooked. We propose three realistic experimental implementations of this new topological behavior that can be immediately tested.