Multiplicative Chern insulator

TL;DR

This paper introduces multiplicative Chern insulators (MCIs) as a new class of topological phases, exploring their properties, responses, and transitions, including 2D and 3D cases, and their relation to fractional quantum Hall states.

Contribution

The paper constructs and analyzes 2D and 3D multiplicative Chern insulators as tensor products of Chern insulators, revealing novel topological responses and phase evolutions.

Findings

Observation of a 4π Aharonov-Bohm effect in 2D MCIs

Evidence of quantized topological invariant to a rational number

Adiabatic evolution into a topological skyrmion phase under symmetry-breaking perturbations

Abstract

We study multiplicative Chern insulators (MCIs) as canonical examples of multiplicative topological phases of matter. Constructing the MCI Bloch Hamiltonian as a symmetry-protected tensor product of two topologically non-trivial parent Chern insulators (CIs), we study two-dimensional (2D) MCIs and introduce 3D mixed MCIs, constructed by requiring the two 2D parent Hamiltonians share only one momentum component. We study the 2D MCI response to time reversal symmetric flux insertion, observing a $4\pi$ Aharonov-Bohm effect, relating these topological states to fractional quantum Hall states via the effective field theory of the quantum skyrmion Hall effect. As part of this response, we observe evidence of quantisation of a proposed topological invariant for compactified many-body states, to a rational number, suggesting higher-dimensional topology may also be relevant. Finally, we study effects of bulk perturbations breaking the symmetry-protected tensor product structure of the child Hamiltonian, finding the MCI evolves adiabatically into a topological skyrmion phase.