Correlated Topological Insulators and the Fractional Magnetoelectric Effect

TL;DR

This paper introduces correlated topological insulators with fractional magnetoelectric responses, demonstrating their existence through theoretical models that feature fractional theta values and deconfined fractional excitations.

Contribution

It constructs theoretical examples of correlated topological insulators with fractional theta/pi, expanding the understanding of topological phases beyond band insulators.

Findings

Fractional theta/pi is possible in gapped, time-reversal invariant systems with fractional excitations.

Correlated bosonic topological insulators can exhibit a fractional theta value of pi/4.

Extensions to electronic fractional topological insulators are discussed.

Abstract

Topological insulators are characterized by the presence of gapless surface modes protected by time-reversal symmetry. In three space dimensions the magnetoelectric response is described in terms of a bulk theta term for the electromagnetic field. Here we construct theoretical examples of such phases that cannot be smoothly connected to any band insulator. Such correlated topological insulators admit the possibility of fractional magnetoelectric response described by fractional theta/pi. We show that fractional theta/pi is only possible in a gapped time reversal invariant system of bosons or fermions if the system also has deconfined fractional excitations and associated degenerate ground states on topologically non-trivial spaces. We illustrate this result with a concrete example of a time reversal symmetric topological insulator of correlated bosons with theta = pi/4. Extensions to electronic fractional topological insulators are briefly described.