Prediction of at topological $p+ip$ excitonic insulator with parity anomaly

TL;DR

This paper predicts a novel topological excitonic insulator with $p+ip$ symmetry exhibiting parity anomaly, fractionalized excitations, and spontaneous magnetization, potentially realizable on topological insulator surfaces via optical pumping.

Contribution

It introduces a new $p+ip$ topological excitonic insulator state with parity anomaly and associated topological properties, expanding the understanding of excitonic phases.

Findings

Proposes a $p+ip$ excitonic insulator with parity anomaly.

Identifies fractionalized excitations with e/2 charge.

Suggests realization on topological insulator surfaces.

Abstract

Excitonic insulators are insulating states formed by the coherent condensation of electron and hole pairs into BCS-like states. Isotropic spatial wave functions are commonly considered for excitonic condensates since the attractive interaction among the electrons and the holes in semiconductors usually leads to $s$-wave excitons. Here, we propose a new type of excitonic insulator that exhibits order parameter with $p+ip$ symmetry and is characterized by a chiral Chern number $C_\textrm{c}=1/2$. This state displays the parity anomaly, which results in two novel topological properties: fractionalized excitations with $\textrm{e}/2$ charge at defects and a spontaneous in-plane magnetization. The topological insulator surface state is a promising platform to realize the topological excitonic insulator. With the spin-momentum locking, the interband optical pumping can renormalize the surface electrons and drive the system towards the proposed $p+ip$ instability.