Textured Exciton Insulators

TL;DR

This paper introduces textured exciton insulators, a new class of topological states arising from spontaneous symmetry breaking and topological obstructions, with potential realization in twisted graphene systems.

Contribution

It proposes the concept of textured exciton insulators supported by explicit models and field theories, linking them to observable phases in twisted bilayer graphene.

Findings

Explicit models of Chern and Euler texture insulators constructed

Demonstrated that textured exciton insulators are competitive ground states

Identified incommensurate Kekulé spiral phase as a realization in graphene

Abstract

We introduce and study new interacting topological states that arise in time-reversal symmetric bands with an underlying obstruction to forming localized states. If the $U(1)$ valley symmetry linked to independent charge conservation in each time-reversal sector is spontaneously broken, the corresponding `excitonic' order parameter is forced to form a topologically non-trivial texture across the Brillouin zone. We show that the resulting phase, which we dub a textured exciton insulator, cannot be given a local-moment description due to a form of delicate topology. Using toy models of bands with Chern or Euler obstructions to localization we construct explicit examples of the Chern or Euler texture insulators (CTIs or ETIs) they support, and demonstrate that these are generically competitive ground states at intermediate coupling. We construct field theories that capture the response properties of these new states. Finally, we identify the incommensurate Kekul\'e spiral phase observed in magic-angle bi- and trilayer graphene as a concrete realization of an ETI.