Textured Exciton Insulators

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 Kekulé spiral phase observed in magic-angle bi- and trilayer graphene as a concrete realization of an ETI.

27+17 pages

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Cited by in corpus (4)

• Chern-Textured Exciton Insulators with Valley Spiral Order in Moiré Materials
• Mean-field Modelling of Moiré Materials: A User's Guide with Selected Applications to Twisted Bilayer Graphene
• Optical selection rules of topological excitons in flat bands
• Tuning between a fractional topological insulator and competing phases at ${\nu }_{\mathrm{T}}=2/3$