Unconventional excitonic insulators in two-dimensional topological materials

Abstract

Bound electron-hole pairs in semiconductors known as excitons can form a coherent state at low temperatures akin to a BCS condensate. The resulting phase is known as the excitonic insulator and has superfluid properties. Here we theoretically study the excitonic insulator in a pair of recently proposed two-dimensional candidate materials with nontrivial band topology. Contrary to previous works, we include interaction channels that violate the individual electron and hole number conservations. These are on equal footing with the number-conserving processes due to the substantial overlap of Wannier orbitals of different bands, which cannot be exponentially localized due to the nontrivial Chern numbers of the latter. Their inclusion is crucial to determine the symmetry of the electron-hole pairing, and by performing mean-field calculations at nonzero temperatures we find that the order parameter in these systems is a chiral $d$-wave. We discuss the nontrivial topology of this unconventional state and discuss some properties of the associated Berezinskii-Kosterlitz-Thouless transition. In particular, we argue that here it becomes a smooth crossover and estimate the associated temperature to lie between 50 K and 75 K on realistic substrates, over an order of magnitude larger than in the number-conserving approximation where $s$-wave pairing is favored. Our results highlight the interplay between topology at the single-particle level and long-range interactions, motivating further research in systems where both phenomena coexist.