Theory of competing excitonic orders in insulating WTe$_2$ monolayers

TL;DR

This paper develops a theoretical framework for excitonic phases in monolayer WTe$_2$, identifying two distinct gapped states and their dependence on electronic interactions, with implications for experimental observations.

Contribution

It introduces a Hartree-Fock based theory revealing two excitonic phases and their relation to band structure and orbital characteristics in WTe$_2$.

Findings

Identified spin density wave and spin spiral excitonic phases.

Mapped phase competition to electronic orbital structure.

Linked excitonic phases to proximity of Dirac points.

Abstract

We develop a theory of the excitonic phase recently proposed as the zero-field insulating state observed near charge neutrality in monolayer WTe$_2$. Using a Hartree-Fock approximation, we numerically identify two distinct gapped excitonic phases: a spin density wave state for weak non-zero interaction strength and spin spiral order at stronger interactions, separated by a narrow window of non-excitonic quantum spin Hall insulator. We introduce a simplified model capturing key features of the WTe$_2$ band structure, in which these phases appear as distinct valley ferromagnetic orders. We link the competition between the excitonic phases to the orbital structure of electronic wavefunctions at the Fermi surface and hence its proximity to the underlying gapped Dirac point in WTe$_2$. We briefly discuss collective modes of the two excitonic states, and comment on implications for experiments.