Flux attachment theory of fractional excitonic insulators

TL;DR

Stabilizing fractional excitonic insulators (FEIs) in zero-field band-inversion systems with angular-momentum mismatch $m$ is addressed. The authors develop composite boson and composite fermion flux-attachment frameworks and show that the excitonic pairing term with angular momentum $m$ selects the flux-attachment $p=m$, locking the electron and hole fluids and producing a gapped neutral sector and a topological Hall response. They predict a Laughlin-like FEI with $\sigma_{xy}=(1/m)e^2/h$ and Jain-like sequences with $\sigma_{xy}=\left(\frac{1}{m-p}+p\right)^{-1}e^2/h$ for odd $m$, including the integer case $m=1$, with the simplest bosonic $m=2$ state yielding $\sigma_{xy}=2e^2/h$ and connections to chiral spin liquids in interacting Chern insulators. A $K$-matrix perspective is provided, linking the FEI states to known topological orders and enabling a unified description. The work offers a physically grounded route to FEIs with realistic interactions, guiding numerical and experimental exploration of FEI and CSL phases in band-inversion systems.

Abstract

The search for fractional quantized Hall phases in the absence of a magnetic field has primarily targeted flat-band systems that mimic the features of a Landau level. In an alternative approach, the fractional excitonic insulator (FEI) has been proposed as a correlated electron-hole fluid that arises near a band inversion between bands of different angular momentum with strong interactions. It remains an interesting challenge to find Hamiltonians with realistic interactions that stabilize this state. Here, we describe composite boson and composite fermion theories that highlight the importance of $(p_x+ip_y)^m$ excitonic pairing in stabilizing FEIs in a class of band inversion models. We predict a sequence of Jain-like and Laughlin-like FEI states, the simplest of which has the topological order of the bosonic $ν=1/2$ fractional quantized Hall state. We discuss implications for recent numerical studies on a chiral spin liquid phase in interacting Chern insulator models.