Fractional Excitonic Insulator

TL;DR

This paper proposes a new fractional excitonic insulator phase in electron-hole systems, introducing a wavefunction and theoretical framework that generalizes Laughlin states to zero magnetic field, with potential realization in engineered materials.

Contribution

It introduces a fractional excitonic insulator phase, develops a wavefunction and mean field theory, and proposes physical conditions for realization in materials.

Findings

Exact ground state for m=1 case in a free fermion model.

Wavefunction describes fractional excitonic insulator for m>1.

Potential realization in systems with band crossings differing by 3 in angular momentum.

Abstract

We argue that a correlated fluid of electrons and holes can exhibit a fractional quantum Hall effect at zero magnetic field analogous to the Laughlin state at filling $1/m$. We introduce a variant of the Laughlin wavefunction for electrons and holes and show that for $m=1$ it is the exact ground state of a free fermion model that describes $p_x + i p_y$ excitonic pairing. For $m>1$ we develop a simple composite fermion mean field theory, and we present evidence that our wavefunction correctly describes this phase. We derive an interacting Hamiltonian for which our wavefunction is the exact ground state, and we present physical arguments that the $m=3$ state can be realized in a system in which energy bands with angular momentum that differ by $3$ cross at the Fermi energy. This leads to a gapless state with $(p_x + i p_y)^3$ excitonic pairing, which we argue is conducive to forming the fractional excitonic insulator in the presence of interactions. Prospects for numerics on model systems and band structure engineering to realize this phase in real materials are discussed.