Composite boson theory of fractional excitonic insulator states

The search for fractional Chern insulating phases has primarily focused on engineering flat bands that mimic a Landau level as closely as possible. There is, however, an alternative limit to consider: inverted dispersive bands close to a topological transition. In this limit, the authors in [1] introduced a Laughlin-like wave function for particles and holes describing the ordinary Chern insulator, which when extended to odd-denominator ν = 1/m fractional quantum Hall phases suggests the existence of a “fractional excitonic insulator” near an inversion between bands carrying relative angular momentum m. In this work, we introduce a composite boson theory that highlights the role of the relative angular momentum in stabilizing these as well as other fractional excitonic insulator states. We first motivate this scheme by introducing a composite boson description of the ordinary Chern insulator. We then apply similar logic to discover a new sequence of fractional states, the simplest example being a bosonic ν = 1/2 state that is a promising target for numerical studies. Our work further broadens the scope of beyond-Landau-level fractional quantum Hall states that may be realized in condensed matter systems.

[1] Y. Hu, J. W. F. Venderbos, and C. L. Kane. Fractional Excitonic Insulator. Phys. Rev. Lett. 121, 126601 (2018).