Variational wavefunctions for fractional topological insulators

TL;DR

This paper proposes a new trial wavefunction for fractional topological insulators in twisted TMDs with opposite Chern numbers, demonstrating its effectiveness through overlaps with exact states when Coulomb interactions are softened.

Contribution

It introduces a novel pairing-based trial wavefunction for opposite Chern number Landau levels, addressing limitations of previous models.

Findings

The trial wavefunction has high overlap with exact ground states.

Softening Coulomb interactions improves the wavefunction's accuracy.

Highlights the importance of suppressing interspin Coulomb repulsion.

Abstract

Twisted transition metal dichalcogenides (TMDs) host bands with opposite Chern number for the two spin species and could thus be host for fractional topological insulator states. In multicomponent quantum Hall systems, where the spins have equal Chern number, the resulting topological liquid states can be well modeled by trial wavefunctions such as the Halperin $(lmn)$ wavefunctions. These wavefunctions are exact zero energy states of certain short-range (pseudopotential) Hamiltonians. However, we show that such a construction fails in the case where the Chern numbers of the two spins are opposite, since the electrons with opposite Chern number cannot avoid one another. This underlines the importance of suppressing the short-range interspin Coulomb repulsion in order to realize fractional topological insulators in twisted TMDs. We introduce a trial wavefunction for the opposite Chern number Landau levels for filling factor $\nu=\frac{1}{3}+\frac{1}{3}$ in terms of pairing of composite fermions and show that it has good overlaps with the exact diagonalization ground state when the short-range Coulomb repulsion is sufficiently softened.