Variational wavefunctions for fractional topological insulators
arXiv:2501.09059 · doi:10.1103/PhysRevB.111.195143
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 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 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.
arXiv comment9 pages, 5 figures
References in corpus (45)
- Quantum Spin Hall Effect
- Fractional quantum Hall states at zero magnetic field
- Topological insulators in twisted transition metal dichalcogenide homobilayers
- Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
- Observation of Fractionally Quantized Anomalous Hall Effect
- Spontaneous Inter-layer Coherence in Double-Layer Quantum-Hall Systems I: Charged Vortices and Kosterlitz-Thouless Phase Transitions
- Fractional quantum Hall effect in the absence of Landau levels
- Fractional Chern Insulator
- Integer and fractional Chern insulators in twisted bilayer MoTe2
- Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
- A mechanism for anomalous Hall ferromagnetism in twisted bilayer graphene
- Fractional topological insulators
- Quasiholes and fermionic zero modes of paired fractional quantum Hall states: the mechanism for nonabelian statistics
- Observation of Wigner crystal of electrons in a monolayer semiconductor
- Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level
- Classification and analysis of two dimensional abelian fractional topological insulators
- Fractional topological liquids with time-reversal symmetry and their lattice realization
- Topological nodal Cooper pairing in doped Weyl metals
- Spatially resolved study of backscattering in the quantum spin Hall state
- Gauge-Fixed Wannier Wave-Functions for Fractional Topological Insulators
- Fractional (Chern and topological) insulators
- Quantum Hall Ferromagnetism in a Two-Dimensional Electron System
- Exciton band topology in spontaneous quantum anomalous Hall insulators: applications to twisted bilayer graphene
- Berry phase in Magnetic Superconductors
- Fractional Topological Insulators -- a Pedagogical Review
- Band mixing in the quantum anomalous Hall regime of twisted semiconductor bilayers
- Skyrmion Superconductivity: DMRG evidence for a topological route to superconductivity
- Interplay between topology and correlations in the second moiré band of twisted bilayer MoTe2
- fractional topological insulators in two dimensions
- Tunneling-driven breakdown of the 331 state and the emergent Pfaffian and composite Fermi liquid phases
- Interaction Driven Quantum Phase Transitions in Fractional Topological Insulators
- Excitonic Laughlin States in Ideal Topological Insulator Flat Bands and Possible Presence in Moiré Superlattice Materials
- DMRG study of strongly interacting flatbands: a toy model inspired by twisted bilayer graphene
- Halperin States of Particles and Holes in Ideal Time Reversal Invariant Pairs of Chern Bands and The Fractional Quantum Spin Hall Effect in Moiré MoTe
- Non-Abelian Two-component Fractional Quantum Hall States
- Electron-phonon coupling and competing Kekulé orders in twisted bilayer graphene
- -wave paired composite-fermion electron-hole trial state for quantum Hall bilayers with
- Global phase diagram of two-component Bose gases in antiparallel magnetic fields
- Quantum Hall Valley Nematics
- Excitonic fractional quantum Hall hierarchy in Moiré heterostructures
- Time-Reversal Invariant Topological Moiré Flatband: A Platform for the Fractional Quantum Spin Hall Effect
- Non-Abelian spin Hall insulator
- Spin separation due to an inherent spontaneous symmetry breaking of the fractional topological insulator
- Successive electron-vortex binding in quantum Hall bilayers at
- Single-parameter variational wavefunctions for quantum Hall bilayers