${\mathbb{Z}}_2$ fractional topological insulators in two dimensions

Abstract

We propose a simple microscopic model to numerically investigate the stability of a two dimensional fractional topological insulator (FTI). The simplest example of a FTI consists of two decoupled copies of a Laughlin state with opposite chiralities. We focus on bosons at half filling. We study the stability of the FTI phase upon addition of two coupling terms of different nature: an interspin interaction term, and an inversion symmetry breaking term that couples the copies at the single particle level. Using exact diagonalization and entanglement spectra, we numerically show that the FTI phase is stable against both perturbations. We compare our system to a similar bilayer fractional Chern insulator. We show evidence that the time reversal invariant system survives the introduction of interaction coupling on a larger scale than the time reversal symmetry breaking one, stressing the importance of time reversal symmetry in the FTI phase stability. We also discuss possible fractional phases beyond $\nu =1/2$.

15 pages, 18 figures

References in corpus (13)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Fractional quantum Hall effect in the absence of Landau levels
• Gauge-Fixed Wannier Wave-Functions for Fractional Topological Insulators
• Adiabatic continuation of Fractional Chern Insulators to Fractional Quantum Hall States
• From fractional Chern insulators to Abelian and non-Abelian fractional quantum Hall states: adiabatic continuity and orbital entanglement spectrum
• Global phase diagram of two-component Bose gases in antiparallel magnetic fields
• Interacting and fractional topological insulators via the ${\mathbb{Z}}_2$ chiral anomaly
• Fermions out of Dipolar Bosons in the lowest Landau level

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