Non-Abelian spin Hall insulator

Abstract

Motivated by a recent experiment reporting the fractional quantum spin Hall effect in twisted ${\mathrm{MoTe}}_2$, we investigate microscopically the prospects of realizing exotic topologically ordered states beyond conventional quantum Hall physics. We show that a non-Abelian spin Hall insulator, a state of two copies of the non-Abelian Moore-Read state, can be stabilized at half filling of time-reversal conjugate Chern bands. We elucidate that the existence of this phase relies on the reduction of opposite-spin interactions at short distances to overcome the Ising ferromagnetism. Moreover, we demonstrate that band mixing provides a generic mechanism for this reduction to be achieved. Quite remarkably, we find that a renormalization of opposite-spin interactions at short distances as small as 15 % of the moiré period is sufficient for a direct transition to a completely spin unpolarized phase which supports the non-Abelian spin Hall insulator. Furthermore, we show that the non-Abelian spin Hall insulator can either break time-reversal symmetry or preserve it depending on the underlying topological order.

10 pages, 7 figures, published version

References in corpus (47)

• Quantum Spin Hall Effect in Graphene
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Quantum Spin Hall Effect
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• 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
• Integer and fractional Chern insulators in twisted bilayer MoTe2
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• 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
• Ground State and Hidden Symmetry of Magic Angle Graphene at Even Integer Filling
• Twisted Bilayer Graphene IV. Exact Insulator Ground States and Phase Diagram
• A Class of $P,T$-Invariant Topological Phases of Interacting Electrons
• Thermal Transport in Chiral Conformal Theories and Hierarchical Quantum Hall States
• Ferromagnetism in narrow bands of moiré superlattices
• Particle-Hole Duality, Emergent Fermi Liquids and Fractional Chern Insulators in Moiré Flatbands
• Fractional topological liquids with time-reversal symmetry and their lattice realization
• Spontaneous fractional Chern insulators in transition metal dichalcogenides Moire superlattices
• Fractional quantum anomalous Hall states in twisted bilayer MoTe${}_2$ and WSe${}_2$
• Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides
• Landau Level Mixing and the Fractional Quantum Hall Effect
• Magic Angles and Fractional Chern Insulators in Twisted Homobilayer TMDs
• Mapping twist-tuned multiband topology in bilayer WSe${}_2$
• Landau-level-mixing and the ground state of the 5/2 quantum Hall effect
• Polarization-driven band topology evolution in twisted MoTe${}_2$ and WSe${}_2$
• Landau Level Mixing in the Perturbative Limit
• Degeneracy of non-abelian quantum Hall states on the torus: domain walls and conformal field theory
• Exciton band topology in spontaneous quantum anomalous Hall insulators: applications to twisted bilayer graphene
• Topological degeneracy of non-Abelian states for dummies
• Non-Abelian fractionalization in topological minibands
• Band mixing in the quantum anomalous Hall regime of twisted semiconductor bilayers
• ${\mathbb{Z}}_2$ fractional topological insulators in two dimensions
• Non-Abelian Fractional Quantum Anomalous Hall States and First Landau Level Physics in Second Moiré Band of Twisted Bilayer MoTe2
• Higher Landau-Level Analogs and Signatures of Non-Abelian States in Twisted Bilayer MoTe${}_2$
• Excitonic Laughlin States in Ideal Topological Insulator Flat Bands and Possible Presence in Moiré Superlattice Materials
• Quantum Hall ferroelectrics and nematics in multivalley systems
• 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${}_2$
• Numerical Study of Quantum Hall Bilayers at Total Filling ${\nu }_T=1$: A New Phase at Intermediate Layer Distances
• Moiré Landau fans and magic zeros
• Excitonic fractional quantum Hall hierarchy in Moiré heterostructures
• Time-Reversal Invariant Topological Moiré Flatband: A Platform for the Fractional Quantum Spin Hall Effect
• Composite helical edges from Abelian fractional topological insulators
• Stability of Topological Insulators with Non-Abelian Edge Excitations
• Exciton Condensation in Quantum Hall Bilayers at Total Filling ${\nu }_T=5$

Cited by in corpus (8)

• Fractionalization as an alternate to charge ordering in electronic insulators
• Electromagnetic response and emergent topological orders in transition metal dichalcogenide MoTe${}_2$ bilayers
• Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
• Quantum Phases in Twisted Homobilayer Transition Metal Dichalcogenides
• Candidate for a Fractional Topological Insulator in Twisted MoTe2
• Variational wavefunctions for fractional topological insulators
• Probing Quantum Anomalous Hall States in Twisted Bilayer WSe2 via Attractive Polaron Spectroscopy
• Topological Order in Neural Wavefunctions