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${}_2$

Abstract

An experiment in moiré MoTe${}_2$ bilayers reported the first observation of a topologically ordered state with zero Hall conductivity and half of the edge conductance of a standard time-reversal invariant quantum spin Hall insulator. This state is believed to emerge at total filling one of a pair of bands with Chern numbers $C=\pm 1$ related by time reversal symmetry. By viewing these bands as a pair of Landau levels with opposite magnetic fields, and starting from a parent magnet with one filled band, we demonstrate that a class of Halperin states constructed by adding particles to the empty Chern band and holes to the occupied Chern band have all the properties observed in MoTe${}_2$. Remarkably, these states break time-reversal symmetry but have exactly zero Hall conductivity and helical edge conductance of $e^2/2h$. These states also feature a spinless composite fermion with the same charge as the electron but split equally between both valleys. In a standard Halperin 331 state, this particle would be a neutral Bogoliubov composite fermion. However, in our context this composite fermion is charged but remains itinerant because it is split into the two valleys that effectively experience opposite magnetic fields. The existence of such charged itinerant particles is a key difference between Landau levels with opposite magnetic fields and standard multi-components Landau levels, where all the itinerant particles are charge neutral, such as the magneto-roton of the Laughlin state or the Bogoliubov composite fermion of the Moore-Read state. When the electron density changes away from the ideal filling and these itinerant charged particles are added to the parent state, the disorder potential is less efficient at localizing them as compared to standard Lanadau levels. This can explain why the state in MoTe${}_2$ did not display a robust Hall plateau upon changing the electron density.

arXiv comment12 pages, 2 figures

References in corpus (58)

• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• 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
• Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
• Intrinsic quantized anomalous Hall effect in a moiré heterostructure
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Observation of the e/3 Fractionally Charged Laughlin Quasiparticles
• 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
• Fractional quantum Hall effect in the absence of Landau levels
• Fractional Chern Insulator
• Quantum anomalous Hall effect from intertwined moiré bands
• Fractional Chern insulators in magic-angle twisted bilayer graphene
• Integer and fractional Chern insulators in twisted bilayer MoTe2
• Direct observation of anyonic braiding statistics at the $\nu$=1/3 fractional quantum Hall state
• Observation of half-integer thermal Hall conductance
• Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
• Randomness at the Edge: Theory of Quantum Hall transport at filling $\nu =2/3$
• Quasiholes and fermionic zero modes of paired fractional quantum Hall states: the mechanism for nonabelian statistics
• Fractional Chern Insulator States in Twisted Bilayer Graphene: An Analytical Approach
• Thermoelectric Response of an Interacting Two-Dimensional Electron Gas in Quantizing Magnetic Field
• Observed Quantization of Anyonic Heat Flow
• Particle-Hole Duality, Emergent Fermi Liquids and Fractional Chern Insulators in Moiré Flatbands
• Spontaneous fractional Chern insulators in transition metal dichalcogenides Moire superlattices
• Fractional Chern Insulator in Twisted Bilayer MoTe${}_2$
• Fractional quantum anomalous Hall states in twisted bilayer MoTe${}_2$ and WSe${}_2$
• Competing zero-field Chern insulators in Superconducting Twisted Bilayer Graphene
• Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides
• Programming Correlated Magnetic States via Gate Controlled Moiré Geometry
• Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
• Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe${}_2$
• Interplay of Fractional Chern Insulator and Charge-Density-Wave Phases in Twisted Bilayer Graphene
• Magic Angles and Fractional Chern Insulators in Twisted Homobilayer TMDs
• Edge reconstruction in the $\nu =2/3$ fractional quantum Hall state
• Zero-field composite Fermi liquid in twisted semiconductor bilayers
• Pressure--enhanced fractional Chern insulators in moiré transition metal dichalcogenides along a magic line
• Maximally Localized Wannier Orbitals, Interaction Models and Fractional Quantum Anomalous Hall Effect in Twisted Bilayer MoTe2
• Anomalous Hall effect at half filling in twisted bilayer graphene
• Gate-Tunable Fractional Chern Insulators in Twisted Double Bilayer Graphene
• Exciton band topology in spontaneous quantum anomalous Hall insulators: applications to twisted bilayer graphene
• Direct Observation of a Fractional Charge
• The Broken Symmetry of Two-Component $\nu =1/2$ Quantum Hall States
• Chiral Magic-Angle Twisted Bilayer Graphene in a Magnetic Field: Landau Level Correspondence, Exact Wavefunctions and Fractional Chern Insulators
• Phase transitions out of quantum Hall states in moiré materials
• Unpaired composite fermion, topological exciton, and zero mode
• Chiral limit and origin of topological flat bands in twisted transition metal dichalcogenide homobilayers
• Streda-like formula in spin Hall effect
• Spin Order in Paired Quantum Hall States
• Excitonic Laughlin States in Ideal Topological Insulator Flat Bands and Possible Presence in Moiré Superlattice Materials
• Composite-fermion pairing at half and quarter filled lowest Landau level
• Electrically tuned topology and magnetism in twisted bilayer MoTe${}_2$ at ${\nu }_h=1$
• Hall Drag in Correlated Double Layer Quantum Hall Systems
• Excitonic fractional quantum Hall hierarchy in Moiré heterostructures
• Supergravity model of the Haldane-Rezayi fractional quantum Hall state

Cited by in corpus (13)

• Interplay between topology and correlations in the second moiré band of twisted bilayer MoTe2
• Variational Mapping of Chern Bands to Landau Levels: Application to Fractional Chern Insulators in Twisted MoTe${}_2$
• Hidden States and Dynamics of Fractional Fillings in tMoTe2 Moiré Superlattices
• Non-Abelian spin Hall insulator
• Composite helical edges from Abelian fractional topological insulators
• Non-Abelian Fractional Chern Insulators and Competing States in Flat Moiré Bands
• 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
• Second-quantized approach to the study of Halperin state in fractional quantum Hall effect
• Symmetric localization of ${\nu }_{\text{tot}}=4/3$ fractional topological insulator edges