Phase transitions out of quantum Hall states in moiré materials

Abstract

Motivated by the recent experimental breakthroughs in observing Fractional Quantum Anomalous Hall (FQAH) states in moiré materials, we propose and study various unconventional phase transitions between quantum Hall phases and Fermi liquids or charge ordered phases upon tuning the bandwidth. At a fixed rational lattice filling $\nu$, we describe a quantum Ginzburg-Landau theory to describe the intertwinement between the FQAH and Charge Density Wave (CDW) orders. We use this theory to describe phase transitions between the FQAH and a CDW insulator. The critical theory for a direct second order transition resembles that of the familiar deconfined quantum critical point (DQCP) but with an additional Chern-Simons term. At filling -1/2, we study the possibility of a continuous transition between the composite Fermi liquid (CFL) and the Fermi liquid (FL) building on and refining previous work by Barkeshli and McGreevy. Crucially we show that filling constraints ignored in that work ensure that translation symmetry alone is enough to enable a second order CFL-FL transition. We argue that there must be critical CDW fluctuations though neither phase has long range CDW order. We present experimental signatures the most striking of which is a universal jump of both longitudinal and Hall resistivities at the critical point. With disorder, we argue that the CDW order gets pinned and the CFL-FL evolution happens through an intermediate electrically insulating phase with mobile neutral fermions. A clean analog of this insulating phase with long range CDW order and a neutral fermi surface can potentially also exist. We also present a critical theory for the CFL to FL transition at filling -3/4. Our work opens up a new avenue to realize deconfined criticality and fractionalized phases beyond familiar Landau level physics in the moire Chern band system.

18+4 pages

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• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• 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
• Quantum anomalous Hall effect from intertwined moiré bands
• Fractional Chern insulators in magic-angle twisted bilayer graphene
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• Interplay of Fractional Chern Insulator and Charge-Density-Wave Phases in Twisted Bilayer Graphene
• Zero-field composite Fermi liquid in twisted semiconductor bilayers
• Continuous Preparation of a Fractional Chern Insulator
• Continuous transitions between composite Fermi liquid and Landau Fermi liquid: a route to fractionalized Mott insulators
• Quantum spin liquids and the metal-insulator transition in doped semiconductors
• Theory of a continuous bandwidth-tuned Wigner-Mott transition
• Deconfined criticalities and dualities between chiral spin liquid, topological superconductor and charge density wave Chern insulator
• Evolution between quantum Hall and conducting phases: simple models and some results
• Quantitative theory of composite fermions in Bose-Fermi mixtures at $\nu =1$

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• 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${}_2$
• Variational Mapping of Chern Bands to Landau Levels: Application to Fractional Chern Insulators in Twisted MoTe${}_2$
• Doping a fractional quantum anomalous Hall insulator
• Extended quantum anomalous Hall effect in moiré structures: phase transitions and transport
• Microscopic Mechanism of Anyon Superconductivity Emerging from Fractional Chern Insulators
• A new series of 3D CFTs with $\mathrm{Sp}(N)$ global symmetry on fuzzy sphere
• Attractive Haldane bilayers for trapping non-Abelian anyons
• From Fractional Quantum Anomalous Hall Smectics to Polar Smectic Metals: Nontrivial Interplay Between Electronic Liquid Crystal Order and Topological Order in Correlated Topological Flat Bands
• Moiré Band Engineering in Twisted Trilayer WSe2
• Corner Charge Fluctuations and Many-Body Quantum Geometry
• Compressible quantum liquid with vanishing Drude weight
• Bipartite Fluctuations of Critical Fermi Surfaces
• Topological magnons and domain walls in twisted bilayer MoTe${}_2$
• Continuous Transition between Bosonic Fractional Chern Insulator and Superfluid
• Free and Interacting Fermionic Conformal Field Theories on the Fuzzy Sphere
• Identifying Instabilities with Quantum Geometry in Flat Band Systems
• Interaction-driven quantum phase transitions between topological and crystalline orders of electrons
• Phases and criticality of the triangular lattice SU(N) Hofstadter-Hubbard model
• Pathways from a chiral superconductor to a composite Fermi liquid
• Proliferation transitions from a topological phase in $2+1$ dimensions
• Continuous transition and gapless roton inside fractional quantum anomalous Hall states
• The Sound of Electrons Shattering: Current Noise Composition Laws for Electron Fractionalization
• Abelian and non-Abelian fractionalized states in twisted MoTe${}_2$: A generalized Landau-level theory
• Unconventional superconductivity mediated by exciton density wave fluctuations
• Dynamic scaling near the Kasteleyn transition in spin ice: critical relaxation of monopoles and strings following a field quench