Pair-Density-Wave Order and Paired Fractional Quantum Hall Fluids

Abstract

The properties of the isotropic incompressible $\nu =5/2$ fractional quantum Hall (FQH) state are described by a paired state of composite fermions in zero (effective) magnetic field, with a uniform $p_x+i{p}_y$ pairing order parameter, which is a non-Abelian topological phase with chiral Majorana and charge modes at the boundary. Recent experiments suggest the existence of a proximate nematic phase at $\nu =5/2$. This finding motivates us to consider an inhomogeneous paired state - a $p_x+i{p}_y$ pair-density-wave (PDW) - whose melting could be the origin of the observed liquid-crystalline phases. This state can viewed as an array of domain and anti-domain walls of the $p_x+i{p}_y$ order parameter. We show that the nodes of the PDW order parameter, the location of the domain walls (and anti-domain walls) where the order parameter changes sign, support a pair of symmetry-protected counter-propagating Majorana modes. The coupling behavior of the domain wall Majorana modes crucially depends on the interplay of the Fermi energy $E_F$ and the PDW pairing energy $E_{\text{pdw}}$. The analysis of this interplay yields a rich set of topological states. The pair-density-wave order state in paired FQH system provides a fertile setting to study Abelian and non-Abelian FQH phases - as well as transitions thereof - tuned by the strength of the paired liquid crystalline order.

arXiv comment27 pages, 11 figures; Published version

References in corpus (68)

• Unpaired Majorana fermions in quantum wires
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Electronic Liquid Crystal Phases of a Doped Mott Insulator
• Theory of Intertwined Orders in High Temperature Superconductors
• Nematic Fermi Fluids in Condensed Matter Physics
• Evidence for an Anisotropic State of Two-Dimensional Electrons in High Landau Levels
• $2n$ Quasihole States Realize $2^{n-1}$-Dimensional Spinor Braiding Statistics in Paired Quantum Hall States
• Charge Density Wave in Two-Dimensional Electron Liquid in Weak Magnetic Field
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Is the Composite Fermion a Dirac Particle?
• Strongly Anisotropic Transport in Higher Two-Dimensional Landau Levels
• Liquid Crystal Phases of Quantum Hall Systems
• The Ground State of a Two-Dimensional Electron Liquid in a Weak Magnetic Field
• Exact results for interacting electrons in high Landau levels
• Striped superconductors: How the cuprates intertwine spin, charge and superconducting orders
• Exact Quantization of Even-Denominator Fractional Quantum Hall State at $\nu$=5/2 Landau Level Filling Factor
• Dynamical layer decoupling in a stripe-ordered, high T_c superconductor
• Charge $4e$ superconductivity from pair density wave order in certain high temperature superconductors
• Dislocations and vortices in pair density wave superconductors
• Bogoliubov Fermi surfaces in superconductors with broken time-reversal symmetry
• Anisotropic States of Two-Dimensional Electron Systems in High Landau Levels: Effect of an In-Plane Magnetic Field
• Robust doubly charged nodal lines and nodal surfaces in centrosymmetric systems
• Strongly Anisotropic Electronic Transport at Landau Level Filling Factor $\nu =9/2$ and $\nu =5/2$ Under Tilted Magnetic Field
• Unified theory of PT and CP invariant topological metals and nodal superconductors
• Theory of the striped superconductor
• Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions
• Bogoliubov Fermi surfaces: General theory, magnetic order, and topology
• Nematic phase of the two-dimensional electron gas in a magnetic field
• Coexistence of charge-density-wave and pair-density-wave orders in underdoped cuprates
• Fluctuations and phase transitions in Larkin-Ovchinnikov liquid crystal states of population-imbalanced resonant Fermi gas
• Unidirectional d-wave superconducting domains in the two-dimensional t-J model
• Topological Blount's theorem of odd-parity superconductors
• Evidence for a fractional quantum Hall state with anisotropic longitudinal transport
• Field theory of the quantum Hall nematic transition
• Theory of Disorder-Induced Half-Integer Thermal Hall Conductance
• Vertical line nodes in the superconducting gap structure of Sr2RuO4
• Observation of a transition from a topologically ordered to a spontaneously broken symmetry phase
• Topological Order from Disorder and the Quantized Hall Thermal Metal: Possible Applications to the $\nu =5/2$ State
• Tilt-Induced Anisotropic to Isotropic Phase Transition at $\nu =5/2$
• Theory of Nematic Fractional Quantum Hall State
• Pairing in Luttinger Liquids and Quantum Hall States
• Pair Density Waves in Superconducting Vortex Halos
• Theory of Disordered $\nu =5/2$ Quantum Thermal Hall State: Emergent Symmetry and Phase Diagram
• An Isotropic to Anisotropic Transition in a Fractional Quantum Hall State
• Weyl nodal surfaces
• Emergent Lorentz symmetry with vanishing velocity in a critical two-subband quantum wire
• Evidence for a $\nu =5/2$ Fractional Quantum Hall Nematic State in Parallel Magnetic Fields
• Effective Field Theory of Fractional Quantized Hall Nematics
• Broken rotation symmetry in the fractional quantum Hall system
• Striped quantum Hall state in a half-filled Landau level
• Spatially Ordered Fractional Quantum Hall States
• Fractional quantum Hall systems near nematicity: bimetric theory, composite fermions, and Dirac brackets
• Majorana bands, Berry curvature, and thermal Hall conductivity in the vortex state of a chiral p-wave superconductor
• Possible nematic to smectic phase transition in a two-dimensional electron gas at half-filling
• Electron-Electron Interactions and the Paired-to-Nematic Quantum Phase Transition in the Second Landau Level
• Pomeranchuk Instability of Composite Fermi Liquids
• Unconventional anisotropic even-denominator fractional quantum Hall state in a system with mass anisotropy
• Phase transitions in superconductor liquid crystals
• Anisotropy Driven Transition from Moore-Read State to Quantum Hall Stripes
• Braiding statistics and classification of two-dimensional charge-$2m$ superconductors
• Onset of Quantum Criticality in the Topological-to-Nematic Transition in a Two-dimensional Electron Gas at Filling Factor $\nu =5/2$
• The Weakly Coupled Pfaffian as a Type I Quantum Hall Liquid
• A Typology for Quantum Hall Liquids
• Impact of the modulation doping layer on the ν=5/2 anisotropy
• Competing quantum Hall phases in the second Landau level in low density limit

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• Triplet Pair-Density Wave Superconductivity on the $\pi$-flux Square Lattice
• Topology and the one-dimensional Kondo-Heisenberg model
• Antichiral and nematicity-wave superconductivity
• Intra-unit-cell singlet pairing mediated by altermagnetic fluctuations
• Intertwined Order in Fractional Chern Insulators from Finite-Momentum Pairing of Composite Fermions
• Weyl Fermions and Broken Symmetry Phases of Laterally Confined ${}^3$He Films
• Highly-Anisotropic Even-Denominator Fractional Quantum Hall State in an Orbitally-Coupled Half-Filled Landau Level
• Anomalous Hall effect in single-band chiral superconductors from impurity superlattices
• Chiral to helical Majorana fermion transition in a $p$-wave superconductor
• Vestigial $d$-wave charge-$4e$ Superconductivity from Bidirectional Pair Density Waves
• Even-denominator fractional quantum Hall states with spontaneously broken rotational symmetry
• Theory of Hofstadter Superconductors