Fractional Topological Insulators: from sliding Luttinger Liquids to Chern-Simons theory

Abstract

The sliding Luttinger liquids (LL) approach is applied to study fractional topological insulators (FTI). We show that FTI is the low energy fixed point of the theory for realistic spin-orbit and electron-electron interaction. We find that the topological phase pertains in the presence of interaction that breaks the spin invariance and its boundaries are even extended by those terms. Finally we show that one dimensional chiral anomaly in the LL leads to the emergence of topological Chern-Simons terms in the effective gauge theory of the FTI state.

15 pages, 6 figures. Changes in style. Supplementary material expanded. Added references

References in corpus (9)

• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
• The Quantum Spin Hall Effect: Theory and Experiment
• Quantum Spin Hall Effect in Strip of Stripes Model
• Integer and Fractional Quantum Anomalous Hall Effect in a Strip of Stripes Model
• Time reversal symmetry broken fractional topological phases at zero magnetic field

Cited by in corpus (44)

• Topological Phases in Two-Dimensional Materials: A Brief Review
• Topological Floquet Phases in Driven Coupled Rashba Nanowires
• Pairing in Luttinger Liquids and Quantum Hall States
• Fractional Topological Superconductivity and Parafermion Corner States
• Floquet Second-Order Topological Superconductor Driven via Ferromagnetic Resonance
• Fractional Topological Insulators -- a Pedagogical Review
• Fractional Charge and Spin States in Topological Insulator Constrictions
• Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
• Wire constructions of Abelian topological phases in three or more dimensions
• From an array of quantum wires to three-dimensional fractional topological insulators
• Fractional topological phases in three-dimensional coupled-wire systems
• Coupled wire model of symmetric Majorana surfaces of topological superconductors
• Non-Abelian SU(N-1)-singlet fractional quantum Hall states from coupled wires
• Coupled-wire constructions: a Luttinger liquid approach to topology
• Theory of a 3+1D fractional chiral metal: interacting variant of the Weyl semimetal
• Pretopological fractional excitations in the two-leg flux ladder
• Quantum Hall hierarchy from coupled wires
• Fractional chiral superconductors
• From coupled-wire construction of quantum Hall states to wave functions and hydrodynamics
• From Dirac semimetals to topological phases in three dimensions: a coupled wire construction
• Synthetic gauge field and chiral physics on two-leg superconducting circuits
• Coupled Wire Model of Z4 Orbifold Quantum Hall States
• From Quantum Wires to the Chern-Simons Description of the Fractional Quantum Hall Effect
• Interaction Protected Topological Insulators with Time Reversal Symmetry
• General scatterings and electronic states in the quantum-wire network of moiré systems
• Unification of parton and coupled-wire approaches to quantum magnetism in two dimensions
• Possible Sliding Regimes in Twisted Bilayer WTe${}_2$
• Attractive Haldane bilayers for trapping non-Abelian anyons
• Electrically tunable correlated domain wall network in twisted bilayer graphene
• Coupled Wire Models of Interacting Dirac Nodal Superconductors
• From Coupled Rashba Electron and Hole Gas Layers to 3D Topological Insulators
• Generalized parafermions and non-local Josephson effect in multi-layer systems
• Fractional second-order topological insulator from a three-dimensional coupled-wires construction
• Metal-insulator transition in a sliding Luttinger liquid with line defects
• Fractional topological insulator precursors in spin-orbit fermion ladders
• Universal conductance dips and fractional excitations in a two-subband quantum wire
• Fractional Spin Quantum Hall Effect in Weakly Coupled Spin Chain Arrays
• Dihedral twist liquid models from emergent Majorana fermions
• A Two-Gauge Field Model for Magnetoelectric Boundaries
• Quantum wires, Chern-Simons theory, and dualities in the quantum Hall system
• Fractional chiral second-order topological insulator from a three-dimensional array of coupled wires
• Coupled-wire descriptions of unconventional quantum states in twisted nanostructures
• Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays
• Breaking of Lorentz invariance caused by the interplay between spin-orbit interaction and transverse phonon modes in quantum wires