Fractional Topological Insulators -- a Pedagogical Review

Abstract

Fractional topological insulators are electronic systems that carry fractionally charged excitations, conserve charge and are symmetric to reversal of time. In this review we introduce the basic essential concepts of the field, and then survey theoretical understanding of fractional topological insulators in two and three dimensions. In between, we discuss the case of "two and a half dimensions", the fractional topological insulators that may form on the two dimensional surface of an unfractionalized three dimensional topological insulator. We focus on electronic systems and emphasize properties of edges and surfaces, most notably the stability of gapless edge modes to perturbations.

To be published in the Annual Review - Condensed Matter Physics. Fourteen pages

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Cited by in corpus (53)

• Spontaneous fractional Chern insulators in transition metal dichalcogenides Moire superlattices
• Second Order Topological Superconductivity in $\pi$-Junction Rashba Layers
• Magnon thermal Hall effect in kagome antiferromagnets with Dzyaloshinskii-Moriya interactions
• Mixing of $t_{2g}$-$e_g$ orbitals in 4d and 5d transition metal oxides
• Flat Chern Band From Twisted Bilayer MnBi${}_2$Te${}_4$
• Topological Magnon Bands and Unconventional Superconductivity in Pyrochlore Iridate Thin Films
• Floquet band structure of a semi-Dirac system
• Quadratic band touching points and flat bands in two-dimensional topological Floquet systems
• Interplay between topology and correlations in the second moiré band of twisted bilayer MoTe2
• Helical Liquids in Semiconductors
• Topological Zero-Dimensional Defect and Flux States in Three-Dimensional Insulators
• Ultra-Strong Spin-Orbit Coupling and Topological Moiré Engineering in Twisted ZrS2 Bilayers
• Perspective: Strongly correlated and topological states in [111] grown transition metal oxide thin films and heterostructures
• Cornering the universal shape of fluctuations
• Intrinsic sign problem in fermionic and bosonic chiral topological matter
• Disorder effects in correlated topological insulators
• Rashba Sandwiches with Topological Superconducting Phases
• Quantum Hall spin liquids and their possible realization in moiré systems
• Topological Green's function zeros in an exactly solved model and beyond
• Floquet topological transitions in extended Kane-Mele models with disorder
• Group theory study of the vibrational modes and magnetic order in the topological antiferromagnet MnBi${}_2$Te${}_4$
• Numerical investigation of gapped edge states in fractional quantum Hall-superconductor heterostructures
• Su-Schrieffer-Heeger quasicrystal: Topology, localization, and mobility edge
• Attractive Haldane bilayers for trapping non-Abelian anyons
• Platforms for the realization and characterization of Tomonaga-Luttinger liquids
• Minimal Fractional Topological Insulator in half-filled conjugate moiré Chern bands
• Topological phases of parafermionic chains with symmetries
• Composite helical edges from Abelian fractional topological insulators
• Statistically induced topological phase transitions in a one-dimensional superlattice anyon-Hubbard model
• Clock model and parafermions in Rashba nanowires
• Textured Exciton Insulators
• Paired parton quantum Hall states: a coupled wire construction
• Fractional topological insulator precursors in spin-orbit fermion ladders
• Universal Wilson Loop Bound of Quantum Geometry
• Surfaces and Slabs of Fractional Topological Insulator Heterostructures
• A Passage to Topological Matter: Colloquium
• Topological end states in a one-dimensional spatially modulated interaction spinless fermion model
• Spin separation due to an inherent spontaneous symmetry breaking of the fractional topological insulator
• Electrically tunable high-Chern-number quasiflat bands in twisted antiferromagnetic topological insulators
• Constructing vortex functions and basis states of Chern insulators: ideal condition, inequality from index theorem, and coherent-like states on von Neumann lattice
• Programmable, Spontaneous Superlattice Memory in a Monolayer Topological Insulator
• Floquet states in (LaNiO${}_3$)${}_2$/(LaAlO${}_3$)${}_N$ heterostructures grown along the (111) direction
• Punctured-Chern topological invariants for semi-metallic bandstructures
• Quantum-geometric dipole: a topological boost to flavor ferromagnetism in flat bands
• Interaction- and phonon-induced topological phase transitions in double helical liquids
• Variational wavefunctions for fractional topological insulators
• Quantum critical points in tunneling junction of topological superconductor and topological insulator
• Symmetric localization of ${\nu }_{\text{tot}}=4/3$ fractional topological insulator edges
• Topological two-body interaction obstructing trivial ground states: an indicator of fractional Chern insulators
• Fermion Number 1/2 of Sphalerons and Spectral Mirror Symmetry
• Tuning between a fractional topological insulator and competing phases at ${\nu }_{\mathrm{T}}=2/3$
• Topological two-particle dynamics in a periodically driven lattice model with on-site interactions
• Introduction to abelian anyons in planar systems