From an array of quantum wires to three-dimensional fractional topological insulators

Abstract

The coupled-wires approach has been shown to be useful in describing two-dimensional strongly interacting topological phases. In this manuscript we extend this approach to three-dimensions, and construct a model for a fractional strong topological insulator. This topologically ordered phase has an exotic gapless state on the surface, called a fractional Dirac liquid, which cannot be described by the Dirac theory of free fermions. Like in non-interacting strong topological insulators, the surface is protected by the presence of time-reversal symmetry and charge conservation. We show that upon breaking these symmetries, the gapped fractional Dirac liquid presents unique features. In particular, the gapped phase that results from breaking time-reversal symmetry has a halved fractional Hall conductance of the form ${\sigma }_{xy}=\frac{1}{2}\frac{e^2}{mh}$ if the filling is $\nu =1/m$. On the other hand, if the surface is gapped by proximity coupling to an $s$-wave superconductor, we end up with an exotic topological superconductor. To reveal the topological nature of this superconducting phase, we partition the surface into two regions: one with broken time-reversal symmetry and another coupled to a superconductor. We find a fractional Majorana mode, which cannot be described by a free Majorana theory, on the boundary between the two regions. The density of states associated with tunneling into this one-dimensional channel is proportional to ${\omega }^{m-1}$, in analogy to the edge of the corresponding Laughlin state.

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• Wire constructions of Abelian topological phases in three or more dimensions
• Coupled wire model of symmetric Majorana surfaces of topological superconductors
• Coupled-layer description of topological crystalline insulators
• Non-Abelian SU(N-1)-singlet fractional quantum Hall states from coupled wires
• Majorana and parafermion corner states from two coupled sheets of bilayer graphene
• Kramers pairs of Majorana corner states in a topological insulator bilayer
• Coupled-wire constructions: a Luttinger liquid approach to topology
• Theory of a 3+1D fractional chiral metal: interacting variant of the Weyl semimetal
• Fractional chiral superconductors
• Interaction Enabled Fractonic Higher-Order Topological Phases
• Ground state degeneracy of non-Abelian topological phases from coupled wires
• From Dirac semimetals to topological phases in three dimensions: a coupled wire construction
• From coupled-wire construction of quantum Hall states to wave functions and hydrodynamics
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• Coupled Wire Model of Z4 Orbifold Quantum Hall States
• From Quantum Wires to the Chern-Simons Description of the Fractional Quantum Hall Effect
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• From coupled wires to coupled layers: Model with three-dimensional fractional excitations
• Unification of parton and coupled-wire approaches to quantum magnetism in two dimensions
• Strongly correlated crystalline higher-order topological phases in two-dimensional systems: A coupled-wire study
• Coupled Wire Models of Interacting Dirac Nodal Superconductors
• Clock model and parafermions in Rashba nanowires
• Generalized parafermions and non-local Josephson effect in multi-layer systems
• From Coupled Rashba Electron and Hole Gas Layers to 3D Topological Insulators
• Photo-induced SU(3) topological material of spinless fermions
• Fractional second-order topological insulator from a three-dimensional coupled-wires construction
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• Majorana zero modes in a quantum wire platform without Rashba spin-orbit coupling
• Dihedral twist liquid models from emergent Majorana fermions
• 3D Network Model for Strong Topological Insulator Transitions
• Topological Dipole Insulator
• 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
• Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays