Fractional chiral superconductors

Abstract

Two-dimensional $p_x+i{p}_y$ topological superconductors host gapless Majorana edge modes, as well as Majorana bound states at the core of $h/2e$ vortices. Here we construct a model realizing the fractional counterpart of this phase: a fractional chiral superconductor. Our model is composed of an array of coupled Rashba wires in the presence of strong interactions, Zeeman field, and proximity coupling to an $s$-wave superconductor. We define the filling factor as $\nu =l_{\text{so}}n/4$, where $n$ is the electronic density and $l_{\text{so}}$ is the spin-orbit length. Focusing on filling $\nu =1/m$, with $m$ being an odd integer, we obtain a tractable model which allows us to study the properties of the bulk and the edge. Using an $\epsilon$-expansion with $m=2+\epsilon$, we show that the bulk Hamiltonian is gapped and that the edge of the sample hosts a chiral ${\mathbb{Z}}_{2m}$ parafermion theory with central charge $c=\frac{2m-1}{m+1}$. The tunneling density of states associated with this edge theory exhibits an anomalous energy dependence of the form ${\omega }^{m-1}$. Additionally, we show that ${\mathbb{Z}}_{2m}$ parafermionic bound states reside at the cores of $h/2e$ vortices. Upon constructing an appropriate Josephson junction in our system, we find that the current-phase relation displays a $4\pi m$ periodicity, reflecting the underlying non-abelian excitations.

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• Coupled-wire constructions: a Luttinger liquid approach to topology
• Probing topological superconductors with emergent gravity
• Spin liquids from Majorana Zero Modes in a Cooper Box
• Coupled wire construction of a topological phase with chiral tricritical Ising edge modes
• From Topological Superconductivity to Quantum Hall States in Coupled Wires
• Coupled Wire Model of Z4 Orbifold Quantum Hall States
• Unification of parton and coupled-wire approaches to quantum magnetism in two dimensions
• General scatterings and electronic states in the quantum-wire network of moiré systems
• Electron pairing induced by repulsive interactions in tunable one-dimensional platforms
• Clock model and parafermions in Rashba nanowires
• Bulk Pumping in 2D Topological Phases
• Insulating regime of an underdamped current-biased Josephson junction supporting ${\mathbb{Z}}_3$ and ${\mathbb{Z}}_4$ parafermions
• Fractional second-order topological insulator from a three-dimensional coupled-wires construction
• Chiral topologically ordered insulating phases in arrays of interacting integer quantum Hall islands
• Interaction- and phonon-induced topological phase transitions in double helical liquids
• Disorder-induced topological superconductivity in a spherical quantum-Hall--superconductor hybrid
• Twisted Nodal Superconductors
• Fractional chiral second-order topological insulator from a three-dimensional array of coupled wires
• Chiral Edge States Emerging on Anyon-Net
• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor
• Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays