From Topological Superconductivity to Quantum Hall States in Coupled Wires

TL;DR

This paper explores the emergence of topological superconductivity and quantum Hall states in coupled wire systems, analyzing phase diagrams, Majorana modes, and potential realizations in solid-state and cold-atom setups.

Contribution

It provides a comprehensive theoretical framework connecting topological superconductivity with quantum Hall phases in coupled wire models, including new phase diagrams and hybrid systems.

Findings

Identification of Majorana zero modes in coupled Kitaev chains

Discovery of quantum Hall and charge density wave phases in hybrid systems

Proposal of engineered $p+ip$ superconductor and fractional quantum Hall phases

Abstract

We present a theoretical study of the interplay between topological p-wave superconductivity, orbital magnetic fields and quantum Hall phases in coupled wire systems. First, we calculate the phase diagram and physical observables of a fermionic ladder made of two coupled Kitaev chains, and discuss the presence of two and four Majorana zero modes. Second, we analyze hybrid systems consisting of a Kitaev chain coupled to a Luttinger liquid. By tuning the magnetic field and the carrier density, we identify quantum Hall and charge density wave phases, as well as regimes in which superconductivity is induced in the second chain by proximity effect. Finally, we consider two-dimensional systems made of weakly coupled ladders. There, we engineer a $p+ip$ superconductor and describe a generalization of the $\nu=1/2$ fractional quantum Hall phase. These phases might be realized in solid-state or cold-atom nanowires.