Spin liquids from Majorana Zero Modes in a Cooper Box

TL;DR

This paper introduces a method to construct and control diverse interacting spin systems using topological nanowires in Cooper Boxes, enabling the realization of models like the XXZ chain, Ising model, and Yao-Kivelson spin-liquid with Majorana modes.

Contribution

It presents a novel approach to engineer tunable spin models from Majorana zero modes in Cooper boxes, including explicit realizations of various quantum spin systems and a scheme for detecting critical behavior.

Findings

Realization of 1D XXZ and Ising models from Majorana modes.

Proposal for detecting critical points via local gate voltages.

Scheme for creating a 2D topologically ordered spin-liquid.

Abstract

We propose a path for constructing diverse interacting spin systems from topological nanowires in Cooper Boxes. The wires are grouped into a three-wire building block called an 'hexon', consisting of six Majorana zero modes. In the presence of a strong charging energy, the hexon becomes a Cooper box equivalent to two spin-$1/2$ degrees of freedom. By considering arrays of hexons and controlling the distances between the various wires, one can tune the Hamiltonian governing the low-energy spins, thus providing a route for controllably constructing interacting spin systems in one- and two-dimensions. We explicitly present realizations of the one-dimensional spin-$1/2$ XXZ chain, as well as the transverse field Ising model. We propose an experiment capable of revealing the nature of critical points in such effective spin systems by applying a local gate voltage and measuring the induced charge at a distance. To demonstrate the applicability of this approach to two-dimensions, we provide a scheme for realizing the topologically ordered Yao-Kivelson spin-liquid model, which has a collective Majorana edge mode, similar to the B-phase of Kitaev's honeycomb model.