Spin liquids from Majorana Zero Modes in a Cooper Box
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- 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- 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.
Keywords
Cite
@article{arxiv.1806.03304,
title = {Spin liquids from Majorana Zero Modes in a Cooper Box},
author = {Eran Sagi and Hiromi Ebisu and Yukio Tanaka and Ady Stern and Yuval Oreg},
journal= {arXiv preprint arXiv:1806.03304},
year = {2019}
}