Quantum transport in coupled Majorana box systems

TL;DR

This paper provides a theoretical analysis of quantum transport in coupled Majorana box systems, revealing how multi-box interactions influence low-energy transport properties and the potential for testing Majorana qubit nonlocality.

Contribution

It develops a comprehensive low-energy theory for multi-terminal Majorana box systems, including nonperturbative analysis of coupled boxes with non-conserved fermion parities.

Findings

Reproduces the topological Kondo effect for a single Majorana box.

Extends the theory to multiple coupled boxes with additional Pauli operators.

Provides a renormalization group analysis and strong-coupling solutions.

Abstract

We present a theoretical analysis of low-energy quantum transport in coupled Majorana box devices. A single Majorana box represents a Coulomb-blockaded mesoscopic superconductor proximitizing two or more long topological nanowires. The box thus harbors at least four Majorana zero modes (MZMs). Setups with several Majorana boxes, where MZMs on different boxes are tunnel-coupled via short nanowire segments, are key ingredients to recent Majorana qubit and code network proposals. We construct and study the low-energy theory for multi-terminal junctions with normal leads connected to the coupled box device by lead-MZM tunnel contacts. Transport experiments in such setups can test the nonlocality of Majorana-based systems and the integrity of the underlying Majorana qubits. For a single box, we recover the previously described topological Kondo effect which can be captured by a purely bosonic theory. For several coupled boxes, however, non-conserved local fermion parities require the inclusion of additional local sets of Pauli operators. We present a renormalization group analysis and develop a nonperturbative strong-coupling approach to quantum transport in such systems. Our findings are illustrated for several examples, including a loop qubit device and different two-box setups.