Transport theory for topological Josephson junctions with a Majorana qubit

TL;DR

This paper develops a semiclassical transport theory for topological Josephson junctions incorporating Majorana qubits, revealing complex dynamical effects and their impact on measurable transport phenomena like Shapiro steps.

Contribution

It introduces a comprehensive semiclassical framework derived from a microscopic Hamiltonian to analyze the interplay of Majorana qubits, Josephson phase, and dissipation.

Findings

Identification of qubit-induced charge pumping and spin-orbit torque

Demonstration of dynamical effects on Shapiro steps, including suppression of the first step

Development of equations of motion for the coupled Majorana qubit and Josephson phase

Abstract

We construct a semiclassical theory for the transport of topological junctions starting from a microscopic Hamiltonian that comprehensively includes the interplay among the Majorana qubit, the Josephson phase, and the dissipation process. With the path integral approach, we derive a set of semiclassical equations of motion that can be used to calculate the time evolution of the Josephson phase and the Majorana qubit. In the equations we reveal rich dynamical phenomena such as the qubit induced charge pumping, the effective spin-orbit torque, and the Gilbert damping. We demonstrate the influence of these dynamical phenomena on the transport signatures of the junction. We apply the theory to study the Shapiro steps of the junction, and find the suppression of the first Shapiro step due to the dynamical feedback of the Majorana qubit.