Charge Resistance in a Majorana RC circuit

TL;DR

This paper studies the charge response of a Majorana-based quantum RC circuit, calculating its effective capacitance and resistance, and confirming the resistance value aligns with theoretical predictions for strongly Coulomb-blockaded systems.

Contribution

It provides a detailed calculation of charge relaxation resistance in a Majorana Coulomb box, confirming the resistance value matches the strong Coulomb blockade limit and connecting it with the Fu model.

Findings

Charge relaxation resistance equals h/2e^2.

Effective capacitance depends on Majorana states.

Results agree with the Korringa-Shiba formula.

Abstract

We investigate the dynamical charge response in a "Majorana Coulomb box" realized by two Majorana bound states hosted at the ends of a mesoscopic topological superconductor. One side of the wire is coupled to a normal lead and low frequency gate voltage is applied to the system. There is no dc-current; the system can be considered as an RC quantum circuit. We calculate the effective capacitance and charge relaxation resistance. The latter is in agreement with the Korringa-Shiba formula where, however, the charge relaxation resistance is equal to h/2e^2. This value corresponds to the strong Coulomb blockade limit described by a resonant model formulated by Fu [PRL 104, 056402 (2010)]. We also performed direct calculations using the latter model and defined its parameters by direct comparison with our perturbation theory results.