Charge resistance in a MajoranaRCcircuit

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 $\mathit{RC}$ 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 $h/2{e}^{2}$. This value corresponds to the strong Coulomb blockade limit described by a resonant model formulated by Fu [Phys. Rev. Lett. 104, 056402 (2010)]. We also performed direct calculations using the latter model and defined its parameters by direct comparison with our perturbation theory results.