Coulomb blockade of Majorana-fermion-induced transport

We study Coulomb charging effects for transport through a topologically nontrivial superconducting wire, where Majorana bound states are present at the interface to normal-conducting leads. We construct the general Keldysh functional integral representation and provide detailed results for the nonlinear current-voltage relation under weak Coulomb blockade conditions.

Figure 1

Setup studied in this work: a topological superconductor (TS) dot containing Majorana bound states at the ends (indicated by black dots) is coupled via tunnel contacts (hybridizations ${\Gamma }_L$ and ${\Gamma }_R$) to normal-conducting (N) metallic electrodes. The charging energy $E_c=e^2/\left(2C\right)$ causes phase fluctuations on the TS dot and influences the current-voltage relation. We assume that the superconducting gap $\Delta$ of the TS is large compared to the other energy scales (i.e., quasiparticle excitations on the dot can be neglected).

Figure 2

Dimensionless linear conductance $g=g(V\to 0)$ vs $E_c/\Gamma$ in the weak-CB regime. The black dashed curve has been obtained from numerical analysis of Eq. (27), with $J\left(t\right)$ in Eq. (35) and $K\left(\omega \right)$ in Eq. (25). The red solid curve gives the analytical result in Eq. (39), which is valid for $E_c\gtrsim \Gamma$.

Figure 3

Dimensionless nonlinear conductance $g\left(V\right)$ vs $eV/\Gamma$ for several values of the charging energy. Results for $E_c>0$ were obtained by numerical integration, the result for $E_c=0$ is exact.