Majorana Single-Charge Transistor

We study transport through a Coulomb blockaded topologically nontrivial superconducting wire (with Majorana end states) contacted by metallic leads. An exact formula for the current through this interacting Majorana single-charge transistor is derived in terms of wire spectral functions. A comprehensive picture follows from three different approaches. We find Coulomb oscillations with universal halving of the finite-temperature peak conductance under strong blockade conditions, where the valley conductance mainly comes from elastic cotunneling. The nonlinear conductance exhibits finite-voltage sidebands due to anomalous tunneling involving Cooper pair splitting.

Figure 1

Majorana single-charge transistor (MSCT): The TS wire with Majorana end states is tunnel coupled (${\Gamma }_L$, ${\Gamma }_R$) to normal metal electrodes and Josephson coupled ($E_J$) to another bulk superconductor. Capacitive charging effects are encoded by $E_c$ and can be tuned by a gate voltage parameter $n_g\propto V_g$.

Figure 2

Coulomb oscillations in the MSCT. Main panel: Conductance $G$ vs $n_g$ from the master equation for $E_J=0$, $T=2\Gamma$ and several $E_c$. Inset: Same but from ZBWM for $T=0$, $E_c=5\Gamma$, and several $E_J$.

Figure 3

Peak conductance $G$ vs $E_c/\Gamma$ on a semi-logarithmic scale. Main panel: Comparison of $T=0$ results using perturbation theory in $E_c/\Gamma$ [25] (blue solid curve), the EOM approach (red dotted-solid curve), and the ZBWM (black dashed curve). The shown EOM results are quantitatively valid only for $E_c\gtrsim \Gamma$ (solid part) but give a lower bound when $E_c\lesssim \Gamma$ (dotted part). Here, $E_J=0$ since $G$ only weakly depends on $E_J$ for $E_J\lesssim E_c$. Inset: Same but from the master equation for several temperatures $T>\Gamma$.

Figure 4

$G=dI/dV$ vs voltage $V$ from the master equation for $T=2\Gamma$, $E_J=0$, and several $E_c/\Gamma$. The main panel (inset) is for half-integer (integer) $n_g$.

Figure 5

Same as Fig. 4 but from ZBWM for $T=0$, $E_c=5\Gamma$, and several $E_J$.