Microwave signatures of Majorana states in a topological Josephson junction

Abstract

We find the admittance of a topological Josephson junction $Y(ω,φ_0, T)$ as a function of frequency $ω$, the static phase bias $φ_0$ applied to the superconducting leads, and temperature $T$. The dissipative part of $Y$ allows for spectroscopy of the sub-gap states in the junction. The resonant frequencies $ω_{\mathcal{M}, n} (φ_0)$ for transitions involving the Majorana ($\mathcal{M}$) doublet exhibit characteristic kinks in the $φ_0$-dependence at $φ_0=π$. The kinks -- associated with decoupled Majorana states -- remain sharp and the corresponding spectroscopic lines are bright at any temperature, as long as the leads are superconducting. The developed theory may help extracting quantitative information about Majorana states from microwave spectroscopy.