Microwave signatures of Majorana states in a topological Josephson junction

TL;DR

This paper develops a theoretical framework to analyze the microwave admittance of topological Josephson junctions, enabling spectroscopic detection of Majorana states through characteristic features in the frequency and phase dependence.

Contribution

The paper introduces a detailed theoretical model for the microwave admittance of topological Josephson junctions, highlighting how Majorana states influence spectroscopic signatures.

Findings

Resonant frequencies show characteristic kinks at phase bias $\

,

,

Abstract

We find the admittance of a topological Josephson junction $Y(\omega,\varphi_0, T)$ as a function of frequency $\omega$, the static phase bias $\varphi_0$ 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 $\omega_{\mathcal{M}, n} (\varphi_0)$ for transitions involving the Majorana ($\mathcal{M}$) doublet exhibit characteristic kinks in the $\varphi_0$-dependence at $\varphi_0=\pi$. 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.