$6\pi$ Josephson effect in Majorana box devices

TL;DR

This paper explores the interplay of superconductivity and multi-channel Kondo physics in Majorana devices, revealing a novel 6π Josephson effect with fractionalized charge transfer in a topologically nontrivial setting.

Contribution

It extends previous single-channel Kondo studies to a multi-channel topological context, predicting a 6π Josephson effect with fractional charge transfer in Majorana box devices.

Findings

For Δ ≫ T_K, the Josephson current is 4π-periodic.

For Δ ≪ T_K, a 6π-periodic Josephson relation emerges.

Critical current scales as eΔ²/ħT_K, indicating fractional charge transfer.

Abstract

We study Majorana devices featuring a competition between superconductivity and multi-channel Kondo physics. Our proposal extends previous work on single-channel Kondo systems to a topologically nontrivial setting of non-Fermi liquid type, where topological superconductor wires (with gap $\Delta$) represent leads tunnel-coupled to a Coulomb-blockaded Majorana box. On the box, a spin degree of freedom with Kondo temperature $T_K$ is nonlocally defined in terms of Majorana states. For $\Delta\gg T_K$, the destruction of Kondo screening by superconductivity implies a $4\pi$-periodic Josephson current-phase relation. Using a strong-coupling analysis in the opposite regime $\Delta \ll T_K$, we find a $6\pi$-periodic Josephson relation for three leads, with critical current $I_c\approx e\Delta^2/ \hbar T_K$, corresponding to the transfer of fractionalized charges $e^*=2e/3$.