Kitaev ring threaded by a magnetic flux: Topological gap, Anderson localization of quasiparticles, and divergence of supercurrent derivative

TL;DR

This paper investigates a superconducting Kitaev ring with magnetic flux, revealing flux-induced supercurrent jumps, Anderson localization of quasiparticles, and a divergence in supercurrent derivative at the topological transition.

Contribution

It provides analytical and numerical insights into flux-induced supercurrent behavior, quasiparticle localization, and the nature of the topological transition in disordered and clean Kitaev rings.

Findings

Supercurrent exhibits jumps at specific flux values in the topological phase.

Quasiparticles are Anderson localized, preventing resistive current contributions.

Supercurrent derivative diverges logarithmically at the topological transition.

Abstract

We study a superconducting Kitaev ring pierced by a magnetic flux, with and without disorder, in a quantum ring configuration, and in a rf-SQUID one, where a weak link is present. In the rf-SQUID configuration, in the topological phase, the supercurrent shows jumps at specific values of the flux $\Phi^*=\frac{hc}{e}(1/4+n)$, with $n\in\mathbb{N}$. In the thermodynamic limit $\Phi^*$ is constant inside the topological phase, independently of disorder, and we analytically predict this fact using a perturbative approach in the weak-link coupling. The weak link breaks the topological ground-state degeneracy, and opens a spectral gap for $\Phi\neq \Phi^*$, that vanishes at $\Phi^*$ with a cusp providing the current jump. Looking at the quasiparticle excitations, we see that they are Anderson localized, so they cannot carry a resistive contribution to the current, and the localization length shows a peculiar behavior at a flat-band point for the quasiparticles. In the absence of disorder, we analytically and numerically find that the chemical-potential derivative of the supercurrent logarithmically diverges at the topological-to-trivial transition, in agreement with the transition being of the second order.