Unique quantum impurity states driven by a vortex in topological superconductors

TL;DR

This paper uncovers unique impurity-induced in-gap states in topological superconductors driven by vortex interactions, revealing complex quantum phase transitions and spin-resolved features relevant for quantum computation.

Contribution

It provides the first accurate solution demonstrating how impurity, vortex, and Majorana zero modes produce novel in-gap states and quantum phase transitions in topological superconductors.

Findings

Identification of in-gap states distinct from YSR states

Observation of a singlet-doublet quantum phase transition

Detection of a robust zero-energy peak with opposite spin polarization

Abstract

The interplay of magnetic impurity and vortex in a topological superconductor is of fundamental interest with major implications for implementing quantum computation. There are multiple degrees of freedom interacting with the impurity in the system, including the Majorana zero mode (MZM), the Caroli de Gennes Matricon (CdGM) states, and the electron bulk states that form Cooper pairs, which makes the impurity pinned vortex state elusive to date in topological superconductors. Here, we present an accurate solution of the problem, based on a generalized mapping scheme and the density-matrix renormalization group (DMRG) method. We identify in-gap states that are distinct from the established Yu-Shiba-Rusinov (YSR) states. The newly found in-gap physics is driven by three prominent mechanisms: (i) the coupling of impurity and bulk states leading to competition between Kondo screening and Cooper pairing, resulting in a singlet-doublet quantum phase transition, (ii) the coupling of impurity and CdGM states introducing an effective Zeeman splitting to the doublet state, and (iii) the coupling of impurity and MZM turning the singlet-doublet transition into a crossover. These mechanisms cooperatively produce a unique spin-resolved local density of states. Despite the MZM, a robust nearly zero-energy peak is generated, with comparable height but opposite spin polarization as that of the MZM. These results signify novel emergent physics and offer insights to elucidate intriguing experimental phenomena.