Quantum impurity coupled to Majorana edge fermions

TL;DR

This paper investigates how quantum impurities interact with Majorana edge states in topological superconductors, revealing distinct magnetic and non-magnetic impurity behaviors and their implications for quantum impurity models.

Contribution

It maps the impurity problem onto a variant of the Kondo model and analyzes magnetic and non-magnetic impurities using bosonization and NRG techniques.

Findings

Magnetic impurities flow to a fixed point with residual entropy ln 2.

Non-magnetic impurities flow to a fixed point with no residual entropy.

Magnetic impurities show anisotropic susceptibilities and diamagnetic responses at low temperatures.

Abstract

We study a quantum impurity coupled to the edge states of a two-dimensional helical topological superconductor, i.e., to a pair of counterpropagating Majorana fermion edge channels with opposite spin polarizations. For an impurity described by the Anderson impurity model, we show that the problem maps onto a variant of the interacting resonant two-level model which, in turn, maps onto the ferromagnetic Kondo model. Both magnetic and non-magnetic impurities are considered. For magnetic impurities, the bosonization and numerical renormalization group analyses show that the system flows to a fixed point with residual ln 2 entropy and we find characteristically anisotropic static and dynamic impurity magnetic susceptibilities. For non-magnetic impurities, the system flows to a fixed point with no residual entropy and we find diamagnetic response at low temperatures. We comment on the Schrieffer-Wolff transformation for problems with non-standard conduction band continua and on the issues related to the differences in describing the impurities by either Anderson or Kondo impurity models.