Single magnetic impurities in the Kane-Mele model

TL;DR

This paper investigates the behavior of a magnetic impurity in a 2D topological insulator's edge state using the Anderson model and quantum Monte Carlo simulations, revealing how the Kondo effect manifests in this system.

Contribution

It provides a detailed numerical study of the Kondo effect in the Kane-Mele model's edge states, highlighting the impurity's spectral and spatial properties.

Findings

Spectral properties vary with temperature across different Anderson model regimes.

Spin-spin correlations decay algebraically along the edge near the impurity.

The impurity's influence on edge transport is characterized in the topological insulator context.

Abstract

The realization of the spin-Hall effect in quantum wells has led to a plethora of studies regarding the properties of the edge states of a 2D topological insulator. These edge states constitute a class of one-dimensional liquids, called the helical liquid, where an electron's spin quantization axis is tied to its momentum. In contrast to one dimensional conductors, magnetic impurities - below the Kondo temperature - cannot block transport and one expects the current to circumvent the impurity. To study this phenomenon, we consider the single impurity Anderson model embedded into an edge of a Kane-Mele ribbon with up to 512x80 sites and use the numerically exact continuous time QMC method to study the Kondo effect. We present results on the temperature dependence of the spectral properties of the impurity and the bulk system that show the behaviour of the system in the various regimes of the Anderson model. A view complementary to the single particle spectral functions can be obtained using the spatial behaviour of the spin-spin correlation functions. Here we show the characteristic, algebraic decay in the edge channel near the impurity.