Kondo lattice on the edge of a two-dimensional topological insulator

TL;DR

This paper investigates the phase diagram of a quantum impurity on the edge of a 2D topological insulator, revealing a large local moment region and novel phases due to strong interactions and Kondo coupling.

Contribution

It provides an exact solution at the decoupling point and a renormalization group analysis to explore strong electron-electron interactions and Kondo effects on the edge.

Findings

Large local moment region identified for antiferromagnetic Kondo coupling.

Gapless phase persists at half-filling unless Luttinger parameter < 1/2.

Strong interactions can induce a gapped phase with Ising antiferromagnetic order.

Abstract

We revisit the problem of a single quantum impurity on the edge of a two-dimensional time-reversal invariant topological insulator and show that the zero temperature phase diagram contains a large local moment region for antiferromagnetic Kondo coupling which was missed by previous poor man's scaling treatments. The combination of an exact solution at the so-called decoupling point and a renormalization group analysis \`a la Anderson-Yuval-Hamann allows us to access the regime of strong electron-electron interactions on the edge and strong Kondo coupling. We apply similar methods to the problem of a regular one-dimensional array of quantum impurities interacting with the edge liquid. When the edge electrons are at half-filling with respect to the impurity lattice, the system remains gapless unless the Luttinger parameter of the edge is less than 1/2, in which case two-particle backscattering effects drive the system to a gapped phase with long-range Ising antiferromagnetic order. This is in marked contrast with the gapped disordered ground state of the ordinary half-filled one-dimensional Kondo lattice.