Edge transport in Haldane-like models with quasi-periodic disorder

TL;DR

This paper analyzes edge transport in Haldane-like topological insulators with quasi-periodic disorder, demonstrating quantized conductance and deriving explicit response functions using rigorous renormalization techniques.

Contribution

It provides a rigorous proof of edge conductance quantization and explicit formulas for response functions in disordered topological insulators, extending understanding to quasi-periodic systems.

Findings

Edge conductance is quantized despite disorder.

Explicit expressions for edge conductance and susceptibility.

Boundary correlations match a massless relativistic model at large distances.

Abstract

We consider Haldane-like $2d$ topological insulators on the cylinder, in the presence of weak quasi-periodic disorder. We prove that, at large distances, the boundary correlations agree with the correlations of a renormalized, translation-invariant, massless relativistic model in $1+1$ dimensions, multiplied by non-universal oscillatory factors, incommensurate with the lattice spacing. Furthermore, we compute the edge conductance and the edge susceptibility, starting from Kubo formula. We obtain explicit expressions for these response functions, completely determined by the renormalized Fermi velocity of the edge modes. In particular, we prove the quantization of the edge conductance, and the non-universality of the susceptibility. The proof relies on multiscale analysis and rigorous renormalization group methods for quasi-periodic systems, and on lattice Ward identities.