Superdiffusion in the topological metal

TL;DR

This paper develops a non-perturbative theory revealing superdiffusive quantum dynamics in topological metals, where wave propagation exhibits a growth pattern of t\,ln t, with implications for experimental photonic systems.

Contribution

The study introduces a non-perturbative analytical framework for understanding superdiffusion in topological metals across various disorder strengths and doping levels.

Findings

Superdiffusion characterized by t\,ln t growth in mean squared displacement.

Conductance obeys a scaling law consistent with previous numerical results.

Existence of transparent channels enabling long-time wave propagation.

Abstract

We develop a non-perturbative theory to study large-scale quantum dynamics of Dirac particles in disordered scalar potentials (the so-called "topological metal"). For general disorder strength and carrier doping, we find that at large times, superdiffusion occurs. I.e., the mean squared displacement grows as $\sim t\ln t$. In the static limit, our analytical theory shows that the conductance of a finite-size system obeys the scaling equation identical to that found in previous numerical studies. These results suggest that in the topological metal, there exist some transparent channels -- where waves propagate "freely" -- dominating long-time transport of the system. We discuss the ensuing consequence -- the transverse superdiffusion in photonic materials -- that might be within the current experimental reach.