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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 $sim tln t$. 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.
The quantum phase transition between the three dimensional Dirac semimetal and the diffusive metal can be induced by increasing disorder. Taking the system of disordered $mathbb{Z}_2$ topological insulator as an important example, we compute the sing
The recently discovered three dimensional or bulk topological insulators are expected to exhibit exotic quantum phenomena. It is believed that a trivial insulator can be twisted into a topological state by modulating the spin-orbit interaction or the crystal lattice via odd number of band
Our understanding of topological insulators is based on an underlying crystalline lattice where the local electronic degrees of freedom at different sites hybridize with each other in ways that produce nontrivial band topology, and the search for mat
Three-dimensional topological insulator (TI) nanowires with quantized surface subband spectra are studied as a main component of Majorana bound states (MBS) devices. However, such wires are known to have large concentration $N sim 10^{19}$ cm$^{-3}$
Disorder inevitably exists in realistic samples, manifesting itself in various exotic properties for the topological states. In this paper, we summarize and briefly review work completed over the last few years, including our own, regarding recent de