Diffusive transport in Weyl semimetals

TL;DR

This paper investigates diffusive transport in Weyl semimetals, revealing an unconventional, slower diffusion process with stretched exponential relaxation, and emphasizes the importance of transport lifetime over quasiparticle lifetime in calculations.

Contribution

The study introduces a new analytical approach to incorporate anisotropic disorder into diffusion calculations in Weyl semimetals, highlighting the significance of transport lifetime.

Findings

Discovered a slower, unconventional diffusion process in Weyl semimetals.

Identified stretched exponential decay in relaxation processes.

Proposed an experimental method to observe this diffusion phenomenon.

Abstract

Diffusion, a ubiquitous phenomenon in nature, is a consequence of particle number conservation and locality, in systems with sufficient damping. In this paper we consider diffusive processes in the bulk of Weyl semimetals, which are exotic quantum materials, recently of considerable interest. In order to do this, we first explicitly implement the analytical scheme by which disorder with anisotropic scattering amplitude is incorporated into the diagrammatic response-function formalism for calculating the `diffuson'. The result thus obtained is consistent with transport coefficients evaluated from the Boltzmann transport equation or the renormalized uniform current vertex calculation, as it should be. We thus demonstrate that the computation of the diffusion coefficient should involve the transport lifetime, and not the quasiparticle lifetime. Using this method, we then calculate the density response function in Weyl semimetals and discover an unconventional diffusion process that is significantly slower than conventional diffusion. This gives rise to relaxation processes that exhibit stretched exponential decay, instead of the usual exponential diffusive relaxation. This result is then explained using a model of thermally excited quasiparticles diffusing with diffusion coefficients which are strongly dependent on their energies. We elucidate the roles of the various energy and time scales involved in this novel process and propose an experiment by which this process may be observed.