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Weyl semimetals harbor topological Fermi-arc surface states which determinethe nontrivial charge current response to external fields. We here study thequasiparticle decay rate of Fermi arc states arising from their coupling toacoustic phonons, as well as the phonon-limited conductivity tensor for a cleanWeyl semimetal slab. Using the phonon modes for an isotropic elastic continuumwith a deformation potential coupling to electrons, we determine thetemperature dependence of the quasiparticle decay rate, both near and far awayfrom the arc termination points. By solving the coupled Boltzmann equations forthe bulk and arc state distribution functions in the slab geometry, we show howthe linear response conductivity depends on key parameters such as thetemperature, the chemical potential, the geometric shape of the Fermi arcs, orthe slab width. The chiral nature of Fermi arc states causes an enhancement ofthe longitudinal conductivity along the chiral direction at low temperatures,together with a 1/T^2 scaling regime at intermediate temperatures withoutcounterpart for the conductivity along the perpendicular direction.

Phonon-limited Transport and Fermi Arc Lifetime in Weyl Semimetals