Relativistic suppression of Auger recombination in Weyl semimetals

Abstract

Auger recombination (AR) being electron-hole annihilation with energy-momentum transfer to another carrier is believed to speed up in materials with small band gap. We theoretically show that this rule is violated in gapless three-dimensional materials with ultra-relativistic electron-hole dispersion, Weyl semimetals (WSM). Namely, AR is prohibited by energy-momentum conservation laws in prototypical WSM with a single Weyl node, even in the presence of anisotropy and tilt. In real multi-node WSM, the geometric dissimilarity of nodal dispersions enables weak inter-node AR, which is further suppressed by strong screening due to large number of nodes. While partial AR rates between the nodes of the same node group are mutually equal, the inter-group processes are non-reciprocal, so that one of groups is geometrically protected from AR. Our calculations show that geometrical protection can help prolonging AR lifetime by the two orders of magnitude, up to the level of nanoseconds.