Crystallographic defects in Weyl semimetal LaAlGe

Crystallographic defects in a topological semimetal can result in charge doping, and the scattering due to the defects may mask its exotic transport properties. Here, we investigate the possible crystallographic defects including vacancy and antisite in Weyl semimetal LaAlGe using hybrid-density-functional theory calculations. We show that a considerable concentration of Al- and Ge-related defects naturally form during growth due to their low formation enthalpy. Specifically, Al can be easily replaced by Ge in the $I4_1md$ phase of LaAlGe, forming the Ge-on-Al antisite, Ge$_{\rm Al}$. The counterpart, Al-on-Ge (Al$_{\rm Ge}$), is also probable. The most abundant defect Ge$_{\rm Al}$ is donor-like, effectively electron-doping, and these defects are therefore not only scattering centers in the electronic transport process but may also induce the substantial vertical shift of the chemical potential. The results imply that the naturally occurring defects hinder both spectroscopic and transport features arising from the Weyl physics in LaAlGe. Our work can be applied to the $R$AlGe family ($R$=rare earth) and help improve the quality of single-crystal magnetic Weyl semimetal.