Probing the semiconductor-to-dirac semimetal transition in Na-Sb-Bi alloys with x-ray Compton scattering

We discuss electron redistribution during the semiconductor-to-Dirac semimetal transition in Na-Sb-Bi alloys using x-ray Compton scattering experiments combined with first-principles electronic structure modeling. A robust signature of the semiconductor-to-Dirac semimetal transition is identified in the spherically averaged Compton profile. We demonstrate how the number of electrons involved in this transition can be estimated to provide a novel descriptor for quantifying the strength of spin-orbit coupling responsible for driving the transition. The associated theoretical deviation of the Born charge of Na in Na$_3$Bi from the expected ionic charge of +1 is found to be consistent with the corresponding experimental value of about 10%. Our study also shows the sensitivity of the Compton scattering technique toward capturing the spillover of Bi 6p relativistic states onto Na sites.