Fermion space charge in narrow-band gap semiconductors, Weyl semimetals and around highly charged nuclei

Abstract

The field of charged impurities in narrow-band gap semiconductors and Weyl semimetals can create electron-hole pairs when the total charge $Ze$ of the impurity exceeds a value $Z_{c}e$. The particles of one charge escape to infinity, leaving a screening space charge. The result is that the observable dimensionless impurity charge $Q_{\infty }$ is less than $Z$ but greater than $Z_c$. There is a corresponding effect for nuclei with $Z>Z_c\approx 170$, however in the condensed matter setting we find $Z_c\simeq 10$. Thomas-Fermi theory indicates that $Q_{\infty }=0$ for the Weyl semimetal, but we argue that this is a defect of the theory. For the case of a highly-charged recombination center in a narrow band-gap semiconductor (or of a supercharged nucleus), the observable charge takes on a nearly universal value. In Weyl semimetals the observable charge takes on the universal value $Q_{\infty }=Z_c$ set by the reciprocal of material's fine structure constant.

14 pages, 1 table and 1 figure

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