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

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_ce. The particles of one charge escape to infinity, leaving a screening space charge. The result is that the observable dimensionless impurity charge Q_∞ is less than Z but greater than Z_c. There is a corresponding effect for nuclei with Z>Z _c≈170, however, in the condensed matter setting we find Z _ca 10. Thomas-Fermi theory indicates that Q_∞=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_∞=Z_c set by the reciprocal of material's fine structure constant.