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 electronhole pairs when the total charge Ze of the impurity exceeds a value Zce. 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 Zc. There is a corresponding effect for nuclei with Z > Zc ≈ 170, however, in the condensed matter setting we find Zc 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∞ = Zc set by the reciprocal of material’s fine structure constant.