Collapse of electrons to a donor cluster in SrTiO₃

It is known that a nucleus with charge Ze, where Z > 170, creates electron-positron pairs from the vacuum. Electrons collapse onto the nucleus resulting in a net charge Z_n < Z while the positrons are emitted. This effect is due to the relativistic dispersion law. The same reason leads to the collapse of electrons to the donor cluster with a large charge number Z in narrow-band-gap semiconductors, Weyl semimetals, and graphene. In this paper, a similar effect of electron collapse and charge renormalization is found for a donor cluster in SrTiO₃ (STO), but with a different origin. At low temperatures, STO has an enormously large dielectric constant and the nonlinear dielectric response becomes dominant when the electric field is still small. This leads to the collapse of electrons into a charged spherical donor cluster with radius R when its total charge number Z exceeds a critical value Z_c ≃ R/a where a is the lattice constant. The net charge Z_ne grows with Z until Z exceeds Z∗ ≃ (R/a)^9/7. After this point, the charge of the compact core Z_n remains ≃ Z∗, while the rest Z∗ electrons form a sparse Thomas-Fermi electron atmosphere around it. We show that the thermal ionization of such two-scale atoms easily strips the outer atmosphere while the inner core remains preserved. We extend our results to the case of long cylindrical clusters. We discuss how our predictions can be tested by measuring the conductivity of chains of disks of charge on the STO surface.