Collapse of electrons to a donor cluster in SrTiO${}_3$

Abstract

It is known that a nucleus with charge $Ze$ where $Z>170$ creates electron-positron pairs from the vacuum. These 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 charged impurity with a large charge number $Z$ in narrow-band gap semiconductors and Weyl semimetals as well as graphene. In this paper, a similar effect of electron collapse and charge renormalization is found for donor clusters in SrTiO${}_3$ (STO), but with a very different origin. At low temperatures, STO has an enormously large dielectric constant. Because of this, the nonlinear dielectric response becomes dominant when the electric field is not too small. We show that this leads to the collapse of surrounding electrons into a charged spherical donor cluster with radius $R$ when its total charge number $Z$ exceeds a critical value $Z_c\simeq R/a$ where $a$ is the lattice constant. Using the Thomas-Fermi approach, we find that the net charge $Z_{n}e$ grows with $Z$ until $Z$ exceeds another value $Z^{\ast }\simeq (R/a{)}^{9/7}$. After this point, $Z_n$ remains $\sim Z^{\ast }$. We extend our results to the case of long cylindrical clusters. Our predictions can be tested by creating discs and stripes of charge on the STO surface.

References in corpus (6)

• The Coulomb impurity problem in graphene
• Emergent properties hidden in plane view: Strong electronic correlations at oxide interfaces
• Atomic Collapse and Quasi-Rydberg States in Graphene
• Screening of a hypercritical charge in graphene
• Accumulation, inversion, and depletion layers in SrTiO${}_3$
• Atomic collapse in graphene and cyclic RG flow

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• Space charge and screening of a supercritical impurity cluster in monolayer graphene
• Reconfigurable Oxide Nanoelectronics by Tip-induced Electron Delocalization