Electron gas induced in SrTiO${}_3$

Abstract

This mini-review is dedicated to the 85th birthday of Prof. L. V. Keldysh, from whom we have learned so much. In this paper we study the potential and electron density depth profiles in surface accumulation layers in crystals with a large and nonlinear dielectric response such as SrTiO${}_3$ (STO) in the cases of planar, spherical and cylindrical geometries. The electron gas can be created by applying an induction $D_0$ to the STO surface. We describe the lattice dielectric response of STO using the Landau-Ginzburg free energy expansion and employ the Thomas-Fermi (TF) approximation for the electron gas. For the planar geometry we arrive at the electron density profile $n(x)\propto (x+d{)}^{-12/7}$, where $d\propto D_0^{-7/5}$. We extend our results to overlapping electron gases in GTO/STO/GTO multi-heterojunctions and electron gases created by spill-out from NSTO (heavily $n$-type doped STO) layers into STO. Generalization of our approach to a spherical donor cluster creating a big TF atom with electrons in STO brings us to the problem of supercharged nuclei. It is known that for an atom with nuclear charge $Ze$, where $Z>170$, electrons collapse onto the nucleus resulting in a net charge $Z_n<Z$. Here, instead of relativistic physics, the collapse is caused by the nonlinear dielectric response. Electrons collapse into the charged spherical donor cluster with radius $R$ when its total charge number $Z$ exceeds the critical value $Z_c\simeq R/a$, where $a$ is the lattice constant. The net charge $e{Z}_n$ grows with $Z$ until $Z$ exceeds $Z^{\ast }\simeq (R/a{)}^{9/7}$. After this point, the charge number of the compact core $Z_n$ remains $\simeq Z^{\ast }$, with the rest $Z^{\ast }$ electrons forming a sparse Thomas-Fermi electron atmosphere around it. We extend our results to the case of long cylindrical clusters as well.

mini-review dedicated to the 85th birthday of Prof. L. V. Keldysh

References in corpus (11)

• 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
• Strong electronic correlation and strain effects at the interfaces between polar and nonpolar complex oxides
• Interface-induced magnetism in perovskite quantum wells
• Accumulation, inversion, and depletion layers in SrTiO${}_3$
• Fractionally delta-doped oxide superlattices for higher carrier mobilities
• Separation of transport lifetimes in SrTiO3-based two-dimensional electron liquids
• Atomic collapse in graphene and cyclic RG flow
• Collapse of electrons to a donor cluster in SrTiO${}_3$

Cited by in corpus (5)

• Electronic structure of FeSe monolayer superconductors
• Electronic structure of FeSe monolayer superconductors: shallow bands and correlations
• Universality of Electron Mobility in LaAlO${}_3$/SrTiO${}_3$ and bulk SrTiO${}_3$
• Anomalous Thermodynamic Properties of Electron Accumulation Layer in SrTiO${}_3$
• Reconfigurable Oxide Nanoelectronics by Tip-induced Electron Delocalization