Quantum interference effects of out-of-plane confinement on two-dimensional electron systems in oxides

• Main Authors: Santander-Syro, A. F, Dai, J, R ödel, T. C, Frantzeskakis, E, Fortuna, F, Weht, R, Rozenberg, M. J
• Format: Journal Article
• Language: English
• Published: 10-07-2020
• Subjects: Physics - Strongly Correlated Electrons
• DOI: 10.48550/arxiv.2007.05605

It was recently discovered that a conductive, metallic state is formed on the
surface of some insulating oxides. Firstly observed on SrTiO$_3$(001), it was
then found in other compounds as diverse as anatase TiO$_2$, KTaO$_3$,
BaTiO$_3$, ZnO, and also on different surfaces of SrTiO$_3$ (or other oxides)
with different symmetries. The spatial extension of the wave function of this
electronic state is of only a few atomic layers. Experiments indicate its
existence is related to the presence of oxygen vacancies induced at or near the
surface of the oxide. In this article we present a simplified model aimed at
describing the effect of its small spatial extension on measurements of its 3D
electronic structure by angular resolved photoemission spectroscopy (ARPES).
For the sake of clarity, we base our discussion on a simple tight binding
scheme plus a confining potential that is assumed to be induced by the oxygen
vacancies. Our model parameters are, nevertheless, obtained from density
functional calculations. With this methodology we can explain from a very
simple concept of selective interference the "wobbling", i.e., the
photoemission intensity modulation and/or apparent dispersion of the Fermi
surface and spectra along the out-of-plane ($k_z$) direction, and the "mixed
2D/3D" characteristics observed in some experiments. We conclude that the
critical model parameters for such an effect are the relative strength of the
electronic hopping of each band and the height/width aspect ratio of the
surface confining potential. By considering recent photoemission measurements
under the light of our findings, we can get relevant information on the
electronic wave functions and of the nature of the confining potential.