Origin and Transport Signatures of Spin-Orbit Interactions in One- and Two-Dimensional SrTiO$_3$-Based Heterostructures

TL;DR

This paper investigates the origin and characteristics of Rashba spin-orbit interactions in SrTiO$_3$-based heterostructures, revealing different momentum dependencies in various bands and their effects on transport phenomena.

Contribution

It provides a theoretical analysis of spin-orbit coupling origins in SrTiO$_3$ heterostructures, highlighting band-dependent momentum dependencies and implications for transport experiments.

Findings

Spin-orbit coupling in $d_{xz}$ and $d_{yz}$ bands is cubic in momentum.

Spin-orbit interaction in the $d_{xy}$ band is linear in momentum.

One-dimensional channels exhibit linear momentum dependence in spin-orbit interaction.

Abstract

We study origin of Rashba spin-orbit interaction at SrTiO$_3$ surfaces and LaAlO$_3$/SrTiO$_3$ interfaces by considering the interplay between atomic spin-orbit coupling and inversion asymmetry at the surface or interface. We show that, in a simple tight-binding model involving 3d $t_{2g}$ bands of Ti ions, the induced spin-orbit coupling in the $d_{xz}$ and $d_{yz}$ bands is cubic in momentum whereas the spin-orbit interaction in the $d_{xy}$ band has linear momentum dependence. We also find that the spin-orbit interaction in one-dimensional channels at LaAlO$_3$/SrTiO$_3$ interfaces is linear in momentum for all bands. We discuss implications of our results for transport experiments on SrTiO$_3$ surfaces and LaAlO$_3$/SrTiO$_3$ interfaces. In particular, we analyze the effect of a given spin-orbit interaction term on magnetotransport of LaAlO$_3$/SrTiO$_3$ by calculating weak anti-localization corrections to the conductance and to universal conductance fluctuations.