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

In their paper "Origin and Transport Signatures of Spin-Orbit Interactions in One- and Two-Dimensional SrTiO$_3$-Based Heterostructures," Younghyun Kim, Roman M. Lutchyn, and Chetan Nayak investigate the origin of Rashba spin-orbit interaction at SrTiO$_3$ surfaces and LaAlO$_3$/SrTiO$_3$ interfaces by examining the interplay between atomic spin-orbit coupling and inversion asymmetry at the surface or interface. Using a simple tight-binding model involving 3d $t_{2g}$ bands of Ti ions, they demonstrate that the induced spin-orbit coupling in the $d_{xz}$ and $d_{yz}$ bands is cubic in momentum, while the spin-orbit interaction in the $d_{xy}$ band has linear momentum dependence. They also find that the spin-orbit interaction in one-dimensional channels at LaAlO$_3$/SrTiO$_3$ interfaces is linear in momentum for all bands.

Exploring the Origin of Spin-Orbit Interactions in SrTiO$_3$-Based Heterostructures

Spin-orbit interactions (SOI) are an important factor in determining the properties of materials, as they can influence a range of phenomena from magnetism to superconductivity. In their paper "Origin and Transport Signatures of Spin-Orbit Interactions in One- and Two-Dimensional SrTiO$_3$-Based Heterostructures," Younghyun Kim, Roman M. Lutchyn, and Chetan Nayak investigate the origin of Rashba spin-orbit interaction at SrTiO$_3$ surfaces and LaAlO$_3$/SrTiO$_3$ interfaces by examining the interplay between atomic spin-orbit coupling and inversion asymmetry at the surface or interface.

Atomic Spin Orbit Coupling

Atomic spin orbit coupling is a relativistic effect that arises due to the interaction between an electron's orbital angular momentum and its intrinsic spin angular momentum. This results in a splitting of energy levels which depends on both the magnitude of the orbital angular momentum as well as its orientation with respect to an external electric field. The strength of this effect is determined by two parameters: $\lambda$, which is related to the magnitude of orbital angular momentum, and $\eta$, which describes how strongly it couples with electric fields.

Inversion Asymmetry

Inversion symmetry occurs when a system has identical properties before and after being inverted through some transformation such as reflection or rotation about an axis. When this symmetry is broken, it can lead to effects such as Rashba SOI where electrons experience different potentials depending on their direction relative to some reference point within a material's crystal structure. This type of SOI can be used for spintronic applications such as manipulating spins without applying magnetic fields or currents.

The Model

To explore these effects further, Kim et al use a simple tight binding model involving 3d $t_{2g}$ bands of Ti ions at SrTiO${}_{\text{ 3}}$. They demonstrate that induced SOI in $d_{xz}$, $d_{yz}$, and $d_{xy}$ bands have cubic, linear,and linear dependence on momentum respectively for one dimensional channels at LaAlO${}_{\text{ 3}}/$SrTiO${}_{\text{ 3}}$. Furthermore they find that while all three bands show linear dependence on momentum for two dimensional channels at LaAlO${}_{\text{ 3}}/$SrTiO${}_{\text{ 3}}$, only $d_{xy }band shows cubic dependence on momentum for one dimensional channels at SrTi0${} _{\text { 3 }}$. These findings suggest that there may be differences between 1D vs 2D systems when it comes to SOI induced by lattice distortions or strain gradients near surfaces or interfaces .