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We formulate the effective Hamiltonian of Rashba spin-orbit coupling (RSOC) in $mathrm{LaAlO_3/SrTiO_3}$ (LAO/STO) heterostructures. We derive analytical expressions of properties, e.g., Rashba parameter, effective mass, band edge energy and orbital occupancy, as functions of material and tunable heterostructure parameters. While linear RSOC is dominant around the $Gamma$-point, cubic RSOC becomes significant at the higher-energy anti-crossing region. We find that linear RSOC stems from the structural inversion asymmetry (SIA), while the cubic term is induced by both SIA and bulk asymmetry. Furthermore, the SOC strength shows a striking dependence on the tunable heterostructure parameters such as STO thickness and the interfacial electric field which is ascribed to the quantum confinement effect near the LAO/STO interface. The calculated values of the linear and cubic RSOC are in agreement with previous experimental results.
Rashba spin splitting in two-dimensional (2D) semiconductor systems is generally calculated in a ${bf k} cdot {bf p}$ Luttinger-Kohn approach where the spin splitting due to asymmetry emerges naturally from the bulk band structure. In recent years, s
The gating effect achieved by an ionic liquid and its electric double layer allows for charge transfer which can be an order of magnitude larger than with conventional dielectrics. However, the large charged ions also causes inevitable Coulomb scatte
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