Abstract
Linear and non-linear transport properties through an atomic-size point contact based on oxides two-dimensional electron gas is examined using the tight-binding method and the k· p approach. The ballistic transport is analyzed in contacts realized at the (001) interface between band insulators LaAlO₃ and SrTiO₃ by using the Landauer-B\"uttiker method for many sub-bands derived from three Ti 3d orbitals (d_yz, d_zx and d_xy) in the presence of an out-of-plane magnetic field. We focus especially on the role played by the atomic spin-orbit coupling and the inversion symmetry breaking term pointing out three transport regimes: the first, at low energies, involving the first d_xy-like sub-bands, where the conductance quantization is robust; a second one, at intermediate energies, entailing further d_xy-like sub-bands, where the sub-band splitting induced by the magnetic field is quenched; the third one, where the mixing between light d_xy-like, heavy d_yz-like and d_zx-like sub-bands is so strong that the conductance plateaus turn out to be very narrow. Very good agreement is found with recent experiments exploring the transport properties at low energies.