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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 $mathbf{kcdot p}$ approach. The ballistic transport is analyzed in contacts realized at the (001) interface between band insulators $LaAlO_3$ and $SrTiO_3$ by using the Landauer-Buttiker 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.
Multi-valued logic gates, which can handle quaternary numbers as inputs, are developed by exploiting the ballistic transport properties of quantum point contacts in series. The principle of a logic gate that finds the minimum of two quaternary number
In the ballistic regime, the transport across a normal metal (N)/superconductor (S) point-contact is dominated by a quantum process called Andreev reflection. Andreev reflection causes an enhancement of the conductance below the superconducting energ
We study a superconducting quantum point contact made of a narrow In$_{0.75}% $Ga$_{0.25}$As channel with Nb proximity electrodes. The narrow channel is formed in a gate-fitted constriction of InGaAs/InAlAs/InP heterostructure hosting a two-dimension
We study nonlinear transport and non-equilibrium current noise in quasi-classical point contacts (PCs) defined in a low-density high-quality two-dimensional electron system in GaAs. At not too high bias voltages $V$ across the PC the noise temperatur
The Kondo effect is the many-body screening of a local spin by a cloud of electrons at very low temperature. It has been proposed as an explanation of the zero-bias anomaly in quantum point contacts where interactions drive a spontaneous charge local