The possibility of exploiting the spin degree of electrons' freedom in devices is a promising target and a currently developing field of research. In particular, semiconductor quantum point contacts (QPCs) are interesting candidates for realizing novel spintronics devices. In this work, we present a theoretical study of the electronic conductance in asymmetric semiconductor two-dimensional (2D) quantum constrictions (QPCs) under the influence of lateral spin-orbit effects. The conductance was calculated within Landauer’s formalism of ballistic quantum transport in which the spin-resolved conductance is determined through spin-dependent transmission probabilities of the asymmetric QPC. The asymmetric electrostatic potential defining the quantum construction (QPC) is modeled through a tilted 2D saddle-type hyperbolic profile. The analytical procedure involves the mapping of the 2D-Hamiltonian describing the electrons in the QPC with lateral spin-orbit interactions, to a decoupled 1D-Hamiltonians separable in momentum (p_x; p_y), position (x; y) and spin; the latter using appropriate Meyer-Kucar-Cederbaum unitary transformations. We show that the generic form of the spin-resolved (σ) electron transmission probabilities has a simple dependence T^σ_n =(1+e^–πε_n)^–1, where ε_n is a dimensionless parameter that depends on the confinement energies and the characteristic energies of the QPC, as well as of the intrinsic spin-orbit effect, being n the propagation mode (n=0,1,2,3...). These analytical results further allow us to calculate the asymmetric QPC's total conductance G = (e² /h)∑_n,σ T^σ_nunder various realistic physical-chemical situations.

Arianiy Guzman-Santiago

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