Spin polarization of edge states and the magnetosubband structure in quantum wires

We provide a quantitative description of the structure of edge states in split-gate quantum wires in the integer quantum Hall regime. We develop an effective numerical approach based on the Green's function technique for the self-consistent solution of Schr\"odinger equation where electron and spin interactions are included within the density functional theory in the local spin density approximation. We use the developed method to calculate the subband structure and propagating states in the quantum wires in perpendicular magnetic field starting with a geometrical layout of the wire. We discuss how the spin-resolved subband structure, the current densities, the confining potentials, as well as the spin polarization of the electron and current densities evolve when an applied magnetic field varies. We demonstrate that the exchange and correlation interactions dramatically affect the magnetosubbands in quantum wires bringing qualitatively new features in comparison to a widely used model of spinless electrons in Hartree approximation.