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

Abstract

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 Schrödinger equation where electron-and spin interactions are included within the density functional theory in the local spin density approximation. The major advantage of this technique is that it can be directly incorporated into magnetotransport calculations, because it provides the self-consistent eigenstates and wave vectors at a given energy, not at a given wavevector (as conventional methods do). 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. I. INRODUCTIONTransport properties of quantum dots, antidots and related structures are affected by the nature of currentcarrying states in the leads connecting these structures to electron reservoirs. In sufficiently high magnetic fields the current-carrying states are the edge states propagating in a close vicinity to the sample boundaries 1 . A detailed information on the structure of the edge states represent a key to the understanding of various features of the magnetotransport in the quantum Hall regime.A quantitative description of the edge states for the case of the gate-induced confinement of the highmobility two-dimensional electron gas (2DEG) was given by Chklovskii et al.2 , who provided an analytical solution for the positions and widths of the compressible and incompressible strips arising in the 2DEG due to the electrostatic screening. In the compressible regions, the Landau bands are pinned at the Fermi energy E F . This leads to a metallic behavior when the electron density is redistributed (compressed) to keep the electrostatic potential constant. In the incompressible regions, where the Fermi energy lies in the Landau gaps, all the levels below E F are completely filled and hence the electron density is constant (which is consistent with the behavior of the incompressible liquid).A number of studies addressing the problem of electron-electron interaction in quantum wires beyond the electrostatic treatment of the edge states of Chklovskii et al.2 have been reported during the recent decade 3,4,5,6,7,8,9,10,11,12,13,14 . The many-body aspects of the problem have been included within ThomasFermi 3 , Hartree-Fock 4,5,6 , screened Hartree-Fock 7 , and the density functional theory 8,9 . The full quantummechanical calc...

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