Magnetosubband and edge state structure in cleaved-edge overgrown quantum wires

TL;DR

This paper systematically analyzes the structure of edge states and magnetosubband evolution in hard wall quantum wires under strong magnetic fields, revealing unique features like a deep potential well and absence of compressible strips compared to smooth confinement.

Contribution

It provides a detailed self-consistent Green's function analysis of edge states in hard wall quantum wires, highlighting differences from smooth confinement and the formation of a potential well near boundaries.

Findings

Deep triangular potential well forms near wire edges.

Magnetosubband depopulation occurs from the center outward.

Spin polarization shows a double-loop pattern with magnetic field.

Abstract

We provide a systematic quantitative description of the structure of edge states and magnetosubband evolution in hard wall quantum wires in the integer quantum Hall regime. Our calculations are based on the self-consistent Green's function technique where the electron- and spin interactions are included within the density functional theory in the local spin density approximation. We analyze the evolution of the magnetosubband structure as magnetic field varies and show that it exhibits different features as compared to the case of a smooth confinement. In particularly, in the hard-wall wire a deep and narrow triangular potential well (of the width of magnetic length $l_B$) is formed in the vicinity of the wire boundary. The wave functions are strongly localized in this well which leads to the increase of the electron density near the edges. Because of the presence of this well, the subbands start to depopulate from the central region of the wire and remain pinned in the well region until they are eventually pushed up by increasing magnetic field. We also demonstrate that the spin polarization of electron density as a function of magnetic field shows a pronounced double-loop pattern that can be related to the successive depopulation of the magnetosubbands. In contrast to the case of a smooth confinement, in hard-wall wires the compressible strips do not form in the vicinity of wire boundaries and spatial spin separation between spin-up and spin-down states near edges is absent.