The quenching of compressible edge states around antidots

TL;DR

This paper systematically analyzes the structure of edge states around quantum antidots in the integer quantum Hall regime, revealing limitations of electrostatic models and the significant role of exchange interactions in spin-dependent edge state formation.

Contribution

It provides a quantitative comparison of electrostatic and density functional theory approaches, highlighting the impact of spin effects on edge state structures around antidots.

Findings

Electrostatic models overestimate compressible strip widths.

Exchange interactions suppress certain compressible strips.

Inner spin-up related compressible strips do not form in antidots.

Abstract

We provide a systematic quantitative description of the edge state structure around a quantum antidot in the integer quantum Hall regime. The calculations for spinless electrons within the Hartree approximation reveal that the widely used Chklovskii et al. electrostatic description greatly overestimates the widths of the compressible strips; the difference between these approaches diminishes as the size of the antidot increases. By including spin effects within density functional theory in the local spin-density approximation, we demonstrate that the exchange interaction can suppress the formation of compressible strips and lead to a spatial separation between the spin-up and spin-down states. As the magnetic field increases, the outermost compressible strip, related to spin-down states starts to form. However, in striking contrast to quantum wires, the innermost compressible strip (due to spin-up states) never develops for antidots.