Activation gaps for the fractional quantum Hall effect: realistic treatment of transverse thickness

TL;DR

This paper calculates activation gaps for fractional quantum Hall states considering realistic transverse thickness effects, showing significant corrections and differing behaviors based on interaction range, bridging theory and experiment.

Contribution

It introduces a realistic treatment of transverse thickness in calculating activation gaps, improving agreement with experimental data for fractional quantum Hall states.

Findings

Finite thickness causes about 30% correction to the activation gap.

Longer-range interactions stabilize fractional quantum Hall states, shorter-range interactions destabilize them.

Theoretical gaps are closer to experimental values when finite thickness is included.

Abstract

The activation gaps for fractional quantum Hall states at filling fractions $\nu=n/(2n+1)$ are computed for heterojunction, square quantum well, as well as parabolic quantum well geometries, using an interaction potential calculated from a self-consistent electronic structure calculation in the local density approximation. The finite thickness is estimated to make $\sim$30% correction to the gap in the heterojunction geometry for typical parameters, which accounts for roughly half of the discrepancy between the experiment and theoretical gaps computed for a pure two dimensional system. Certain model interactions are also considered. It is found that the activation energies behave qualitatively differently depending on whether the interaction is of longer or shorter range than the Coulomb interaction; there are indications that fractional Hall states close to the Fermi sea are destabilized for the latter.