Filling factor dependence of the fractional quantum Hall effect gap

TL;DR

This study measures the chemical potential jumps at fractional quantum Hall gaps in 2D electron systems, revealing linear magnetic field dependence and a proportional relationship involving the filling factor denominator.

Contribution

It provides direct measurements of fractional quantum Hall gaps and their dependence on magnetic field and filling factor in GaAs/AlGaAs heterojunctions.

Findings

Gaps are linear in magnetic field with slopes proportional to 1/q.

Chemical potential jump scales with q^{-1} and B^{1/2}.

Partial gap closure occurs when the Fermi level is outside the gap.

Abstract

We directly measure the chemical potential jump in the low-temperature limit when the filling factor traverses the nu = 1/3 and nu = 2/5 fractional gaps in two-dimensional (2D) electron system in GaAs/AlGaAs single heterojunctions. In high magnetic fields B, both gaps are linear functions of B with slopes proportional to the inverse fraction denominator, 1/q. The fractional gaps close partially when the Fermi level lies outside. An empirical analysis indicates that the chemical potential jump for an IDEAL 2D electron system, in the highest accessible magnetic fields, is proportional to q^{-1}B^{1/2}.