Methods to measure the charge of the quasiyarticles in the fractional quantum Hall effect

This paper proposes various experimental conditions under which the longitudinal resistance of a two-dimensional electron gas in a high transverse magnetic field could be dependent on the charge of quasiparticle excitations. The objective is to establish a method to directly measure the charge of these excitations, which are responsible for the dissipative portion of the current. The methodology involves analyzing the observable effects in the resistance measurements that would indicate the presence of quasiparticles with fractional charge, a prediction of the fractional quantum Hall effect theory. The results suggest that while earlier arguments by Laughlin demonstrated that the Hall conductance reflects quasiparticle charge, the relationship was indirect, as the Hall current is predominantly carried by the collective motion of the electron gas. This study aims to reinforce the necessity of observing measurable effects that are directly attributable to quasiparticles, in an effort to substantiate theoretical predictions with experimental evidence.