Fractional Charge Experiments: What quantity is measured in quantum Hall effect or calculated by Laughlin?

Abstract

We have examined the experiments performed by Goldman and Su, de-Picciotto et al, Samanadayar et al and Conforti et al in which it is claimed that a fractional charge of e/3 is found. In all of the measurements, the quantity measured is the product of the charge and the magnetic field but not the charge. It is possible to interpret that charge per unit area has been measured, where the area is the square of the magnetic length. This type of correction to Laughlin's result does not affect the exactness of the calculation. Anderson has suggested the extension of Laughlin's state to particles of charge 2/m or 3/m with m=odd integer. We find that the quasiparticle charge depends on the angular momenta, e_{eff}/e=({\it l}+(1/2)\pm s)/(2{\it l}+1) which agrees with the data. Therefore, Laughlin's 1/odd becomes an angular momentum so the charge depends on spin, s.