We measure the chemical potential jump across the fractional gap in the low-temperature limit in the two-dimensional electron system of GaAs/AlGaAs single heterojunctions. In the fully spinpolarized regime, the gap for filling factor ν = 1/3 increases linearly with magnetic field and is coincident with that for ν = 2/3, reflecting the electron-hole symmetry in the spin-split Landau level. In low magnetic fields, at the ground-state spin transition for ν = 2/3, a correlated behavior of the ν = 1/3 and ν = 2/3 gaps is observed.PACS numbers: 73.40. Kp, Plateaux of the Hall resistance corresponding to zeros in the longitudinal resistance at fractional filling factors of Landau levels in two-dimensional (2D) electron systems, known as the fractional quantum Hall effect [1], are believed to be caused by electron-electron interactions (for a recent review, see Ref.[2]). Two theoretical approaches to the phenomenon have been formulated over the years. One approach is based on a trial wave function of the ground state [3], and the other exploits an introduction of composite fermions to reduce the problem to a single-particle one [4,5]. The fractional gap is predicted to be determined by the Coulomb interaction in the form e 2 /εl B (where ε is the dielectric constant and l B = ( c/eB) 1/2 is the magnetic length), which leads to a square-root dependence of the gap on magnetic field, B. Observation of such a behavior would confirm the predicted gap origin.Attempts to experimentally estimate the fractional gap value yielded similar results, at least, in high magnetic fields [6,7,8,9,10]. Still, the expected dependence of the gap on magnetic field has not been either confirmed or rejected. The problems with experimental verification are as follows. Standard measurements of activation energy at the longitudinal resistance minima allow one to determine the mobility gap [6,7] which may be different from the gap in the spectrum. The data for the gap obtained by thermodynamic measurements depended strongly on temperature [8]; for this reason, the magnetic field dependence of the gap may be distorted.In this paper, we report measurements of the chemical potential jump across the fractional gap at filling factor ν = 1/3 and ν = 2/3 in the 2D electron system in GaAs/AlGaAs single heterojunctions using a magnetocapacitance technique. We find that the gap, ∆µ e , increases with decreasing temperature and in the lowtemperature limit, it saturates and becomes independent of temperature. In magnetic fields above ≈ 5 T, the limiting value, ∆µ 0 e , for ν = 1/3 is described with good accuracy by a linear increase of the gap with magnetic field and is practically coincident with the gap for ν = 2/3. In lower magnetic fields, the minimum of the gap ∆µ 0 e at ν = 2/3 occurring at a critical field of ≈ 4 T, which corresponds to ground-state spin transition [11,12,13,14], is accompanied with a change in the behavior of that at ν = 1/3. The correlation between the magnetic field dependences of both gaps indicates the presence of a spin transitio...

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).