On the dependence on the magnetic field orientation of the composite fermion effective mass

Abstract

The composite fermion (CF) model has been strikingly successful in describing many aspects of the fractional quantum Hall effect (FQHE) observed in two-dimensional electron systems (2DES). In the CF picture, the FQHE is the integer quantum Hall effect of the CFs. In order to assess the effect of an in-plane magnetic field on the CFs we have examined the temperature dependence of the oscillations in in a high-mobility GaAs - (Ga, Al)As heterojunction close to Landau level filling factors and for many different values of , the angle between the normal to the 2DES and the magnetic field. The CF energy gaps were evaluated at each angle using a variant of the Lifshitz - Kosevich approach. Close to , it was found that the CF gaps at each angle could be fitted to within experimental errors using a constant CF effective mass. However, the CF effective mass was found not to follow the -dependence expected for a purely 2D system; i.e. the CF energy gap at fixed grows markedly with increasing in-plane field. Around the situation is more complex, and the oscillations of the energy gaps at and as varied were interpreted using a recent model of two independent CF Landau fans separated by the Pauli spin splitting (Du R R, Yeh A S, Stormer H L, Tsui D C, Pfeiffer L N and West K W 1995 Phys. Rev. Lett. 75 3926). However, whilst the model qualitatively predicts some of the behaviour of the -minima, it is unable to account for the absolute sizes of the energy gaps. In order to reproduce the gaps at and quantitatively, an angle-dependent CF mass (as observed close to ) is required. The data suggest that the compression of the electronic wave function due to the in-plane field and exchange effects both play a role in determining the size of the CF gaps and cast doubts on the supposed `universal' behaviour of the CF mass.