1,2D.R. Leadley, 2M.S. Daly, 2R.J. Nicholas, 3D.K. Maude, 3J.C. Portal, 4J.J. Harris and 5C.T. Foxon
The energy difference between electron states of spin up and spin down may be reduced by applying hydrostatic pressure. We use this technique to study experimentally the influence of spin splitting on the Fractional Quantum Hall Effect (FQHE) and interpret the results within the composite fermion (CF) framework. Theoretical only one spin state is usually considered, i.e. the electrons are treated either as spinless particles or in the limit of infinite spin splitting. In this limit the FQHE is neatly described by a model of spinless CFs and can be interpreted as an Integer QHE of these CFs, explaining all the features seen for \nu < 1 at high magnetic fields. However when 2 > \nu > 1 and at low fields it is necessary to consider both spin states. By using hydrostatic pressure to tune the Landé g-factor we can investigate the influence of spin splitting. In bulk GaAs the g-factor is -0.44, which is the result of subtracting band structure effects from the free electron value of 2. At higher pressure the band structure contribution reduces, and so does the magnitude of the g-factor which passes through zero at ~20 kbar.
At high pressures, where the g-factor approaches zero, even numerator fractions such as \nu=2/3 and 4/3 are enhanced, with new features appearing at 4/5 and 6/5. Meanwhile the odd numerator fractions are suppressed. This is consistent with removal of the spin degeneracy. For example, with a large spin splitting the state at \nu=2/3 is fully spin polarised and consists of two full CF Landau levels (LLs) formed only from spin-down electrons. When g tends to zero the same particles fill one CF LL of each spin state and so this can be considered as \nu=1/3 for the degenerate system. In the same way 4/5 (initially a weak state formed from second generation CFs) becomes a strong feature as it now corresponds to \nu=2/5. Likewise all the features at odd numerator fractions have half full CF LLs in the degenerate system without an energy gap at the Fermi energy and so do not form quantum Hall states. At high pressure \nu=1 also becomes much weaker. When the g-factor is identically zero this state should vanish, but for any finite spin splitting the g-factor will be enhanced by exchange interactions. The energy gap at exactly \nu=1 and at fields either side is deduced from activation measurements and the results discussed in terms of exciting single particles or Skyrmions across the spin gap.
In particular we study the mixed spin region around \nu=3/2 where the features at \nu=4/3 and 8/5 increase in strength relative to those at 5/3 and 7/5. These results are consistent with changes in spin polarisation brought about by tilting the sample in a magnetic field or changing the electron density. We can explain all the experimental data by considering CF energy level schemes arising from attaching flux tubes either to electrons or to holes depending on the filling of the relevant LLs. For example the energy gap of the 5/3 state corresponds to the Zeeman energy of CF holes, and goes continuously to zero following the single particle electron g-factor enhanced by a factor of two.
Similar effects have previously been observed in bilayer systems where the splitting between symmetric and antisymmetric states is varied by changing the separation between electrons in adjacent 2DEGs. In this case the situation was modelled by assigning an isospin index to each layer. The advantage of the present system is that there is no spatial separation between the two species of particles and so interaction effects should be much greater.
23rd International Conference on the Physics of Semiconductors - Vol. 3, eds. M. Scheffler and R. Zimmermann (World Scientific, Singapore 1996) p. 2539.