Theory of the fractional quantum Hall effect

Abstract

A theoretical framework is presented which provides a unified description of the integer and the fractional quantum Hall effects. The main assertion is that new candidate incompressible states can be constructed by taking products of some known incompressible states, and all incompressible states can thus be generated starting from the states at integer filling factors. The crucial difference from previous theories is that the higher Landau levels play an essential role in identifying the correlations responsible for the fractional quantum Hall effect. The quasiparticle excitations of the fractional states can be understood simply in this approach by analogy to the quasiparticles of the integer states. Numerical results show that these trial states very accurately describe the transition from the 1/3 state to the 2/5 state for a four-electron system. It is further shown that the predictions of the theory are completely consistent with the phenomenology of the fractional quantum Hall effect; in particular, the predicted order of stability of the various fractions is in agreement with experiments. Even though the fractional quantum Hall effect is found to be possible at all rational filling factors in this approach, it is indicated why the odd-denominator fractions are in general more stable than the even-denominator ones.