Even-Denominator States

Abstract

When the denominator of the Landau-level filling factor is odd, the fractional quantum Hall effect is obtained with suitable interactions. On the other hand, the quantum Hall effect is not observed for even-denominator filling factors of the lowest Landau level, except for the systems considered in the previous chapter, namely systems with spin degeneracy and bilayer systems which can be represented by pseudospins. What happens at even-denominator filling factors in the ground state? This question was almost ignored until 1989, when several anomalous phenomena began to be observed around v = 1/2. These observations aroused interest in the even-denominator states, and it has been shown the composite-fermion mean-field theory is quite effective at this filling factor. In this theory, an even-denominator state is reduced to a system of fermions in the absence of a magnetic field, and various experimental facts can be understood. In this chapter we first introduce the anomalous phenomena which triggered the theoretical developments, and give explanations for these phenomena by using the composite-fermion theory. The theory led to proposals for experiments to confirm the concepts. We shall explain these proposals and the results of the experiments.