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The Half-Full Landau Level

At even-denominator Landau level filling fractions, such as $ν=1/2$, the ground state, in most cases, has no energy gap, and there is no quantized plateau in the Hall conductance. Nevertheless, the states exhibit non-trivial low-energy phenomena. Open questions concerning the proper description of these systems have attracted renewed attention during the last few years. Issues at $ν=1/2$ include consequences of particle-hole symmetry, which should be present for a spin-aligned system in the limit where one can neglect mixing between Landau levels. Other issues concern questions of anisotropy and geometry, properties at non-zero temperature, and effects of relatively strong disorder. In cases where one does find a gapped even-denominator quantized Hall state, such as $ν=5/2$ in GaAs structures, major questions have arisen about the nature of the quantum state, which will be discussed briefly in this chapter. The chapter will also discuss phenomena that can occur in a two-component system near half filling, i.e., when the total filling factor $ν_{\rm{tot}} $ is close to 1.