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The width of the Hall plateau and the activation energy were measured in the bilayer quantum Hall state at filling factors n 2, 1, and 2͞3 by changing the total electron density and the density ratio in the two quantum wells. Their behaviors are remarkably different. The n 1 state is found to be stable over all measured range of the density difference. The n 2͞3 state is stable only around the balanced point. The n 2 state shows a phase transition between these two types of states as the electron density is changed. [S0031-9007(98)06109-2] PACS numbers: 73.40.Hm, 72.20.My, 73.20.Dx, 73.40.Kp Electron systems in confined geometries exhibit a rich variety of physical properties due to the interaction effects in reduced dimensions. One of the most interesting phenomena is the quantum Hall (QH) effect in the planar electron system. In particular, the QH effect in double quantum wells has recently attracted much attention [1,2], where the structure introduces additional degrees of freedom in the third direction. Various bilayer QH states are realized [3,4] by controlling system parameters such as the strengths of the interlayer and intralayer Coulomb interaction, the tunneling interaction, and the Zeeman effect. A good example is the n 1͞2 state [4] for which there is no counterpart in the monolayer system. Here, n is the total filling factor. It has also been pointed out [5,6] that a novel interlayer quantum coherence (IQC) may develop spontaneously in the n 1͞m state with m being an odd integer. Murphy et al. [7] have reported an anomalous activation energy dependence in the bilayer n 1 QH state on the tilted magnetic field, which is probably one of the signals [8,9] of the IQC. Another unique feature of this IQC [10] is that the QH state is stable at any electron density ratio n f ͞n b , where n f (n b ) is the electron density in the front (back) quantum wells.So far the QH states at n odd integers have been extensively investigated from the viewpoints of "phase transition" due to the interlayer correlation. The n 2 bilayer QH state has attracted less attention because it has been thought of as a simple "compound" state with n 1 1 1 made of two noninteracting monolayer n 1 states.In this Letter we report the width of the Hall plateau and the activation energy in three typical bilayer QH states at n 2͞3, 1, and 2 by changing the total electron density n t n f 1 n b as well as the density ratio n f ͞n b . By changing the total density, we can change the ratio of the interlayer to the intralayer Coulomb interactions, which governs the basic nature of the bilayer QH states. Furthermore, the stability of the bilayer QH state, which is quite sensitive to the density ratio in general, is also tested to clarify the origin of the QH state. The behaviors of these three states have been found to be remarkably different. The n 2͞3 state is identified as a compound state with n 1͞3 1 1͞3, whereas the n 1 state is found to be the "coherent" state [11]. The n 2 state, on the other hand, shows a phase transition from the compo...

We present a microscopic theory of the fractional quantum Hall effect at the filling factor ν with even denominator, which is recently observed in a double-layer electron system. In our approach electrons belonging to different layers are interpreted as different types of anyons with appropriate statistics. The wavefunction of the Hall state is calculated, which is found to coincide with that of Halperin. We also analyze vortex (quasihole) excitations. It is shown that a single vortex carries electric charges on both of the layers; for instance, a vortex at ν=½ has the electric charge [Formula: see text] on one layer and -⅛e on the other layer. The ground state at the vicinity of ν=½ is given by a Wigner crystal made of these vortices.

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