No abstract

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 have measured the Hall-plateau width and the activation energy of the bilayer quantum Hall (BLQH) states at the Landau-level filling factor ν = 1 and 2 by tilting the sample and simultaneously changing the electron density in each quantum well. The phase transition between the commensurate and incommensurate states are confirmed at ν = 1 and discovered at ν = 2. In particular, three different ν = 2 BLQH states are identified; the compound state, the coherent commensurate state, and the coherent incommensurate state.A spontaneous development of interlayer quantum coherence [1,2] is one of the most interesting phenomena in bilayer quantum Hall (BLQH) systems. One can experimentally prove the existence of such an interlayer quantum coherence by manipulating the macroscopic quantum conjugate observables; the phase difference and the interlayer electron number difference. The interlayer phase difference, if exists, can be controlled by applying a parallel magnetic field between the two layers, which can be achieved by tilting the bilayer system in a magnetic field. Murphy et al. [3] have found an activation-energy anomaly together with a phase transition in the ν = 1 BLQH state by increasing the parallel magnetic field. It was suggested to be a signal of the interlayer quantum coherence [4,5]. The interlayer number difference can also be controlled experimentally by applying gate bias voltages to the two layers. When the interlayer coherence exists, the BLQH state persists even if the electron density is arbitrarily unbalanced between two quantum wells. Sawada et al. [6] have found precisely this behavior in certain BLQH states; furthermore they have found that the activation energy increases as the density difference becomes larger. This behavior is presumably due to a capasitive charging energy stored in Skyrmions excited across the two layers in the coherent state [7]. These two experiments [3,6] indicate strongly the spontaneous development of the interlayer coherence in the ν = 1 BLQH state.An intriguing problem is whether an interlayer coherence develops also in the ν = 2 BLQH systems. Sawada et al. have found [6] a phase transition at ν = 2 by changing the electron density continuously. The phase transition occurs seemingly between the ν = 1 + 1 compound state and the ν = 2 "coherent state". Phase transitions have also been observed at ν = 2 in optical experiments by Pellegrini et al.: first they used samples with different densities [8]; second they tilted samples in the magnetic field [9]. In each of them, they have found two distinctive phases with respect to spin-excitation modes. They have concluded a phase transition between spin polarized and unpolarized states at ν = 2. It is important to relate the phase transitions found in the magnetotransport [6] and optical [8,9] experiments, if any.In this paper, we report the results of experiments on the ν = 1 and 2 BLQH states, where we have measured the Hall-plateau width and the activation energy by changing the density in each quantum well and simultaneo...