Interlayer coherence inν=1andν=2bilayer quantum Hall states

Abstract

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...

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