Quantized Hall effect and quantum phase transitions in coupled two-layer electron systems

We study the nature of the many-body electron states (and quantum phase transitions between them) in a double-quantum-well structure under a strong external magnetic field as a function of the materials parameters that define the two-layer system, namely, the thickness of individual layers, the separation between them, the individual well potentials confining the electrons, and the potential barrier between them. Motivated by two recent experiments, we consider two different situations, one with (almost) no quantum tunneling between the wells, and the other with substantial interwell quantum tunneling. We use the spherical system finite-size exact diagonalization technique for our calculations. By calculating the overlap of our exact small-system numerical wave functions with various (postulated) analytic wave functions, we comment on the nature of the incompressibility for various Landau-level filling factors (ν). We investigate, in particular details, the possibility of ν=1/2 (i.e., 1/4 average occupancy in each well), and, 1 (i.e., 1/2 occupancy in each well) incompressible states where ν is the total filling factor for the system. We also provide results for the ν=2/3 situation. Our conclusion, based on our use of realistic system parameters in our calculations, is that in both the recent experimental realizations of the ν=1/2 fractional quantum Hall effect, the relevant ground state is the so-called ‘‘331’’ state which is stabilized by the competition between intrawell and interwell electron-electron correlations.

We calculate for various double-quantum-well structural parameters and magnetic fields the ν=1/2 excitation spectra and the energy gaps, and compare it with the recent experimental data, obtaining excellent quantitative agreement. We provide a detailed quantum phase diagram for the ν=1 state as a function of the interwell Coulomb interaction and the symmetric-antisymmetric single-particle gap, and find that the ν=1 quantum Hall effect observed in the two recent experiments, in contrast to the ν=1/2 effect, belongs in some sense to two different universality classes. We also predict the existence of a reentrant ν=1 quantum Hall effect in double-quantum-well systems.