Abstract
The effect of a parallel magnetic field on the quantum Hall state of a double-layer system at total filling factor \ensuremath{\nu}=(4n+1), with n being the Landau-level index, is studied. While our result is consistent with previous ones, which indicate that the system at \ensuremath{\nu}=1 undergoes a parallel-magnetic-field-induced phase transition, we find that the phase transition also takes place at higher filling factors. For a certain parameter range, we observe an instability of the quantum Hall state towards probably a charge-density-wave state at a smaller parallel magnetic field before the phase transition takes place.
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