Onset temperature for the Kosterlitz-Thouless transition in the ν t = 1 bilayer quantum Hall state

We investigate the onset temperature ${T}^{*}$ of the bilayer quantum Hall state at the total Landau level filling factor ${\ensuremath{\nu}}_{\mathrm{t}}=1$ together with the activation energy gap $\ensuremath{\Delta}$. The onset temperature is the temperature at which the quantum Hall state starts to form. We make two remarkable experimental observations: (1) As the total electron density decreases, ${T}^{*}$ increases while $\ensuremath{\Delta}$ decreases on account of the deterioration of electron mobility. (2) As the in-plane magnetic field increases, ${T}^{*}$ exhibits a rise at the point where $\ensuremath{\Delta}$ becomes a minimum. The minimum of $\ensuremath{\Delta}$ occurs at the transition point from the commensurate phase to the recently discovered soliton lattice phase. We discuss the relation between ${T}^{*}$ and the Kosterlitz-Thouless transition on the basis of the $\mathit{XY}$ symmetry possessed by the ${\ensuremath{\nu}}_{\mathrm{t}}=1$ bilayer system and discuss the experimentally observed behavior of ${T}^{*}$.