Current scaling in the integer quantum Hall effect

Abstract

We report a current (I)-dependent transport measurement in between two adjacent integer quantum Hall plateaus at different bath temperatures (${\mathit{T}}_{\mathit{b}}$) for 10 nAI10 \ensuremath{\mu}A. We find the maximum slope in ${\mathrm{\ensuremath{\rho}}}_{\mathit{x}\mathit{y}}$ scales with I when I is larger than a characteristic value. Combined with previous T scaling results, we find the current-dependent effective temperature of the two-dimensional electron gas in the integer quantum Hall effect regime, ${\mathit{T}}_{\mathit{e}}$\ensuremath{\sim}${\mathit{I}}^{0.5}$, independent of Landau levels and the spin degeneracy. This result allows us to deduce that p=2 for the T exponent of the inelastic scattering length (${\mathit{l}}_{\mathrm{in}}$\ensuremath{\sim}${\mathit{T}}_{\mathit{e}}^{\mathrm{\ensuremath{-}}\mathit{p}/2}$). Therefore, the values of the localization exponent \ensuremath{\nu} and of the dynamical exponent z can be obtained directly and independently.