Scaling in spin-degenerate Landau levels in the integer quantum Hall effect

Abstract

In a low-mobility ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As/InP heterostructure, we find that the quantized Hall resistance plateau, ${\mathrm{\ensuremath{\rho}}}_{\mathit{x}\mathit{y}}$=h/${\mathit{ie}}^{2}$ with i=3, starts developing only when T is below 50 mK. For higher T, the plateau and the associated minimum in the diagonal resistivity ${\mathrm{\ensuremath{\rho}}}_{\mathit{x}\mathit{x}}$ can be made to appear by tilting the sample with respect to the B field. We have studied the T dependence of the ${\mathrm{\ensuremath{\rho}}}_{\mathit{x}\mathit{x}}$ minimum and deduced the thermal-activation energy (\ensuremath{\Delta}). We find that \ensuremath{\Delta} is 67 times smaller than the Landau-level broadening deduced from the electron mobility. This result implies that there is no gap in the density of states and that, for T>50 mK, the Landau level is spin degenerate. In this higher T range, we observe a ${\mathit{T}}^{\mathrm{\ensuremath{-}}0.21}$ power law for the maximum value of d${\mathrm{\ensuremath{\rho}}}_{\mathit{x}\mathit{y}}$/dB between the i=2 and 4 plateaus, and ${\mathit{T}}^{\mathrm{\ensuremath{-}}0.42}$ for the minimum value of ${\mathit{d}}^{2}$${\mathrm{\ensuremath{\rho}}}_{\mathit{x}\mathit{x}}$/${\mathit{dB}}^{2}$. These exponents are a factor 2 smaller than those for spin-polarized levels.