Experimental study ofσxx(T) for quasiparticle charge determination in the fractional quantum Hall effect

The temperature dependence of the diagonal conductivity, ${\mathrm{\sigma }}_{\mathit{x}\mathit{x}}$(T), at integer and fractional quantum Hall effect (FQHE) minima was measured in a sample at various densities. We find ${\mathrm{\sigma }}_{\mathit{x}\mathit{x}}^{\mathit{c}}$, the 1/T→0 extrapolated value of ${\mathrm{\sigma }}_{\mathit{x}\mathit{x}}$(T) from Arrhenius plots, is different for different densities. While a reasonable (1/q${)}^2$ scaling of ${\mathrm{\sigma }}_{\mathit{x}\mathit{x}}^{\mathit{c}}$ at the filling factors ν=p/q is observed at lower densities, the scaling is not seen in the highest density data. We explain this loss of scaling by a breakdown of the assumption for a simple activated formula caused by a crossover between the extended state width, Γ, and T for the measurement. For kT>Γ, the scaling of the 1/T intercept is recovered by plotting ${\mathrm{\sigma }}_{\mathit{x}\mathit{x}}$(T)×T vs 1/T and fitting to ${\mathrm{\sigma }}_{\mathit{x}\mathit{x}}$(T)=(${\mathrm{\sigma }}_{\mathit{x}\mathit{x}}^{\mathrm{*}\mathit{c}}$/T)exp(-ΔE/kT). We attribute the (1/q${)}^2$ scaling in ${\mathrm{\sigma }}_{\mathit{x}\mathit{x}}^{\mathit{c}}$ and ${\mathrm{\sigma }}_{\mathit{x}\mathit{x}}^{\mathrm{*}\mathit{c}}$ observed at each density to a (1/q${)}^2$ scaling in the T=0 conductivity. This supports the assertion of Clark et al. that the charge ${\mathit{e}}^{\mathrm{*}}$ of the quasiparticle excitation from the FQHE ground state at ν=p/q can be determined from ${\mathrm{\sigma }}_{\mathit{x}\mathit{x}}$(T) and the charge is ${\mathit{e}}^{\mathrm{*}}$=e/q.