Signatures of spin in the $\nu =1∕3$ fractional quantum Hall effect

The activation gap $\Delta$ of the fractional quantum Hall state at constant filling $\nu =1∕3$ is measured in a wide range of perpendicular magnetic field $B$. Despite the full spin polarization of the incompressible ground state, we observe a sharp crossover between a low-field linear dependence of $\Delta$ on $B$ and a Coulomblike square root behavior at large $B$. From the global gap reduction we get information about the mobility edges in the fractional quantum Hall regime.

Figure 1

(Color online) Variation of the longitudinal resistivity ${\rho }_{xx}$ with the magnetic field at different electronic densities $n_e$. The different curves have been shifted for clarity. The inset shows the Hall bar geometry with a metallic topgate.

Figure 2

Temperature dependence of the resistivity for filling factor $\nu =1∕3$ at different perpendicular magnetic fields. The solid lines are fits to the activated scaling ${\rho }_{xx}\propto \exp (-\Delta ∕2T)$.

Figure 3

(Color online) The activation gap $\Delta$ at $\nu =1∕3$ versus $B$. The linear and square root scalings are clearly visible, as stressed by the two fit lines based on the free-CF model. A constant gap reduction of $1.7\mathrm{K}$ has been included, yielding the negative intercept of the curves at $B=0$. The relevant disorder-broadened CF-Landau bands are depicted in the inset.