Probing the extended-state width of disorder-broadened Landau levels in epitaxial graphene

Abstract

We experimentally investigate the width of extended states in disorder-broadened Landau levels (LLs) in top-gated epitaxial graphene on silicon carbide using two different methods: gated transport spectroscopy and activation gap measurements on integer quantum Hall states. The transport spectroscopy reveals that the widths of the extended states in the zero-energy ($N=0$) and first excited ($N=1$) LLs are of similar magnitude over the ranges of magnetic field (4--16 T) and temperature studied (1.6--150 K). Under certain assumptions we find that the extended-state width follows a power-law temperature dependence with the exponent $\ensuremath{\eta}\ensuremath{\sim}0.3$ in the $N=0$ ($N=1$) LL, with almost no (very weak) magnetic-field dependence. Activation gap measurements at the filling factors of $\ensuremath{\nu}=2$ and 6 give results consistent with transport spectroscopy for the $N=1$ LL, but indicate a larger broadening for the $N=0$ LL than deduced from the spectroscopy.