Fractional quantum Hall effect in suspended graphene: Transport coefficients and electron interaction strength

Abstract

Recently, fractional-quantized Hall effect was observed in suspended graphene (SG), a free-standing monolayer of carbon, where it was found to persist up to $T=10\text{ }\text{K}$. The best results in those experiments were obtained on micron-size flakes, on which only two-terminal transport measurements could be performed. Here we address the problem of extracting transport coefficients of a fractional quantum Hall state from the two-terminal conductance. We develop a general method, based on the conformal invariance of two-dimensional magnetotransport, and employ it to analyze the measurements on SG. From the temperature dependence of longitudinal conductivity, extracted from the measured two-terminal conductance, we estimate the energy gap of quasiparticle excitations in the fractional-quantized $\ensuremath{\nu}=1/3$ state. The gap is found to be significantly larger than in GaAs-based structures, signaling much stronger electron interactions in suspended graphene. Our approach provides a tool for the studies of quantum transport in suspended graphene and other nanoscale systems.