  Strongly correlated electron liquids which occur in quantizing magnetic
fields reveal a cornucopia of fascinating quantum phenomena such as
fractionally charged quasiparticles, anyonic statistics, topological order, and
many others. Probing these effects in GaAs-based systems, where electron
interactions are relatively weak, requires sub-kelvin temperatures and
record-high electron mobilities, rendering some of the most interesting states
too fragile and difficult to access. This prompted a quest for new
high-mobility systems with stronger electron interactions. 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 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 pose
and solve the problem of extracting transport coefficients of a fractional
quantum Hall state from the two-terminal conductance. We develop a method,
based on the conformal invariance of two-dimensional magnetotransport, and
illustrate its use by analyzing 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 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 new tool
for the studies of quantum transport in suspended graphene and other nanoscale
systems.
