Fractional Quantum Hall Effect in Suspended Graphene: Transport Coefficients and Electron Interaction Strength

TL;DR

This paper introduces a method to extract transport coefficients from two-terminal conductance measurements in suspended graphene, revealing stronger electron interactions and larger energy gaps in fractional quantum Hall states compared to GaAs systems.

Contribution

The authors develop a conformal invariance-based technique to analyze two-terminal transport data, enabling the study of fractional quantum Hall effects in small graphene samples.

Findings

Energy gap in suspended graphene's fractional quantum Hall state is larger than in GaAs.

Method allows extraction of transport coefficients from two-terminal measurements.

Strong electron interactions are evidenced by the larger energy gap.

Abstract

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.