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

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 subkelvin 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 highmobility 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 ν = 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.

Bilayer Graphene as the Material for Study of the Unconventional Fractional Quantum Hall Effect

“…The nowadays experimental data of FQHE in graphene [31][32][33][34][35] are consistent with the predictions of the braid group commensurability approach. In the case of graphene, the specific band structure with pseudo-relativistic conical Dirac bands leads to equal division of the LLL between the valence band of holes and the conduction band of electrons, which itself via an anomalous "relativistic" IQHE [20,36,37].…”

“…FQHE in suspended graphene is observed at relatively high temperatures around 10 K [33], and even higher (up to 20 K) [34], which seems to be explained by the relative strengthening of the electric interaction due to the absence, for suspended samples, of a dielectric substrate Table 3. Comparison of filling hierarchy in the LLL level in the bilayer graphene for two mutually inverted successions of two lowest subbands: n ¼ 0; 2↑ n ¼ 1; 2↑ (upper) and n ¼ 1; 2↑ n ¼ 0; 2↑ (lower).…”

Measurement of theν=1/3Fractional Quantum Hall Energy Gap in Suspended Graphene

“…In recent investigations of transport properties in two-terminal high-mobility suspended graphene devices [7,8], a quantized conductance corresponding to the ν = 1/3 FQH state has been observed, suggesting the presence of strong e-e interactions in this system. However, due to the inherent mixing between longitudinal and transverse resistivities in this twoterminal measurement [9], quantitative characterization of the observed FQH states such as the FQH energy gap is only possible in an indirect way [10]. Although multiterminal measurements on suspended graphene samples have been reported previously [11,12], the mechanical [13] or thermal instability [14] of these samples has precluded even the observation of a fully-quantized IQH effect.…”

Phase diagram for theν=0quantum Hall state in monolayer graphene

“…As the quality of graphene devices progressed, the strongly correlated quantum Hall physics clearly emerged [12][13][14][15][16][17][18][19] at integer and fractional filling factors ν. To date, one of the most intriguing questions concerns the nature of the ν = 0 quantum Hall state, in which the orbitals of the n = 0 LL, four-fold degenerate in the KK ⊗ s isospin-spin space in the absence of the Zeeman effect, are occupied on average by two electrons, Fig.…”