Fractional quantum Hall effect in suspended graphene probed with two-terminal measurements

Abstract

Recently, fractional quantization of two-terminal conductance was reported in suspended graphene. The quantization, which was clearly visible in fields as low as 2 T and persistent up to 20 K in 12 T, was attributed to the formation of an incompressible fractional quantum Hall state. Here, we argue that the failure of earlier experiments to detect the integer and fractional quantum Hall effect with a Hall-bar lead geometry is a consequence of the invasive character of voltage probes in mesoscopic samples, which are easily shorted out owing to the formation of hot spots near the edges of the sample. This conclusion is supported by a detailed comparison with a solvable transport model. We also consider, and rule out, an alternative interpretation of the quantization in terms of the formation of a p-n-p junction, which could result from contact doping or density inhomogeneity. Finally, we discuss the estimate of the quasi-particle gap of the quantum Hall state. The gap value, obtained from the transport data using a conformal mapping technique, is considerably larger than in GaAs-based two-dimensional electron systems, reflecting the stronger Coulomb interactions in graphene.

High-Quality Multiterminal Suspended Graphene Devices

“…16,35 In all cases, the value of the quantized transverse resistance plateaus (up to  = 36) matches with the value expected from the filling factor at which each plateau occurs (see Supporting information for the data at low filling 7 factors). 26,27 What is particularly remarkable is the low magnetic field values at which these phenomena are already visible. For instance, the broken symmetry states appear already at B ≈ 200 mT, whereas usually much larger values of magnetic field are needed.…”

“…1,2,[14][15][16][17][18][19][20][21][22][23] In multi-terminal geometries, however, it was found that passing a large current through graphene does not result in the systematic out-diffusion of adsorbates, and current annealing does not normally result in uniform, high-quality devices. 22,24 The problem originates from the invasive nature of the additional electrodes that are present in multi terminal devices: [24][25][26][27] hot electrons can easily leak out through these electrodes, which effectively act as heat sinks, causing a very inhomogeneous temperature profile. Adsorbates still move around upon current annealing, but in such a temperature profile, they are just redistributed over the flake (depending on which contacts are used to current anneal the device) without being removed completely from the area of graphene probed in the transport experiments.…”

“…1,2,[14][15][16][17][18][19][20][21][22][23] Unfortunately, suspended graphene allows only rather small devices to be realized (larger devices are mechanically unstable), and even more stringent limitations on the experiments have been posed so far by the inability to controllably realize high-quality multi-terminal devices. 22,[24][25][26][27] To address this last issue, here we discuss a strategy to fabricate multi-terminal suspended devices with an electronic mean-free path exceeding the device size, and demonstrate the high quality of these devices through different transport measurements. In particular, we report the observation of a negative multiterminal resistance due to the ballistic transport on suspended bilayer graphene, and very high quality quantum Hall data that include the independent determination of the transverse and the longitudinal resistance, as well as the observation of a pronounced quantum Hall plateau at magnetic field B as low as 30 mT.…”

Observation of Even Denominator Fractional Quantum Hall Effect in Suspended Bilayer Graphene

“…The majority of transport experiments on suspended graphene devices performed in the past to probe the quantum Hall effect were carried out in a two-terminal configuration, 6,7,38,43,45 Additional features are present in the data, and in order to identify those associated to FQHE we investigate the full dependence of Rxx on VBG and B (Figure 2a). 27,44 When VBG is changed, the fractional features in Figure 1a appear at different values of B (see Figure 2a), and exhibit a linear dispersion as expected for the quantum Hall states that occur at fixed filling factor ν.…”

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

“…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).…”