How Close Can One Approach the Dirac Point in Graphene Experimentally?

Abstract

The above question is frequently asked by theorists who are interested in graphene as a model system, especially in context of relativistic quantum physics. We offer an experimental answer by describing electron transport in suspended devices with carrier mobilities of several 10 6 cm 2 V -1 s -1and with the onset of Landau quantization occurring in fields below 5 mT. The observed charge inhomogeneity is as low as 10 8 cm -2 , allowing a neutral state with a few charge carriers per entire micron-scale device. Above liquid helium temperatures, the electronic properties of such devices are intrinsic, being governed by thermal excitations only. This yields that the Dirac point can be approached within 1 meV, a limit currently set by the remaining charge inhomogeneity.No sign of an insulating state is observed down to 1 K, which establishes the upper limit on a possible bandgap.KEYWORDS (graphene, suspended graphene, high mobility, clamped contacts) 2 Graphene has a unique conical spectrum and its electronic properties at low energies E are often described by a two-dimensional Dirac-like equation. 1,2 The resulting difference from the conventional electronic systems becomes most prominent and interesting near zero E where graphene's Fermi surface shrinks into a point (Dirac point). Unfortunately, experimental devices are always subject to disorder, finite size and other factors limiting graphene's both quality and homogeneity. In particular, local variations of chemical doping and/or strain 3 disallow the Dirac point (DP) to be achieved uniformly over the entire device area so that neutral graphene is usually split into a system of electron-hole (e-h) puddles, 4,5 a state usually referred to as the neutrality point (NP). This charge inhomogeneity impedes investigation of graphene's intrinsic properties in the immediate proximity of the DP.  min is close but still notably higher than  min = 4e 2 /h predicted in the ballistic limit. 22,23 No sign of diverging resistivity  yields a conservative estimate on any possible bandgap as <0.5 meV. Figure 1a shows a micrograph of one of our suspended graphene devices, which was fabricated following the procedures described in refs. 8,10,11. In short, graphene was cleaved onto an oxidized Si wafer (300 nm SiO 2 ), and metallic contacts (Cr 3 nm/Au 100 nm) were deposited on top as shown in Figure 1a. Approximately a half of SiO 2 was etched away, allowing graphene to be suspended between the contacts whereas the remaining oxide served as a gate dielectric. In the second type of suspended devices, graphene was clamped between two metal pads to achieve better mechanical stability. To this end, graphene was transferred onto Au pads prefabricated on the Si wafer, and Cr/Au contacts were deposited on top of them, clamping graphene between two metal layers. This stopped graphene from moving and scrolling. Let us mention that the latter approach allowed us to fabricate a number of 4-probe devices with graphene crystals being etched into the proper Hall bar geometry. 24 Unfortunatel...

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“…From our theory, we predict an enhancement of two orders of magnitude in comparison to previous estimations for flat graphene, putting this gap close to the present experimental limits 27 . Note that the frequency of flexural modes depends on the coupling to the substrate, if any, and can be tuned by applied strains 28 .…”

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“…Note that electrons in natural suspended graphene are characterized by α ee ∼ 2.2 (since, in this case, ∼ 1 and v F ∼ 10 6 m/s). Weak-field magnetotransport experiments have been carried out [102,103] in high quality suspended samples (with mobilities of the order of ∼ 10 6 cm 2 V −1 s −1 ), with carrier density fluctuations and temperatures as low as 10 8 cm −2 and 1 K, respectively. No experimental evidence of a gapped phase has been reported so far in nearly-neutral natural graphene [102,103].…”

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