Gap opening in the zeroth Landau level of graphene

Abstract

We have measured a strong increase of the low-temperature resistivity ρxx and a zero-value plateau in the Hall conductivity σxy at the charge neutrality point in graphene subjected to high magnetic fields up to 30 T. We explain our results by a simple model involving a field dependent splitting of the lowest Landau level of the order of a few Kelvin, as extracted from activated transport measurements. The model reproduces both the increase in ρxx and the anomalous ν = 0 plateau in σxy in terms of coexisting electrons and holes in the same spin-split zero-energy Landau level.PACS numbers: 71.70.Di In a magnetic field, graphene displays an unconventional Landau-level spectrum of massless chiral Dirac fermions [1,2,3,4]. In particular, a Landau level shared equally between electrons and holes of opposite chirality exists at zero-energy around the charge neutrality point (CNP). Due to the coexistence of carriers with opposite charge, graphene behaves as a compensated semimetal at the CNP with a finite resistivity ρ xx and a zero Hall resistivity ρ xy .Recently, the nature of the CNP in high magnetic fields has attracted considerable theoretical interest (see Ref.[5] and references there in). Experimentally, in the metallic regime, the transport behavior around the CNP can be explained using counter-propagating edge channels [6]. On the other hand, the high-field resistivity at the CNP was shown to diverge strongly, an effect recently analyzed in terms of a Kosterlitz-Thouless-type localization behavior [7]. In high quality graphene samples, made from Kish-graphite, Zhang et al. [8,9] have observed an additional fine structure of the lowest Landau level in the form of a ν = ±1 state. The existence of this state is proposed to be caused by a spontaneous symmetry breaking at the CNP and an interaction-induced splitting of the two levels resulting from this.Here we present an experimental study of the transport properties of the zero-energy Landau level in high magnetic fields and at low temperatures. Calculating the conductivities from an increasing magneto-resistance at the CNP and a zero-crossing of the Hall resistance yields a zero minimum in the longitudinal conductivity σ xx and a quantized zero-plateau in the Hall-conductivity σ xy . The temperature dependence of the σ xx -minimum displays an activated behavior. We explain this transition with a simple model involving the opening of a spingap (30 K at 30 T) in the zeroth Landau level. We do not observe any indication for a spontaneous symmetry breaking and an interaction-induced splitting at ν = ±1 as reported in Refs. 8 and 9 and we tentatively assign this to the relatively larger disorder in our samples made from natural graphite.The monolayer graphene devices (see top left inset Fig. 1a) are deposited on Si/SiO 2 substrate using methods as already reported elsewhere [10,11]. The doped Si acts as a back-gate and allows to adjust the chargecarrier concentration in the graphene film from highly hole-doped to highly electron-doped. Prior to the experiments the...

Giant Current-Perpendicular-to-Plane Magnetoresistance in Multilayer Graphene as Grown on Nickel

“…Since we have observed giant negative magnetoresistance even at the lowest temperature of 10 for which Γ ~ 30 45 , clearly c < 30K ≈ 2.6 meV. This matches reasonably well with ref.…”

Landau level spectra and the quantum Hall effect of multilayer graphene

“…We considered a single-particle picture in order to provide a simple description of a broad range of features. Depending on sample quality, electron-electron interactions also contribute to symmetry breaking and Landau level splitting, [67][68][69][70][71][72][73][74][75][76][77][78][79] as does interlayer asymmetry due to the presence of an external gate or doping. 28,31,42,45,[80][81][82] Nevertheless, an experimental observation of features related to next-nearest layer couplings should be possible in high-mobility samples including suspended graphene 69,[83][84][85][86] or graphene on a boron nitride substrate.…”

The enigma of the quantum Hall effect in graphene

“…We thus believe the recent observation 20,21,22,23 of divergent resistivity at the graphene neutral point in a high magnetic field is a direct manifestation of the SU(4) symmetry-broken ν = 0 QHE.…”

“…It is conceivable however, that small graphene samples used in experiments may be in the mesoscopic regime at sufficiently low temperatures, and edges may play an important or even a dominant role in transport; transport theories based on edge channels have been developed. 30,31 It is also conceivable that differences 10,19,20,21,22,23,30 observed in the transport properties near the Dirac point may also be due to the differences in edge properties of different samples. This leads us to a straightforward prediction: If one measures the bulk conductivity directly using the Corbino geometry, one should get σ xx → 0 in all samples exhibiting the ν = 0 QHE, due to the absence of edge contribution to transport.…”

“…In graphene, however, the n = 0 LL resides precisely at the particle-hole symmetric point of E = 0, which allows for a σ xy = 0 QHE when the SU(4) symmetry is broken, as indeed observed experimentally. 10,19,20,21,22,23 Putting σ xy = 0 in Eqs. (13) we get ρ xy = 0; ρ xx = 1/σ xx .…”