Quantum-Hall Activation Gaps in Graphene

Abstract

We have measured the quantum-Hall activation gaps in graphene at filling factors ν = 2 and ν = 6 for magnetic fields up to 32 T and temperatures from 4 K to 300 K. The ν = 6 gap can be described by thermal excitation to broadened Landau levels with a width of 400 K. In contrast, the gap measured at ν = 2 is strongly temperature and field dependent and approaches the expected value for sharp Landau levels for fields B > 20 T and temperatures T > 100 K. We explain this surprising behavior by a narrowing of the lowest Landau level. The quantum Hall effect (QHE) observed in twodimensional electron systems (2DESs) is one of the fundamental quantum phenomena in solid state physics. Since its discovery in 1980 [1] it has been important for fundamental physics [2] and application to quantum metrology [3]. Recently a new member joined the family of 2DESs: graphene, a single layer of carbon atoms [4,5,6,7,8]. Graphene displays a unique charge carrier spectrum of chiral Dirac fermions [9,10] and enriches the QHE with a half integer QHE of massless relativistic particles observed in single-layer graphene [11,12,13,14] and a novel type of integer QHE of massive chiral fermions in bilayers [15,16]. Moreover, the band structure of graphene even allows the observation of the QHE up to room temperature [17]. Since localization in conventional quantum Hall systems is already fully destroyed at moderate temperatures, no QHE has been observed at temperatures above 30 K until very recently. Therefore, understanding a room temperature QHE in graphene goes far beyond our comprehension of the traditional QHE.In order to access this intriguing phenomenon in more detail we report here systematic measurements of the inter Landau level activation gap in graphene for magnetic fields up to 32 T. We will show that the gap between the zeroth and the first Landau level approaches the bare, unbroadened Landau-level separation for high magnetic fields and we explain these findings by a much narrower lowest Landau level compared to the other ones. In contrast, for higher Landau levels, the measured activation gap behaves as expected for equally broadened states.The single-layer graphene samples (Fig. 1c) were made by the micromechanical exfoliation of crystals of natural graphite, followed by the selection of single-layer flakes using optical microscopy and atomic force microscopy [4,5]. A large enough single-layer flake is contacted by Au electrodes and patterned into a Hall bar by ebeam lithography with subsequent reactive plasma etching. The structures are deposited on a SIMOX-substrate with a 300 nm thick SiO 2 layer on top of heavily doped Si. The Si is used as a backgate allowing to tune the carrier concentration n to either holes (n < 0) or electrons (n > 0) with a mobility µ = 15000 cm 2 (Vs) −1 at 4.2 K. Due to the presence of surface impurities on the graphene sheet [18] the devices are generally stronglyhole doped with a charge neutrality point situated at a positive back-gate voltage. In order to restore a pristine undoped situation we...

Cyclotron radiation and emission in graphene

“…The situation should also depend on whether the disorder is short range or long range; but, in ordinary QHE systems, a sum rule guarantees the total intensity of the cyclotron resonance intact. 10 As for the "ripples" ͑known to exist in actual graphene samples 18 ͒, the n = 0 Landau level remains sharp ͑which is topologically protected since the slowly varying potential does not destroy the chiral symmetry 19 ͒ while other levels become broadened 20 and this should favor the situation proposed in the presented Brief Report. 22…”

High-Field Electronic Properties of Graphene

“…In experiments performed on highmobility SLG (made from Kish-graphite) a lifting of this chiral degeneracy was observed by the appearance of a ν = ±1 state [24,25]. Most other experiments [16,17,[26][27][28] did not find such state, which points to a larger disorder preventing spontaneous symmetry breaking [29]. Instead, a divergence of ρ xx from its metallic value [26], h/4e 2 , towards a large resistance ρ xx h/e 2 is observed.…”

“…Since the results at ν = 6 show that the N = 1 Landau level behaves as expected, the behaviour at ν = ±2 can only be explained by the nature of the N = 0 Landau level. Indeed, as we have shown in more detail elsewhere [16], the zerothLandau level is insensitive to important broadening mechanisms such as inter-valley scattering and random magnetic-field fluctuations, and can become extremely narrow in high magnetic fields. Consequently, thermal excitations from ν = 2 minimum to this level reflect the bare level splitting.…”

“…The slightly higher slope of the experimentally measured gap may be explained by a sharpening of the zeroth Landau level, i.e. a reduction of its width with increasing field [16], or, alternatively by a slight exchange enhancement of the splitting.…”

“…More specifically, we use activated transport experiments to map out the unconventional Landau-level spectrum of SLG and BLG. We show in particular that the gap between the zeroth and the first Landau level in SLG approaches the bare Landau-level separation for high magnetic fields, which is explained by a narrowing of the zero-energy Landau level [16]. For high magnetic fields and low temperatures, this narrow zeroth Landau level splits up into two levels separated by an activation gap of about 30 K at 30 T [17].…”