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...

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...

The thermopower of electrons at zero magnetic field and composite fermions ͑CF's͒ at high fields in GaAs/Ga 1Ϫx Al x As heterojunctions has been measured in the temperature range 0.1-1.2 K. In both cases the data are completely consistent with phonon drag being the only visible contribution. The results have been used to evaluate the phonon-limited mobility of electrons and CF's as a function of temperature. The electron mobility is in good agreement with calculation and with previous results deduced directly from the resistivity, but the CF mobility is not. We have previously reported that the thermopowers at filling factors ϭ 3 2 and 1 2 are identical. New data at fields up to 30 T show that this is also true for ϭ 3 4 and 1 4 . The effect of the substrate crystallographic orientation on phonon drag thermopower is reported.

Shubnikov-de Haas oscillations are observed in Bi 2 Se 3 flakes with high carrier concentration and low bulk mobility. These oscillations probe the protected surface states and enable us to extract their carrier concentration, effective mass, and Dingle temperature. The Fermi momentum obtained is in agreement with angle-resolved photoemission spectroscopy measurements performed on crystals from the same batch. We study the behavior of the Berry phase as a function of magnetic fields. The standard theoretical considerations fail to explain the observed behavior.

We have determined the magnetic properties of single-crystalline Au nanorods in solution using an optically detected magnetic alignment technique. The rods exhibit a large anisotropy in the magnetic volume susceptibility (Á V ). Á V increases with decreasing rod size and increasing aspect ratio and corresponds to an average volume susceptibility ( V ), which is drastically enhanced relative to bulk Au. This high value of V is confirmed by SQUID magnetometry and is temperature independent (between 5 and 300 K). Given this peculiar size, shape, and temperature dependence, we speculate that the enhanced V is the result of orbital magnetism due to mesoscopic electron trajectories within the nanorods. DOI: 10.1103/PhysRevLett.111.127202 PACS numbers: 75.75.Àc, 73.22.Àf, 75.20.En, 78.67.Qa Bulk Au is a diamagnetic material, i.e., one with a negative volume magnetic susceptibility Au . Recently, it was reported that Au nanoparticles (NPs), with functionalized surfaces, show a broad range of magnetic behavior, ranging from (enhanced) diamagnetic [1,2] to (super)paramagnetic [3][4][5] and even ferromagnetic up to room temperature [6,7]. The NP size and the type of capping molecules, strongly binding to or weakly interacting with Au, appear to influence the magnetic response. Several explanations were suggested, such as competing magnetic contributions of the NP core and surface [3], the formation of a magnetic moment due to the exchange of charges at the Au-ligand interface [5,6,8], the creation of large orbital moments due to electron motion within surface clusters [9], and the occurrence of persistent currents in the Au core [2]. However, so far, the origin of this unexpected magnetism and why it differs strongly between different types of NPs is not yet understood [2,10,11].We employ a novel magnetic alignment technique to measure the magnetic properties of rod-shaped Au NPs in solution. We focus on relatively large NPs (all dimensions >7 nm) that are single crystalline. The degree of alignment is measured optically, through the magnetic field-induced linear dichroism and birefringence, across the Au surface plasmon resonance (SPR) that arises due to collective oscillation modes of the conduction electrons [12,13]. We find an enhanced (dia)magnetic behavior, which does not depend on temperature (in the range 5-300 K). We speculate that this enhanced magnetism is an orbital effect, resulting from mesoscopic electron trajectories within the NPs [2,14].The optically detected magnetic alignment technique relies on the anisotropy of both the optical and magnetic properties of the Au nanorods. Because of their shape, the rods exhibit an anisotropic optical response, determined by their longitudinal ( k ) and transverse ( ? ) polarizabilities [15]. Polarized light, therefore, provides a sensitive tool to determine the alignment of rods [16][17][18][19]. In this Letter, rod alignment is induced by a magnetic field (B) because of the difference in the magnetic susceptibility parallel ( k ) and perpendicular ( ? ) to the lo...