A.J.M. Giesbers

Nanolithography and manipulation of graphene using an atomic force microscope

We use an atomic force microscope (AFM) to manipulate graphene films on a nanoscopic length scale. By means of local anodic oxidation with an AFM we are able to structure isolating trenches into single-layer and few-layer graphene flakes, opening the possibility of tabletop graphene based device fabrication. Trench sizes of less than 30 nm in width are attainable with this technique. Besides oxidation we also show the influence of mechanical peeling and scratching with an AFM of few layer graphene sheets placed on different substrates.

Quantum resistance metrology in graphene

We performed a metrological characterization of the quantum Hall resistance in a 1u2002μm wide graphene Hall bar. The longitudinal resistivity in the center of the ν=±2 quantum Hall plateaus vanishes within the measurement noise of 20u2002mΩ up to 2u2002μA. Our results show that the quantization of these plateaus is within the experimental uncertainty (15 ppm for 1.5u2002μA current) equal to that in conventional semiconductors. The principal limitation of the present experiments is the relatively high contact resistances in the quantum Hall regime, leading to a significantly increased noise across the voltage contacts and a heating of the sample when a high current is applied.

Quantum-hall activation gaps in graphene

We have measured the quantum-Hall activation gaps in graphene at filling factors nu=2 and nu=6 for magnetic fields up to 32 T and temperatures from 4 to 300 K. The nu=6 gap can be described by thermal excitation to broadened Landau levels with a width of 400 K. In contrast, the gap measured at nu=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.

Gap opening in the zeroth Landau level of graphene

We have measured a strong increase of the low-temperature resistivity rho(xx) and a zero-value plateau in the Hall conductivity sigma(xy) 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 rho(xx) and the anomalous nu = 0 plateau in sigma(xy) in terms of coexisting electrons and holes in the same split zero-energy Landau level.

Scaling of the quantum Hall plateau-plateau transition in graphene

The integer quantum Hall effect in two-dimensional electron systems 2DESs is caused by localized states in the tails of individual Landau levels which give rise to quantized plateaus in the Hall resistance. The states in the center of the Landau levels are extended; their wave functions are delocalized. Their delocalization is governed by a localization length, which decays exponentially away from the Landau level centers 1,2 with a universal critical scaling exponent related to this decay. 3 In this Rapid Communication we investigate the scaling behavior of the quantum Hall plateau-plateau transitions in the recently discovered new type of 2DES, graphene. 4,5 When changing the carrier concentration n at a constant field, the peak width of the longitudinal conductivity for higher Landau levels N 1 and the inverse slope of the Hall conductivity scale as T. Our experimentally measured scaling exponent = 0.40 0.02 is consistent with universal scaling theory. 1–3,6–8 The transition through the zeroth Landau level, however, shows no clear scaling behavior which we explain by a different scaling mechanism governed by a temperature independent intrinsic length scale. Our sample was made by micromechanical exfoliation of natural graphite and subsequently contacted by gold contacts and patterned into a 1-m-wide Hall bar by electron-beam lithography and reactive plasma etching. 9 The structure was deposited on a 300 nm Si/ SiO2 substrate thereby forming a graphene ambipolar field effect transistor. Prior to the measurements the sample was annealed at 400 K, placing its charge neutrality point CNP at zero gate voltage with a mobility of = 1.0 m 2 Vs �1 .

Aharonov-Bohm effect in the quantum Hall regime

We have fabricated quantum rings in a GaAs/GaAlAs heterostructure 2DEG by local anodic oxidation with an atomic force microscope. In low magnetic fields we observe Aharonov-Bohm oscillations with a period of 60 mT corresponding to an effective ring diameter of 300 nm. In the high field regime, between filling factors ν = 2/3 and ν = 3, we observe Aharonov-Bohm oscillations of quantum Hall edge channels with a surprisingly large period, ΔB = 163 mT, corresponding to an edge channel around the inner diameter of the ring.