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 K 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.Comment: 4 pages, 4 figures, updated version after review, accepted for PR

High sensitive quasi freestanding epitaxial graphene gassensor on 6H-SiC

We have measured the electrical response to NO$_2$, N$_2$, NH$_3$ and CO for epitaxial graphene and quasi freestanding epitaxial graphene on 6H-SiC substrates. Quasi freestanding epitaxial graphene shows a 6 fold increase in NO2 sensitivity compared to epitaxial graphene. Both samples show a sensitivity better than the experimentally limited 1 ppb. The strong increase in sensitivity of quasi freestanding epitaxial graphene can be explained by a Fermi-energy close to the Dirac Point leading to a strongly surface doping dependent sample resistance. Both sensors show a negligible sensitivity to N$_2$, NH$_3$ and CO

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 spin-split zero-energy Landau level.Comment: 4 pages, 3 figure

Pedestrian index theorem a la Aharonov-Casher for bulk threshold modes in corrugated multilayer graphene

Zero-modes, their topological degeneracy and relation to index theorems have attracted attention in the study of single- and bilayer graphene. For negligible scalar potentials, index theorems explain why the degeneracy of the zero-energy Landau level of a Dirac hamiltonian is not lifted by gauge field disorder, for example due to ripples, whereas other Landau levels become broadened by the inhomogenous effective magnetic field. That also the bilayer hamiltonian supports such protected bulk zero-modes was proved formally by Katsnelson and Prokhorova to hold on a compact manifold by using the Atiyah-Singer index theorem. Here we complement and generalize this result in a pedestrian way by pointing out that the simple argument by Aharonov and Casher for degenerate zero-modes of a Dirac hamiltonian in the infinite plane extends naturally to the multilayer case. The degeneracy remains, though at nonzero energy, also in the presence of a gap. These threshold modes make the spectrum asymmetric. The rest of the spectrum, however, remains symmetric even in arbitrary gauge fields, a fact related to supersymmetry. Possible benefits of this connection are discussed.Comment: 6 pages, 2 figures. The second version states now also in words that the conjugation symmetry that in the massive case gets replaced by supersymmetry is the chiral symmetry. Changes in figure

Scaling of the quantum-Hall plateau-plateau transition in graphene

The temperature dependence of the magneto-conductivity in graphene shows that the widths of the longitudinal conductivity peaks, for the N=1 Landau level of electrons and holes, display a power-law behavior following $\Delta \nu \propto T^{\kappa}$ with a scaling exponent $\kappa = 0.37\pm0.05$. Similarly the maximum derivative of the quantum Hall plateau transitions $(d\sigma_{xy}/d\nu)^{max}$ scales as $T^{-\kappa}$ with a scaling exponent $\kappa = 0.41\pm0.04$ for both the first and second electron and hole Landau level. These results confirm the universality of a critical scaling exponent. In the zeroth Landau level, however, the width and derivative are essentially temperature independent, which we explain by a temperature independent intrinsic length that obscures the expected universal scaling behavior of the zeroth Landau level

Quantum resistance metrology in graphene

We have performed a metrological characterization of the quantum Hall resistance in a 1 $\mu$m wide graphene Hall-bar. The longitudinal resistivity in the center of the $\nu=\pm 2$ quantum Hall plateaus vanishes within the measurement noise of 20 m$\Omega$ upto 2 $\mu$A. Our results show that the quantization of these plateaus is within the experimental uncertainty (15 ppm for 1.5$\mu$A current) equal to that in conventional semiconductors. The principal limitation of the present experiments are 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

Coexistence of electron and hole transport in graphene

When sweeping the carrier concentration in monolayer graphene through the charge neutrality point, the experimentally measured Hall resistivity shows a smooth zero crossing. Using a two- component model of coexisting electrons and holes around the charge neutrality point, we unambiguously show that both types of carriers are simultaneously present. For high magnetic fields up to 30 T the electron and hole concentrations at the charge neutrality point increase with the degeneracy of the zero-energy Landau level which implies a quantum Hall metal state at \nu=0 made up by both electrons and holes.Comment: 5 pages, 6 figure

The value of competitive employment:In-depth accounts of people with intellectual disabilities

Background Increasing the societal participation of people with intellectual disabilities via competitive employment requires a full understanding of what this means to them. This paper aims to provide an in‐depth examination of the lived experiences of people with intellectual disabilities in competitive employment. Method Interviews were conducted with six participants with mild intellectual disability or borderline functioning and good verbal communication skills. Interviews were analysed according to the guidelines of interpretative phenomenological analysis (IPA). Member checks were conducted. Results Analysis yielded three main themes: (a) Building on my life experiences, (b) My place at work and (c) Being a valuable member of society, like everyone else. Conclusions Competitive employment could make a substantial contribution to the sense of belonging to society and quality of life of people with intellectual disabilities. Nevertheless, they must cope with stigma‐related obstacles and feelings of being dependent on others in the work environment

Splitting of critical energies in the nn=0 Landau level of graphene

The lifting of the degeneracy of the states from the graphene $n$=0 Landau level (LL) is investigated through a non-interacting tight-binding model with random hoppings. A disorder-driven splitting of two bands and of two critical energies is observed by means of density of states and participation ratio calculations. The analysis of the probability densities of the states within the $n$=0 LL provides some insights into the interplay of lattice and disorder effects on the splitting process. An uneven spatial distribution of the wave function amplitudes between the two graphene sublattices is found for the states in between the two split peaks. It is shown that as the splitting is increased (linear increasing with disorder and square root increasing with magnetic field), the two split levels also get increasingly broadened, in such a way that the proportion of the overlapped states keeps approximately constant for a wide range of disorder or magnetic field variation.Comment: 6 figure