Unconventional Features in the Quantum Hall Regime of Disordered Graphene: Percolating Impurity States and Hall Conductance Quantization

We report on the formation of critical states in disordered graphene, at the origin of variable and unconventional transport properties in the quantum Hall regime, such as a zero-energy Hall conductance plateau in the absence of an energy bandgap and Landau level degeneracy breaking. By using efficient real-space transport methodologies, we compute both the dissipative and Hall conductivities of large size graphene sheets with random distribution of model single and double vacancies. By analyzing the scaling of transport coefficients with defect density, system size and magnetic length, we elucidate the origin of anomalous quantum Hall features as magnetic-field dependent impurity states, which percolate at some critical energies. These findings shed light on unidentified states and quantum transport anomalies reported experimentally.Comment: 7 pages, 7 figures. Accepted in PR

Efficient Linear Scaling Approach for Computing the Kubo Hall Conductivity

We report an order-N approach to compute the Kubo Hall conductivity for disorderd two-dimensional systems reaching tens of millions of orbitals, and realistic values of the applied external magnetic fields (as low as a few Tesla). A time-evolution scheme is employed to evaluate the Hall conductivity $\sigma_{xy}$ using a wavepacket propagation method and a continued fraction expansion for the computation of diagonal and off-diagonal matrix elements of the Green functions. The validity of the method is demonstrated by comparison of results with brute-force diagonalization of the Kubo formula, using (disordered) graphene as system of study. This approach to mesoscopic system sizes is opening an unprecedented perspective for so-called reverse engineering in which the available experimental transport data are used to get a deeper understanding of the microscopic structure of the samples. Besides, this will not only allow addressing subtle issues in terms of resistance standardization of large scale materials (such as wafer scale polycrystalline graphene), but will also enable the discovery of new quantum transport phenomena in complex two-dimensional materials, out of reach with classical methods.Comment: submitted PRB pape

Velocity renormalization and Dirac cone multiplication in graphene superlattices with various barrier edge geometries

The electronic properties of one-dimensional graphene superlattices strongly depend on the atomic size and orientation of the 1D external periodic potential. Using a tight-binding approach, we show that the armchair and zigzag directions in these superlattices have a different impact on the renormalization of the anisotropic velocity of the charge carriers. For symmetric potential barriers, the velocity perpendicular to the barrier is modified for the armchair direction while remaining unchanged in the zigzag case. For asymmetric barriers, the initial symmetry between the forward and backward momentum with respect to the Dirac cone symmetry is broken for the velocity perpendicular (armchair case) or parallel (zigzag case) to the barriers. At last, Dirac cone multiplication at the charge neutrality point occurs only for the zigzag geometry. In contrast, band gaps appear in the electronic structure of the graphene superlattice with barrier in the armchair direction.Comment: 13 pages, 14 figure

Moir\'e pattern interlayer potentials in van der Waals materials from random-phase approximation calculations

Stacking-dependent interlayer interactions are important for understanding the structural and electronic properties in incommensurable two dimensional material assemblies where long-range moir\'e patterns arise due to small lattice constant mismatch or twist angles. Here, we study the stacking-dependent interlayer coupling energies between graphene (G) and hexagonal boron nitride (BN) homo- and hetero-structures using high-level random-phase approximation (RPA) ab initio calculations. Our results show that although total binding energies within LDA and RPA differ substantially between a factor of 200%-400%, the energy differences as a function of stacking configuration yield nearly constant values with variations smaller than 20% meaning that LDA estimates are quite reliable. We produce phenomenological fits to these energy differences, which allows us to calculate various properties of interest including interlayer spacing, sliding energetics, pressure gradients and elastic coefficients to high accuracy. The importance of long-range interactions (captured by RPA but not LDA) on various properties is also discussed. Parameterisations for all fits are provided.Comment: 10 pages, 6 figures, 2 table

Magnetoresistance and Magnetic Ordering Fingerprints in Hydrogenated Graphene

Spin-dependent features in the conductivity of graphene, chemically modified by a random distribution of hydrogen adatoms, are explored theoretically. The spin effects are taken into account using a mean-field self-consistent Hubbard model derived from first-principles calculations. A Kubo-Greenwood transport methodology is used to compute the spin-dependent transport fingerprints of weakly hydrogenated graphene-based systems with realistic sizes. Conductivity responses are obtained for paramagnetic, antiferromagnetic, or ferromagnetic macroscopic states, constructed from the mean-field solutions obtained for small graphene supercells. Magnetoresistance signals up to $\sim 7$ are calculated for hydrogen densities around 0.25%. These theoretical results could serve as guidance for experimental observation of induced magnetism in graphene.Comment: 4 pages, 4 figure

Electrophorèse : application à l'identification clonale de l'hévéa

Chez l'hévéa, la multiplication à grande échelle de matériel végétal non conforme peut gravement compromettre la rentabilité économique des plantations. Afin de réaliser, à un stade précoce de leur croissance, la caractérisation génotypique des clones, l'électrophorèse d'isoenzymes a été développée. Avec 98 % de pouvoir de séparation pour les principaux clones cultivés, cette technique s'est révélée particulièrement performante. L'équipement nécessaire simple et le coût de fonctionnement relativement faible de cette technique permettent son application en routine à l'identification clonale de l'hévéa. Une unité mobile d'électrophorèse ou "laboratoire portable" a été créée en vue d'intervenir directement sur plantation pour effectuer des contrôles de conformité en jardins à bois de greffe. Elle a été utilisée avec succès en Côte d'Ivoire, en Indonésie, en Guyane et en Guadeloupe sur un grand nombre d'individus. Elle est proposée sous forme de missions d'expertise ou de transferts de technologie [résumé d'auteur

Quantum transport in graphene in presence of strain-induced pseudo-Landau levels

Wereport on mesoscopic transport fingerprints in disordered graphene caused by strain-field induced pseudomagnetic Landau levels (pLLs). Efficient numerical real space calculations of the Kubo formula are performed for an ordered network of nanobubbles in graphene, creating pseudomagnetic fields up to several hundreds of Tesla, values inaccessible by real magnetic fields. Strain-induced pLLs yield enhanced scattering effects across the energy spectrum resulting in lower mean free path and enhanced localization effects. In the vicinity of the zeroth order pLL, we demonstrate an anomalous transport regime, where the mean free paths increases with disorder.We attribute this puzzling behavior to the low-energy sub-lattice polarization induced by the zeroth order pLL, which is unique to pseudomagnetic fields preserving time-reversal symmetry. These results, combined with the experimental feasibility of reversible deformation fields, open the way to tailor a metal-insulator transition driven by pseudomagnetic fields

Dynamic band structure tuning of graphene moir\'e superlattices with pressure

Heterostructures of atomically-thin materials have attracted significant interest owing to their ability to host novel electronic properties fundamentally distinct from their constituent layers. In the case of graphene on boron nitride, the closely-matched lattices yield a moir\'e superlattice that modifies the graphene electron dispersion and opens gaps both at the primary Dirac point (DP) and the moir\'e-induced secondary Dirac point (SDP) in the valence band. While significant effort has focused on controlling the superlattice period via the rotational stacking order, the role played by the magnitude of the interlayer coupling has received comparatively little attention. Here, we modify the interaction between graphene and boron nitride by tuning their separation with hydrostatic pressure. We observe a dramatic enhancement of the DP gap with increasing pressure, but little change in the SDP gap. Our surprising results identify the critical role played by atomic-scale structural deformations of the graphene lattice and reveal new opportunities for band structure engineering in van der Waals heterostructures.Comment: 26 Pages, 16 Figures. (v2) Main text and figures are update