Klein tunneling and electron optics in Dirac-Weyl fermion systems with tilted energy dispersion

The outstanding electronic properties of relativistic-like fermions have been extensively studied in solid state systems with isotropic linear dispersions such as graphene. Here, we show that 2D and 3D Dirac-Weyl (DW) materials exhibiting tilted energy dispersions could induce drastically different transport phenomena, compared to the non-tilted case. Indeed, the Klein tunneling of DW fermions of opposite chiralities is predicted to appear along two separated oblique directions. In addition, valley filtering and beam splitting effects are easily tailored by dopant engineering techniques while the refraction of electron waves is dramatically modified by the tilt, thus paving the way for emerging applications in electron optics and valleytronics.Comment: 5 pages, 5 figures and Supplemental Material, submitted for publicatio

Dissipative boundary conditions for nonlinear 1-D hyperbolic systems: sharp conditions through an approach via time-delay systems

We analyse dissipative boundary conditions for nonlinear hyperbolic systems in one space dimension. We show that a previous known sufficient condition for exponential stability with respect to the C^1-norm is optimal. In particular a known weaker sufficient condition for exponential stability with respect to the H^2-norm is not sufficient for the exponential stability with respect to the C^1-norm. Hence, due to the nonlinearity, even in the case of classical solutions, the exponential stability depends strongly on the norm considered. We also give a new sufficient condition for the exponential stability with respect to the W^{2,p}-norm. The methods used are inspired from the theory of the linear time-delay systems and incorporate the characteristic method

Stepped Graphene-based Aharonov-Bohm Interferometers

Aharonov-Bohm interferences in the quantum Hall regime are observed when electrons are transmitted between two edge channels. Such a phenomenon has been realized in 2D systems such as quantum point contacts, anti-dots and p-n junctions. Based on a theoretical investigation of the magnetotransport in stepped graphene, a new kind of Aharonov-Bohm interferometers is proposed herewith. Indeed, when a strong magnetic field is applied in a proper direction, oppositely propagating edge states can be achieved in both terrace and facet zones of the step, leading to the interedge scatterings and hence strong Aharonov-Bohm oscillations in the conductance in the quantum Hall regime. Taking place in the unipolar regime, this interference is also predicted in stepped systems of other 2D layered materials.Comment: 6 pages + 6 figures and a supplemental material, revised and resubmitte

An elementary proof of Euler formula using Cauchy's method

The use of Cauchy's method to prove Euler's well-known formula is an object of many controversies. The purpose of this paper is to prove that Cauchy's method applies for convex polyhedra and not only for them, but also for surfaces such as the torus, the projective plane, the Klein bottle and the pinched torus

A Bayesian fusion model for space-time reconstruction of finely resolved velocities in turbulent flows from low resolution measurements

The study of turbulent flows calls for measurements with high resolution both in space and in time. We propose a new approach to reconstruct High-Temporal-High-Spatial resolution velocity fields by combining two sources of information that are well-resolved either in space or in time, the Low-Temporal-High-Spatial (LTHS) and the High-Temporal-Low-Spatial (HTLS) resolution measurements. In the framework of co-conception between sensing and data post-processing, this work extensively investigates a Bayesian reconstruction approach using a simulated database. A Bayesian fusion model is developed to solve the inverse problem of data reconstruction. The model uses a Maximum A Posteriori estimate, which yields the most probable field knowing the measurements. The DNS of a wall-bounded turbulent flow at moderate Reynolds number is used to validate and assess the performances of the present approach. Low resolution measurements are subsampled in time and space from the fully resolved data. Reconstructed velocities are compared to the reference DNS to estimate the reconstruction errors. The model is compared to other conventional methods such as Linear Stochastic Estimation and cubic spline interpolation. Results show the superior accuracy of the proposed method in all configurations. Further investigations of model performances on various range of scales demonstrate its robustness. Numerical experiments also permit to estimate the expected maximum information level corresponding to limitations of experimental instruments.Comment: 15 pages, 6 figure