Quantum spin Hall phase in multilayer graphene

The so called quantum spin Hall phase is a topologically non trivial insulating phase that is predicted to appear in graphene and graphene-like systems. In this work we address the question of whether this topological property persists in multilayered systems. We consider two situations: purely multilayer graphene and heterostructures where graphene is encapsulated by trivial insulators with a strong spin-orbit coupling. We use a four orbital tight-binding model that includes the full atomic spin-orbit coupling and we calculate the $Z_{2}$ topological invariant of the bulk states as well as the edge states of semi-infinite crystals with armchair termination. For homogeneous multilayers we find that even when the spin-orbit interaction opens a gap for all the possible stackings, only those with odd number of layers host gapless edge states while those with even number of layers are trivial insulators. For the heterostructures where graphene is encapsulated by trivial insulators, it turns out that the interlayer coupling is able to induce a topological gap whose size is controlled by the spin-orbit coupling of the encapsulating materials, indicating that the quantum spin Hall phase can be induced by proximity to trivial insulators.Comment: 7 pages, 6 figure

Dynamics of a magnetic dimer with exchange, dipolar and Dzyalozhinski-Moriya interaction

We investigate the dynamics of a magnetic system consisting of two magnetic moments coupled by either exchange, dipole-dipole, or Dzyalozhinski-Moriya interaction. We compare the switching mechanisms and switching rates as induced by the three couplings. For each coupling and each configuration of the two anisotropy axes, we describe the switching modes and, using the kinetic theory of Langer, we provide (semi-)analytical expressions for the switching rate. We then compare the three interactions with regard to their efficiency in the reversal of the net magnetic moment of the dimer. We also investigate how the energy barriers vary with the coupling. For the dipole-dipole interaction we find that the energy barrier may either increase or decrease with the coupling depending on whether the latter is weak or strong. Finally, upon comparing the various switching rates, we find that the dipole-dipole coupling leads to the slowest magnetic dimer, as far as the switching of its net magnetic moment is concerned.Comment: 20 pages, 18 Figures, 2 table

Real space mapping of topological invariants using artificial neural networks

Topological invariants allow to characterize Hamiltonians, predicting the existence of topologically protected in-gap modes. Those invariants can be computed by tracing the evolution of the occupied wavefunctions under twisted boundary conditions. However, those procedures do not allow to calculate a topological invariant by evaluating the system locally, and thus require information about the wavefunctions in the whole system. Here we show that artificial neural networks can be trained to identify the topological order by evaluating a local projection of the density matrix. We demonstrate this for two different models, a 1-D topological superconductor and a 2-D quantum anomalous Hall state, both with spatially modulated parameters. Our neural network correctly identifies the different topological domains in real space, predicting the location of in-gap states. By combining a neural network with a calculation of the electronic states that uses the Kernel Polynomial Method, we show that the local evaluation of the invariant can be carried out by evaluating a local quantity, in particular for systems without translational symmetry consisting of tens of thousands of atoms. Our results show that supervised learning is an efficient methodology to characterize the local topology of a system.Comment: 9 pages, 6 figure

Stochastic theory of lineshape broadening in quasielastic He atom scattering with interacting adsorbates

The activated surface diffusion of interacting adsorbates is described in terms of the so-called interacting single adsorbate approximation, which is applied to the diffusion of Na atoms on Cu(001) for coverages up to 20% in quasielastic He atom scattering experiments. This approximation essentially consists of solving the standard Langevin equation with two noise sources and frictions: a Gaussian white noise accounting for the friction with the substrate, and a white shot noise characterized by a collisional friction simulating the adsorbate-adsorbate collisions. The broadenings undergone by the quasielastic peak are found to be in very good agreement with the experimental data reported at two surface temperatures 200 and 300 K.Comment: 6 pages, 3 figure

Minkowski-type and Alexandrov-type theorems for polyhedral herissons

Classical H.Minkowski theorems on existence and uniqueness of convex polyhedra with prescribed directions and areas of faces as well as the well-known generalization of H.Minkowski uniqueness theorem due to A.D.Alexandrov are extended to a class of nonconvex polyhedra which are called polyhedral herissons and may be described as polyhedra with injective spherical image.Comment: 19 pages, 8 figures, LaTeX 2.0