Identification of Piecewise Linear Models of Complex Dynamical Systems

The paper addresses the realization and identification problem or a subclass of piecewise-affine hybrid systems. The paper provides necessary and sufficient conditions for existence of a realization, a characterization of minimality, and an identification algorithm for this subclass of hybrid systems. The considered system class and the identification problem are motivated by applications in systems biology

Electronic properties of bilayer phosphorene quantum dots in the presence of perpendicular electric and magnetic fields

Using the tight-binding approach, we investigate the electronic properties of bilayer phosphorene (BLP) quantum dots (QDs) in the presence of perpendicular electric and magnetic fields. Since BLP consists of two coupled phosphorene layers, it is of interest to examine the layer-dependent electronic properties of BLP QDs, such as the electronic distributions over the two layers and the so-produced layer-polarization features, and to see how these properties are affected by the magnetic field and the bias potential. We find that in the absence of a bias potential only edge states are layer-polarized while the bulk states are not, and the layer-polarization degree (LPD) of the unbiased edge states increases with increasing magnetic field. However, in the presence of a bias potential both the edge and bulk states are layer-polarized, and the LPD of the bulk (edge) states depends strongly (weakly) on the interplay of the bias potential and the interlayer coupling. At high magnetic fields, applying a bias potential renders the bulk electrons in a BLP QD to be mainly distributed over the top or bottom layer, resulting in layer-polarized bulk Landau levels (LLs). In the presence of a large bias potential that can drive a semiconductor-to-semimetal transition in BLP, these bulk LLs exhibit different magnetic-field dependences, i.e., the zeroth LLs exhibit a linear-like dependence on the magnetic field while the other LLs exhibit a square-root-like dependence.Comment: 11 pages, 6 figure

DC conductivity of twisted bilayer graphene: Angle-dependent transport properties and effects of disorder

The in-plane DC conductivity of twisted bilayer graphene (TBLG) is calculated using an expansion of the real-space Kubo-Bastin conductivity in terms of Chebyshev polynomials. We investigate within a tight-binding (TB) approach the transport properties as a function of rotation angle, applied perpendicular electric field and vacancy disorder. We find that for high-angle twists, the two layers are effectively decoupled, and the minimum conductivity at the Dirac point corresponds to double the value observed in monolayer graphene. This remains valid even in the presence of vacancies, hinting that chiral symmetry is still preserved. On the contrary, for low twist angles, the conductivity at the Dirac point depends on the twist angle and is not protected in the presence of disorder. Furthermore, for low angles and in the presence of an applied electric field, we find that the chiral boundary states emerging between AB and BA regions contribute to the DC conductivity, despite the appearance of strongly localized states in the AA regions. The results agree with recent conductivity experiments on twisted bilayer graphene

Nano-engineered non-uniform strain in graphene

Recent experiments showed that non-uniform strain can be produced by depositing graphene over pillars. We employed atomistic calculations to study the non-uniform strain and the induced pseudo-magnetic field up to 5000 Tesla in graphene on top of nano-pillars. By decreasing the distance between the nano-pillars a complex distribution for the pseudo-magnetic field can be generated. Furthermore, we performed tight-binding calculations of the local density of states (LDOS) by using the relaxed graphene configuration obtained from the atomistic calculations. We find that the quasiparticle LDOS are strongly modified near the pillars, both at low energies showing sub-lattice polarization, and at high energies showing shifts of the van Hove singularity. Our study shows that changing the specific pattern of the nano-pillars allows us to create a desired shape of the pseudo-magnetic field profile while the LDOS maps provide an input for experimental verifications by scanning tunneling microscopy.Comment: 5 pages, 2 figure

Quantum states in a magnetic anti-dot

We study a new system in which electrons in two dimensions are confined by a non homogeneous magnetic field. The system consists of a heterostructure with on top of it a superconducting disk. We show that in this system electrons can be confined into a dot region. This magnetic anti-dot has the interesting property that the filling of the dot is a discrete function of the magnetic field. The circulating electron current inside and outside the anti-dot can be in opposite direction for certain bound states. And those states exhibit a diamagnetic to paramagnetic transition with increasing magnetic field. The absorption spectrum consists of many peaks, some of which violate Kohn's theorem, and which is due to the coupling of the center of mass motion with the other degrees of freedom.Comment: 6 pages, 12 ps figure

Vortex-antivortex nucleation in magnetically nanotextured superconductors: Magnetic-field-driven and thermal scenarios

Within the Ginzburg-Landau formalism, we predict two novel mechanisms of vortex-antivortex nucleation in a magnetically nanostructured superconductor. Although counterintuitive, nucleation of vortex-antivortex pairs can be activated in a superconducting (SC) film covered by arrays of submicron ferromagnets (FMs) when exposed to an external homogeneous magnetic field. In another scenario, we predict the thermal induction of vortex-antivortex configurations in SC/FM samples. This phenomenon leads to a new type of Little-Parks oscillations of the FM magnetization-temperature phase boundary of the superconducting film.Comment: 4 pages, 5 figures, to appear in Physical Review Letter

Disordered graphene Josephson junctions

A tight-binding approach based on the Chebyshev-Bogoliubov-de Gennes method is used to describe disordered single-layer graphene Josephson junctions. Scattering by vacancies, ripples or charged impurities is included. We compute the Josephson current and investigate the nature of multiple Andreev reflections, which induce bound states appearing as peaks in the density of states for energies below the superconducting gap. In the presence of single atom vacancies, we observe a strong suppression of the supercurrent that is a consequence of strong inter-valley scattering. Although lattice deformations should not induce inter-valley scattering, we find that the supercurrent is still suppressed, which is due to the presence of pseudo-magnetic barriers. For charged impurities, we consider two cases depending on whether the average doping is zero, i.e. existence of electron-hole puddles, or finite. In both cases, short range impurities strongly affect the supercurrent, similar to the vacancies scenario