Riccardo Farchioni

Base and salt 3D forms of Emeraldine II polymers by Car–Parrinello molecular dynamics

Abstract We have studied structural and electronic properties of the three-dimensional crystalline regions of Emeraldine II polymers, in the base (EB-II) and salt (ES-II) forms, by means of first principle Car–Parrinello molecular dynamics. We compare the geometrical structures of the polymer chains in the primitive cells of EB-II and ES-II, pointing out the structural effects due to the protonation with HCl of the iminic nitrogens in the EB-II chains, and the effect of the counterions between neighboring chains. We also analyze the HOMO electron density distribution, band structure and density of states of the resulting bipolaronic structure of ES-II, which is energetically stable and maintains semiconductor character.

Current distribution and conductance quantization in the integer quantum Hall regime

Charge transport of a two-dimensional electron gas in the presence of a magnetic field is studied by means of the Keldysh–Green function formalism and the tight-binding method. We evaluate the spatial distributions of persistent (equilibrium) and transport (nonequilibrium) currents, and give a vivid picture of their profiles. In the quantum Hall regime, we find exact conductance quantization both for persistent currents and for transport currents, even in the presence of impurity scattering centres and moderate disorder.

Acidification of three-dimensional emeraldine polymers: Search for minimum energy paths from base to salt.

We present a numerical simulation of the HCl acidification process of a three-dimensional semiconducting emeraldine base (EB) polymer leading to the corresponding metallic emeraldine salt form. We have searched minimum energy paths connecting the initial configuration, composed of two EB polymer chains per cell each one attached by two HCl molecules, with the Pc2a polaronic configuration which is the final state of the acidification process. For this aim, the variational nudged elastic band method has been adopted. We provide a pictorial representation of the acidification process at T=0 K, monitoring the EB protonation and the evolution of the polymeric chains and of the positions of the Cl(-) counterions on the lowest potential energy surface. To include also temperature effects, we have explored the potential energy surface around the final equilibrium configuration, heating the system and following its dynamics by the Car-Parrinello procedure.

Tight-Binding Effective Hamiltonians for the Electronic States of Polyaniline Chains

By means of strictly one-dimensional effective Hamiltonians, in the tight-binding scheme, we obtain band structures and densities of states of the main forms of polyanilines, which compare favourably with existing theoretical and experimental studies. We first consider the band structures of the three polymeric base forms: leucoemeraldine, emeraldine and pernigraniline; then we study the pernigraniline salt and the emeraldine salt in the polaronic and bipolaronic configurations. The 1D π-electron effective Hamiltonians are obtained exploiting a modified version of the recursion method and successively the application of the renormalization method. The procedure here outlined can be adopted for any polymeric chain; it is so flexible to embody known relevant structural and optical properties of the polymer, moreover it provides a useful tool for successive iterative calculations in the study of the electronic transport properties of the polymer also in the presence of disorder.

Recursive Algorithms for Polymeric Chains

The implementation of real-space recursive methods for the evaluation of the electronic structure and transport properties of selected representative conjugated polymers is the main topic of this chapter. For this it is convenient to evaluate the matrix elements of the resolvent operator of the polymer Hamiltonian. In fact, by knowing these matrix elements we can infer information on the energy spectrum, on the density of states, and on the transmittivity of finite and infinite strands of polymer. The evaluation of the Green’s function matrix becomes computationally simpler when the corresponding Hamiltonian is represented on a local basis; moreover, the transport properties can also be easier deduced if this kind of basis is assumed. A very attractive point is that the Green’s function matrix elements can be represented by iterative procedures as continued fractions [1–4] which can be calculated without the explicit knowledge of the eigenvalues and eigenvectors of the Hamiltonian: this is very convenient for large-scale eigenvalue problems in particular for systems without periodicity or with complex unit cells.

Theoretical investigation of near gap electronic states of Si∕SiGe multiple quantum wells on (001)-Si or SiGe substrates

We present a theoretical study of the near gap electronic states of Si∕Ge based multiple quantum well systems composed of Si and Si1−xGex alloys coherently grown on (001)-Si or SiGe substrates. We interpret the experimental photoluminescence spectra recently reported [S. R. Sheng et al., Appl. Phys. Lett. 83, 857 (2003); 83, 2790 (2003)] in terms of direct or indirect k-space transitions. The effect of the spatial localization of the valence and conduction states is analyzed. We investigate the structures in the experiments within the tight binding renormalization method. Strain conditions, spin orbit effects, and quantum confinement are fully considered. Our calculations give an accurate description of the near gap experimental photoluminescence peaks.

Morphing Graphene-Based Systems for Applications: Perspectives from Simulations

Graphene, the one-atom-thick sp2-hybridized carbon crystal, displays unique electronic, structural and mechanical properties, which promise a large number of interesting applications in diverse high-tech fields. Many of these applications require its functionalization, e.g., with substitution of carbon atoms or adhesion of chemical species, creation of defects, modification of structure or morphology, to open an electronic band gap to use it in electronics, or to create 3D frameworks for volumetric applications. Understanding the morphology–properties relationship is the first step to efficiently functionalize graphene. Therefore, a great theoretical effort has been recently devoted to model graphene in different conditions and with different approaches involving different levels of accuracy and resolution. Here, we review the modeling approaches to graphene systems, with a special focus on atomistic level methods, but extending our analysis onto coarser scales. We illustrate the methods by means of applications with possible potential impact.

Incommensurate potentials : analytic and numerical progress

Incommensurate potentials present quite peculiar physical properties due to the deterministic break of translational symmetry; among others the authors mention generalized metal-insulator transitions, mobility edges and the singular behaviour of localization length. The authors stress here how these aspects can be fruitfully described by the joint use of the renormalization procedure and an appropriate envelope function formalism. The application to some significant examples clearly reveals that their approach is well suited to treat more complex and realistic incommensurate potentials.

Beyond exponential localization in one-dimensional electrified chains

We interpret a new kind of localization in a finite one-dimensional tight-binding model under a weak applied electric field. This phenomenon is quite general and manifests itself in a more than exponential decreasing behaviour of the chain transmittivity. We provide analytic expressions for the transmittivity and confirm the theoretical results by transfer matrix numerical calculations. We show that this phenomenon is present in ordered as well as in aperiodic (incommensurate and pseudorandom systems) irrespective of the number of allowed bands.

Renormalization and envelope function formalism for incommensurate systems

SummaryWe study the localization-delocalization transition in one-dimensional incommensurate crystals both numerically and analytically. From the numerical point of view we provide an implementation of the renormalization method, which allows to process with high accuracy millions of sites (whenever necessary). From the analytic point of view we extend the envelope function concepts to incommensurate potentials, smoothly varying on lattice constant scale. The control of the transition is made by numerical calculation of the Lyapunov exponent: it presents surprising aspects of universality and simplicity, with plateaux, linear regions and, at times, much more complicated behaviours. The envelope function method, together with semi-analytic considerations, allows to understand, in a number of situations, the presence of mobility edges, pseudo-mobility edges, and gaps in the energy spectrum.