Gerardo G. Naumis

Energy landscape and rigidity.

The effects of floppy modes in the thermodynamical properties of a system are studied. From thermodynamical arguments, we deduce that floppy modes are not at zero frequency and thus a modified Debye model is used to take into account this effect. The model predicts a deviation from the Debye law at low temperatures. Then, the connection between the topography of the energy landscape, the topology of the phase space, and the rigidity of a glass is explored. As a result, we relate the number of constraints and floppy modes to the statistics of the landscape. We apply these ideas to a simple model for which we provide an approximate expression for the number of energy basins as a function of the rigidity. This helps to understand certain features of the glass transition, like the jump in the specific heat or the reversible window observed in chalcogenide glasses.

Glass transition temperature variation, cross-linking and structure in network glasses: A stochastic approach

Stochastic network description provide useful information about the link between the glass transition temperature Tg and network connectivity. In multicomponent glasses, this permits to distinguish homogeneous compositions (random network) from inhomogeneous ones (local phase separation). The stochastic origin of the Gibbs-Di Marzio equation is predicted at low connectivity and the analytical expression of its parameter emerges naturally from the calculation.

Variation of the glass transition temperature with rigidity and chemical composition

The effects of flexibility and chemical composition in the variation of the glass transition temperature are obtained by using the Lindemann criteria, which relates melting temperature with atomic vibrations, and rigidity theory. Using this criteria and that floppy modes produce an excess of vibrational states at low frequencies which enhance in a considerable way the average quadratic displacement, we show that the consequence is a modified glass transition temperature. This approach allows us to obtain in a simple way the empirically modified Gibbs-DiMarzio law, which has been widely used in chalcogenide glasses to fit the changes in the glass transition temperature with the chemical composition. The method predicts that the constant that appears in the law depends upon the ratio of two characteristic frequencies (or temperatures). This constant is estimated for the

Electronic and optical properties of strained graphene and other strained 2D materials: a review

{\mathrm{Se}}_{1\ensuremath{-}x\ensuremath{-}y}{({\mathrm{Ge}}_{y}{\mathrm{As}}_{1\ensuremath{-}y})}_{x}

Tail universalities in rank distributions as an algebraic problem: The beta-like function

glass by using the experimental density of vibrational states, and the result shows a good agreement with the experimental fit from glass transition temperature variation.

Perfect light transmission in Fibonacci arrays of dielectric multilayers

This review presents the state of the art in strain and ripple-induced effects on the electronic and optical properties of graphene. It starts by providing the crystallographic description of mechanical deformations, as well as the diffraction pattern for different kinds of representative deformation fields. Then, the focus turns to the unique elastic properties of graphene, and to how strain is produced. Thereafter, various theoretical approaches used to study the electronic properties of strained graphene are examined, discussing the advantages of each. These approaches provide a platform to describe exotic properties, such as a fractal spectrum related with quasicrystals, a mixed Dirac-Schrödinger behavior, emergent gravity, topological insulator states, in molecular graphene and other 2D discrete lattices. The physical consequences of strain on the optical properties are reviewed next, with a focus on the Raman spectrum. At the same time, recent advances to tune the optical conductivity of graphene by strain engineering are given, which open new paths in device applications. Finally, a brief review of strain effects in multilayered graphene and other promising 2D materials like silicene and materials based on other group-IV elements, phosphorene, dichalcogenide- and monochalcogenide-monolayers is presented, with a brief discussion of interplays among strain, thermal effects, and illumination in the latter material family.

Understanding electron behavior in strained graphene as a reciprocal space distortion

Although power laws of the Zipf type have been used by many workers to fit rank distributions in different fields like in economy, geophysics, genetics, soft-matter, networks, etc. these fits usually fail at the tail. Some distributions have been proposed to solve the problem, but unfortunately they do not fit at the same time the body and the tail of the distribution. We show that many different data in rank laws, like in granular materials, codons, author impact in scientific journal, etc. can be very well fitted by the integrand of a beta function (that we call beta-like function). Then we propose that such universality can be due to the fact that systems made from many subsystems or choices, present stretched exponential frequency-rank functions which qualitatively and quantitatively are well fitted with the beta-like function distribution in the limit of many random variables. We give a plausibility argument for this observation by transforming the problem into an algebraic one: finding the rank of successive products of numbers, which is basically a multinomial process. From a physical point of view, the observed behavior at the tail seems to be related with the onset of different mechanisms that are dominant at different scales, providing crossovers and finite size effects.

The tails of rank-size distributions due to multiplicative processes: from power laws to stretched exponentials and beta-like functions

In this paper we study the propagation of light through an asymmetric array of dielectric multilayers built by joining two porous silicon substructures in a Fibonacci sequence. Each Fibonacci substructure follows the well-known recursive rule but in the second substructure dielectric layers A and B are exchanged. Even without mirror symmetry, this array gives rise to multiple transparent states, which follow the scaling properties and self-similar spectra of a single Fibonacci multilayer. We apply the transfer matrix formalism to calculate the transmittance. By setting the transfer matrix of the array equal to ± I, the identity matrix, frequencies of perfect light transmission are reproduced in our theoretical calculations. Although the light absorption of porous silicon in the optical range limits our experimental study to low Fibonacci generations, the positions of the transparent states are well predicted by the above-mentioned condition. We conclude that mirror symmetry in arrays of Fibonacci multilayers is sufficient but not necessary to generate multiple transparent states, opening broader applications of quasiperiodic systems as filters and microcavities of multiple frequencies.

Design of graphene electronic devices using nanoribbons of different widths

The behavior of electrons in strained graphene is usually described using effective pseudomagnetic fields in a Dirac equation. Here we consider the particular case of a spatially constant strain. Our results indicate that lattice corrections are easily understood using a strained reciprocal space, in which the whole energy dispersion is simply shifted and deformed. This leads to a directional dependent Fermi velocity without producing pseudomagnetic fields. The corrections due to atomic wavefunction overlap changes tend to compensate such effects. Also, the analytical expressions for the shift of the Dirac points as well as the corresponding Dirac equation are found. In view of the former results, we discuss the range of applicability of the usual approach of considering pseudomagnetic fields in a Dirac equation derived from the old Dirac points of the unstrained lattice. Such considerations are important if a comparison is desired with experiments or numerical simulations.

Stochastic matrix description of the glass transition

Although power laws have been used to fit rank distributions in many different contexts, they usually fail at the tail. Here we show that many different data in rank laws, like in granular materials, codons, author impact in scientific journals, etc are very well fitted by a β-like function ({a, b} distribution). Since this distribution is indeed ubiquitous, it is reasonable to associate it with some kind of general mechanism. In particular, we have found that the macrostates of the product of discrete probability distributions imply stretched exponential-like frequency-rank functions, which qualitatively and quantitatively can be fitted with the {a,b} distribution in the limit of many random variables. We show this by transforming the problem into an algebraic one: finding the rank of successive products of a given set of numbers.