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Transition metal dichalcogenides (TMDs) are an exciting family of 2D materials; a member of this family, MoS$_2$, became the first measured monolayer semiconductor. In this article, a generalized phenomenological continuum model for the optical vibrations of the monolayer TMDs valid in the long-wavelength limit is developed. Non-polar oscillations involve differential equations for the phonon displacement vector that describe phonon dispersion up to a quadratic approximation. On the other hand, the polar modes satisfy coupled differential equations for the displacement vectors and the inner electric field. The two-dimensional phonon dispersion curves for in-plane and out-of-plane oscillations are thoroughly analyzed. This model provides an efficient approach to obtain the phonon dispersion curves at the $\Gamma$-point of the Brillouin zone of the whole family of TMD monolayers. The model parameters are fitted from density functional perturbation theory calculations. A detailed evaluation of the intravalley Pekar-Fr\"ohlich (P-F) and the $A_1$-homopolar mode deformation potential (Dp) coupling mechanisms is performed. The effects of metal ions and chalcogen atoms on polaron mass and binding energy are studied, considering these two contributions, the short-range Dp and P-F. It is argued that both mechanisms must be considered for a correct analysis of the polaron properties., Comment: 16 pages, 4 figures

We foretell a new pseudospin-dependent phenomenon in mono-layer graphene (MLG), which is numerically simulated \emph{via} an innovator nano-spintronic device. We proposed a novel theoretical procedure for describing the dynamics of Dirac fermions, departing from classic theoretical modelling. More importantly, we have found appealing evidences of wiggling anti-phase oscillations in the probability density time-distribution for each sub-lattice state, which we called pseudospinorial Zitterbewegung effect (PZBE). The PZBE undergoes modulated by a robust transient character, with decay time of femtoseconds. Interestingly, several features of the PZBE become tunable, even up to fully vanishing it at the vicinity of the Dirac points, as well as for a symmetric pseudospin configuration. We have observed evidences of perfect Klein tunneling and perfect anti-Klein backscattering in a single simulation, which is unprecedented for Q1D-MLG, as far as we know., Comment: 9 pages, 8 figures

Fano and hybrid resonances of bilayer graphene could be attractive for thermoelectric devices. The special profile presented by such resonances could significantly enhance the Seebeck coefficient and the power factor. In this work, we study the thermoelectric properties of bilayer graphene single and double barrier structures. The charge carriers are described as massive chiral particles through an effective Dirac-like Hamiltonian. The Hybrid matrix method, the Landauer-B\"{u}ttiker formalism and the Cutler-Mott formula are implemented to obtain the transmission, transport and thermoelectric properties, respectively. The Seebeck coefficient and the power factor are analyzed for gapless and gapped single and double barriers. We find that in the energy range where Fano resonances occur, the Seebeck coefficient attains values of tens of mV/K and the power factor reaches values of the order nW/K. Hybrid resonances also sustain high values for the thermoelectric properties, however not as high as Fano resonances. We also find that despite the Fano and hybrid profiles are manifested in the conductance of gapped barrier structures, the Seebeck coefficient and the power factor are systematically reduced as the bandgap gets larger. So, our findings indicate that bilayer graphene barrier structures can be used to improve the response of thermoelectric devices., Comment: 17 pages, 12 figures, J.A.B.-T. acknowledges to PRODEP-SEP-Mexico for the Posdoctoral Research Fellowship 511-6/2019.-10959

Gapless bilayer graphene (GBG), like monolayer graphene, is a material system with unique properties, such as anti-Klein tunneling and intrinsic Fano resonances. These properties rely on the gapless parabolic dispersion relation and the chiral nature of bilayer graphene electrons. In addition, propagating and evanescent electron states coexist inherently in this material, giving rise to these exotic properties. In this sense, bilayer graphene is unique, since in most material systems in which Fano resonance phenomena are manifested an external source that provides extended states is required. However, from a numerical standpoint, the presence of evanescent-divergent states in the eigenfunctions linear superposition representing the Dirac spinors, leads to a numerical degradation (the so called $\Omega$d problem) in the practical applications of the standard Coefficient Transfer Matrix ($K$) method used to study charge transport properties in Bilayer Graphen based multi-barrier systems. We present here a straightforward procedure based in the hybrid compliance-stiffness matrix method ($H$) that can overcome this numerical degradation. Our results show that in contrast to standard matrix method, the proposed $H$ method is suitable to study the transmission and transport properties of electrons in GBG superlattice since it remains numerically stable regardless the size of the superlattice and the range of values taken by the input parameters: the energy and angle of the incident electrons, the barrier height and the thickness and number of barriers. We show that the matrix determinant can be used as a test of the numerical accuracy in real calculations.

The transfer matrix method is usually employed to study problems described by $N$ equations of matrix Sturm-Liouville (MSL) kind. In some cases a numerical degradation (the so called $\Omega d$ problem) appears thus impairing the performance of the method. We present here a procedure that can overcome this problem in the case of multilayer systems having piecewise constant coefficients. This is performed by studying the relations between the associated transfer matrix and other transfer matrix variants. In this way it was possible to obtain the matrices which can overcome the $\Omega d$ problem in the general case and then in problems which are particular cases of the general one. In this framework different strategies are put forward to solve different boundary condition problems by means of these numerically stable matrices. Numerical and analytic examples are presented to show that these stable variants are more adequate than other matrix methods to overcome the $\Omega d$ problem. Due to the ubiquity of the MSL system, these results can be applied to the study of many elementary excitations in multilayer structures., Comment: 23 pages, 2 figures

We settle a general expression for the Hamiltonian of the electron-phonon deformation potential (DP) interaction in the case of non-polar core-shell cylindrical nanowires (NWs). On the basis of long range phenomenological continuum model for the optical modes and by taking into account the bulk phonon dispersions, we study the size dependence and strain-induced shift of the electron-phonon coupling strengths for Ge-Si and Si-Ge NWs. We derive analytically the DP electron-phonon Hamiltonian and report some numerical results for the frequency core modes and vibrational amplitudes. Our approach allows for the unambiguous identification of the strain and confinement effects. We explore the dependence of mode frequencies and hole-DP scattering rates on the structural parameters of these core-shell structures, which constitute a basic tool for the characterization and device applications of these novel nanosystems., Comment: 10 pages, 5 figures

We obtain the the long-wavelength polar optical vibrational modes of semiconductor core-shell nanowires by means of a phenomenological continuum model. A basis for the space of solutions is derived, and by applying the appropriate boundary conditions, the transcendental equations for the coupled and uncoupled modes are attained. Our results are applied to the study of the GaAs-GaP core-shell nanowire, for which we calculate numerically the polar optical modes, analyzing the role of strain in the vibrational properties of this nanosystem.

Using the formal analysis made by Bohm in his book, {\em "Quantum theory"}, Dover Publications Inc. New York (1979), to calculate approximately the phase time for a transmitted and the reflected wave packets through a potential barrier, we calculate the phase time for a semiconductor system formed by different mesoscopic layers. The transmitted and the reflected wave packets are analyzed and the applicability of this procedure, based on the stationary phase of a wave packet, is considered in different conditions. For the applicability of the stationary phase method an expression is obtained in the case of the transmitted wave depending only on the derivatives of the phase, up to third order. This condition indicates whether the parameters of the system allow to define the wave packet by its leading term. The case of a multiple barrier systems is shown as an illustration of the results. This formalism includes the use of the Transfer Matrix to describe the central stratum, whether it is formed by one layer (the single barrier case), or two barriers and an inner well (the DBRT system), but one can assume that this stratum can be comprise of any number or any kind of semiconductor layers., Comment: 15 pages, 4 figures although figure 4 has 5 graphs

This article is concerned with a mathematical tool, the Associated Transfer Matrix T, which proves useful in the study of a wide class of physical problems involving multilayer heterostructures. General properties of linear, second order differential matrix Sturm Liouville operators are discussed as a basis for establishing general properties of T, which is also generally related to the Green function G. Some identities satisfied by T are derived, which prove useful in practice to monitor the numerical quality of computational processes., Comment: 11 pages, none figures. Submitted to Physica Scripta

An appropriate combination of the scattering theory and the transfer matrix formalism, for the solution of a (4 x 4) Kohn-Luttinger model, allow us to study the multichannel-multiband transmission process of heavy and light holes through a (GaAs/AlAs) superlattice. Appealing effects and interesting channel coupling phenomena, mediated by quasi-bond states, are clearly foreseen., Comment: 4 pages, 4 figures,Reduced version of a talk presented at the Iberoamerican Meeting on Nanostructures (Madrid, March 2003)

We study the time reversal and space inversion symmetry properties of those transfer matrices mostly used in the calculation of energy spectra and transport-process. We study the time reversal and space inversion symmetry properties of those transfer matrices mostly used in the calculation of energy spectra and transport-process quantities. We determine the unitary transformation relating transfer matrices. We consider the Kohn-Luttinger model for a quasi-2D system and show that even though the system studied in the (4 x 4) scheme satisfies all the symmetry requirements, the (2 x 2)subspaces do not fulfill such constrains, except in the Gamma point of the Brillouin Zone. We find new exchange properties between the (2\times 2)subspace quantities., Comment: 12 pages, none figures