arXiv subjects

Erik Díaz-Bautista

Publications and source records attributed to Erik Díaz-Bautista.

At least 19 recordsLinked to original sources

arXiv2026

Spectral design of confining optical structures by supersymmetry techniques

In this work, we apply supersymmetric transformations to an optical medium with quadratic index distributions on both transversal coordinates defining an elliptic profile. In particular, we implement first- and second-order transformations to construct new multi-parametric gradient index patterns that may host one or two subsidiary guided modes with a wide range of spectral properties and transversal intensity and phase distributions. These transformations may be continued up to an arbitrary order enabling the possibility to control the spectral and propagation properties of light beams.

physics.optics↗

arXiv2026

Anomalous Klein tunnelling with magnetic barriers in strained graphene

We study electron transport in a strained graphene sheet subjected to a sequence of $N$ electrostatic and magnetic barriers. Employing a modified and improved transfer-matrix framework, we examine how the transmission and reflection coefficients evolve with variations in uniaxial strain and in the number of barriers. The interplay of mechanical deformation and external magnetic fields is found to generate an anomalous Klein tunnelling, allowing the conductance to be effectively modulated through strain and barrier configurations. These findings highlight the role of strain engineering and magnetic field modulation as powerful tools for tailoring charge transport in two-dimensional materials. More broadly, they underscore how mechanical and electromagnetic control can be used to design next-generation solid-state devices with tunable electronic properties.

cond-mat.mes-hall↗

arXiv2025

Spectral analysis of Dirac materials in position-dependent magnetic and electric fields via Heun functions

This work focuses on the study of the spectral problem for Dirac materials immersed in position-dependent magnetic and electric fields. To achieve this, the system of differential equations satisfied by the eigenfunction components of the Hamiltonian has been decoupled, and the solutions for some specific cases have been analyzed using Heun functions, which provide us with a quantization relation and allow us to determine the solutions for the bound states.

math-ph↗

arXiv2024

Phase-space representation of coherent states generated through SUSY QM for tilted anisotropic Dirac materials

In this paper, we examine the electron interaction within tilted anisotropic Dirac materials when subjected to external electric and magnetic fields possessing translational symmetry. Specifically, we focus on a distinct non-zero electric field magnitude, enabling the decoupling of the differential equation system inherent in the eigenvalue problem. Subsequently, employing supersymmetric quantum mechanics facilitates the determination of eigenstates and eigenvalues corresponding to the Hamiltonian operator. To delve into a semi-classical analysis of the system, we identify a set of coherent states. Finally, we assess the characteristics of these states using fidelity and the phase-space representation through the Wigner function.

cond-mat.mtrl-sci↗

arXiv2024

An algorithm for exact analytical solutions for tilted anisotropic Dirac materials

In this article, we obtain the exact solutions for bound states of tilted anisotropic Dirac materials under the action of external electric and magnetic fields with translational symmetry. In order to solve the eigenvalue equation that arises from the effective Hamiltonian of these materials, we describe an algorithm that allow us to decouple the differential equations that are obtained for the spinor components.

cond-mat.mes-hall↗

arXiv2022

Extended transfer matrix method for electron transmission in anisotropic 2D materials: Interplay of strain and (a)periodicity of potentials

We extend the conventional transfer matrix method to include anisotropic features for electron transmission in two-dimensional materials, such as breaking reflection law in pseudo-spin phases and wave vectors. This method allows to study transmission properties of anisotropic and stratified electrostatic potential media from a wide range of tunable parameters, which include strain tensor and gating. We apply the extended matrix method to obtain the electron transmission, conductance, and Fano factor for the interplay of an uniaxially strained graphene sheet with external one-dimensional aperiodic potentials. Our results suggest the possibility of visualizing this interplay from conductance measurements.

cond-mat.mtrl-sci↗

arXiv2022

Ritus functions for graphene-like systems with magnetic fields generated by first-order intertwining operators

In this work, we construct the exact propagator for Dirac fermions in graphene-like systems immersed in external static magnetic fields with non-trivial spatial dependence. Such field profiles are generated within a first-order supersymmetric framework departing from much simpler (seed) magnetic field examples. The propagator is spanned on the basis of the Ritus eigenfunctions, corresponding to the Dirac fermion asymptotic states in the non-trivial magnetic field background which nevertheless admits a simple diagonal form in momentum space. This strategy enlarges the number of magnetic field profiles in which the fermion propagator can be expressed in a closed-form. Electric charge and current densities are found directly from the corresponding propagator and compared against similar findings derived from other methods.

quant-ph↗

arXiv2022

Valley-dependent time evolution of coherent electron states in tilted anisotropic Dirac materials

The effect of the Dirac cone tilt of anisotropic two-dimensional materials on the time evolution of coherent electron states in the presence of electric and magnetic fields is studied. We propose a canonical transformation that maps the anisotropic Dirac-Weyl Hamiltonian with tilted Dirac cones to an effective and isotropic Dirac Hamiltonian under these fields. In this way, the well-known Landau-level spectra and wave functions allow calculating the Wigner matrix representation of Landau and coherent states. We found a valley dependency in the behavior of the Wigner function for both Landau and coherent electron states. The time evolution shows that the interplay of the Dirac cone tilt and the electric field keeps the uncertainties of both position and momentum in one valley significantly lower than in the other valley. The increment of quantum noise correlates with the emergence of negative values in the Wigner function. These results may help us to understand the generation of coherent electron states under the interaction with electromagnetic fields. The reported valley-dependent signatures in the Wigner function of materials with tilted Dirac cones may be revealed by quantum tomography experiments, even in the absence of electric fields.

cond-mat.mes-hall↗

arXiv2021

Coherent states for dispersive pseudo-Landau-levels in strained honeycomb lattices

Dirac fermions in graphene may experiment dispersive pseudo-Landau levels due to a homogeneous pseudomagnetic field and a position-dependent Fermi velocity induced by strain. In this paper, we study the (semi-classical) dynamics of these particles under such a physical context from an approach of coherent states. For this purpose we use a Landau-like gauge to built Perelomov coherent states by the action of a non-unitary displacement operator $D(α)$ on the fundamental state of the system. We analyze the time evolution of the probability density and the generalized uncertainty principle as well as the Wigner function for the coherent states. Our results show how $x$-momentum dependency affects the motion periodicity and the Wigner function shape in phase space.

cond-mat.mes-hall↗

arXiv2021

Coherent states in the symmetric gauge for graphene under a constant perpendicular magnetic field

In this work we describe semiclassical states in graphene under a constant perpendicular magnetic field by constructing coherent states in the Barut-Girardello sense. Since we want to keep track of the angular momentum, the use of the symmetric gauge and polar coordinates seemed the most logical choice. Different classes of coherent states are obtained by means of the underlying algebra system, which consists of the direct sum of two Heisenberg-Weyl algebras. The most interesting cases are a kind of partial coherent states and the coherent states with a well-defined total angular momentum.

cond-mat.mes-hall↗

arXiv2020

Schrödinger-type 2D coherent states of magnetized uniaxially strained graphene

We revisit the uniaxially strained graphene immersed in a uniform homogeneous magnetic field orthogonal to the layer in order to describe the time evolution of coherent states build from a semi-classical model. We consider the symmetric gauge vector potential to render the magnetic field, and we encode the tensile and compression deformations on an anisotropy parameter $ζ$. After solving the Dirac-like equation with an anisotropic Fermi velocity, we define a set of matrix ladder operators and construct electron coherent states as eigenstates of a matrix annihilation operator with complex eigenvalues. Through the corresponding probability density, we are able to study the anisotropy effects on these states on the $xy$-plane as well as their time evolution. Our results show clearly that the quasi-period of electron coherent states is affected by the uniaxial strain.

cond-mat.mes-hall↗

arXiv2020

Coherent states for graphene under the interaction of crossed electric and magnetic fields

We construct the coherent states for charge carriers in a graphene layer immersed in crossed external electric and magnetic fields. For that purpose, we solve the Dirac-Weyl equation in a Landau-like gauge avoiding applying techniques of special relativity, and thus we identify the appropriate rising and lowering operators associated to the system. We explicitly construct the coherent states as eigenstates of a matrix annihilation operator with complex eigenvalues. In order to describe the effects of both fields on these states, we obtain the probability and current densities, the Heisenberg uncertainty relation and the mean energy as functions of the parameter $β=c\,\mathcal{E}/(v_{\rm F}B)$. In particular, these quantities are investigated for magnetic and electric fields near the condition of the Landau levels collapse ($β\rightarrow1$).

quant-ph↗

arXiv2020

Phase-space representation of Landau and electron coherent states for uniaxially strained graphene

Recent experimental advances in the reconstruction of the Wigner function (WF) for electronic systems have led us to consider the possibility of employing this theoretical tool in the analysis of electron dynamics of uniaxially strained graphene. In this paper, we study the effect of strain on the WF of electrons in graphene under the interaction of a uniform magnetic field. This mechanical deformation modifies drastically the shape of the Wigner function of Landau and coherent states. The WF has a different behavior straining the material along the zigzag direction in comparison with the armchair one and favors the creation of electron coherent states. The time evolution of the WF for electron coherent states shows fluctuations between classical and quantum behavior around a closed path as time increases. The phase-space representation shows more clearly the effect of nonequidistant relative Landau levels in the time evolution of electron coherent states compared with other approaches. Our findings may be useful in establishing protocols for the realization of electron coherent states in graphene as well as a bridge between condensed matter and quantum optics.

quant-ph↗

arXiv2020

Coherent states in magnetized anisotropic 2D Dirac materials

In this work, we construct coherent states for electrons in anisotropic 2D Dirac materials immersed in a uniform magnetic field perpendicularly oriented to the sample. In order to describe the bidimensional effects on electron dynamics in a semiclassical approach, we adopt the symmetric gauge vector potential to describe the external magnetic field through a vector potential. By solving a Dirac-like equation with an anisotropic Fermi velocity, we identify two sets of scalar ladder operators that allow us to define generalized annihilation operators, which are generators of either the Heisenberg-Weyl or su(1,1) algebra. We construct both bidimensional and su(1,1) coherent states as eigenstates of such annihilation operators with complex eigenvalues. In order to illustrate the effects of the anisotropy on these states, we obtain their probability density and mean energy value. Depending upon the anisotropy, expressed by the ration between the Fermi velocities along the $x$- and $y$-axes, the shape of the probability density is modified on the $xy$-plane with respect to the isotropic case and according to the classical dynamics.

quant-ph↗

arXiv2019

Barut-Girardello coherent states for anisotropic 2D-Dirac materials

We construct the Barut-Girardello coherent states for charge carriers in anisotropic 2D-Dirac materials immersed in a constant homogeneous magnetic field which is orthogonal to the sample surface. For that purpose, we solve the anisotropic Dirac equation and identify the appropriate arising and lowering operators. Working in a Landau-like gauge, we explicitly construct nonlinear coherent states as eigenstates of a generalized annihilation operator with complex eigenvalues which depends on an arbitrary function $f$ of the number operator. In order to describe the anisotropy effects on these states, we obtain the Heisenberg uncertainty relation, the probability density, mean energy value and occupation number distribution for three different functions $f$. For the case in which the anisotropy is caused by uniaxial strain, we obtain that when a stress is applied along the $x$-axis of the material surface, the probability density for the nonlinear coherent states is smaller compared to when the material is stressed along the orthogonal axis.

quant-ph↗

arXiv2019

Multiphoton supercoherent states

In this paper we are going to build the multiphoton supercoherent states for the supersymmetric harmonic oscillator as eigenstates of the $m$-th power of a special form (but still with a free parameter) of the Kornbluth-Zypman supersymmetric annihilation operator. They become expressed in terms of the multiphoton coherent states for the standard harmonic oscillator. The Heisenberg uncertainty relation and some statistical properties for these states will be studied. Since the multiphoton supercoherent states turn out to be periodic, then the associated geometric phases will be as well evaluated.

quant-ph↗

arXiv2019

Polynomial Heisenberg algebras, multiphoton coherent states and geometric phases

In this paper we will realize the polynomial Heisenberg algebras through the harmonic oscillator. We are going to construct then the Barut-Girardello coherent states, which coincide with the so-called multiphoton coherent states, and we will analyze the corresponding Heisenberg uncertainty relation and Wigner distribution function for some particular cases. We will show that these states are intrinsically quantum and cyclic, with a period being a fraction of the oscillator period. The associated geometric phases will be as well evaluated.

math-ph↗

arXiv2017

Nonlinear supercoherent states and geometric phases for the supersymmetric harmonic oscillator

Nonlinear supercoherent states, which are eigenstates of nonlinear deformations of the Kornbluth-Zypman annihilation operator for the supersymmetric harmonic oscillator, will be studied. They turn out to be expressed in terms of nonlinear coherent states, associated to the corresponding deformations of the standard annihilation operator. We will discuss as well the Heisenberg uncertainty relation for a special particular case, in order to compare our results with those obtained for the Kornbluth-Zypman linear supercoherent states. As the supersymmetric harmonic oscillator executes an evolution loop, such that the evolution operator becomes the identity at a certain time, thus the linear and nonlinear supercoherent states turn out to be cyclic and the corresponding geometric phases will be evaluated.

math-ph↗