Exact solution of the Schrödinger equation for a hydrogen atom at the interface between the vacuum and a topologically insulating surface

Bonilla, Daniel; Martín-Ruiz, A.; Urrutia, L. F.

doi:10.1140/epjd/e2019-90347-2

Cited by 5 publications

(4 citation statements)

References 53 publications

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“…It is worth mentioning that the boundary conditions are perfectly consistent in relating field discontinuities at the interface with components of the fields which are continuous there. A number of magnetoelectric effects have been predicted on the basis of this theory [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57]. However, it has been experimentally verified only through the measurement of Kerr and Faraday angles at the surface of a strained HgTe 3D TI [58].…”

Section: A Electrodynamics Of Topological Insulatorsmentioning

confidence: 99%

Optical response of a topological-insulator–quantum-dot hybrid interacting with a probe electric field

2020

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We study the interaction between a topological insulator nanoparticle and a quantum dot subject to an applied electric field. The electromagnetic response of the topological insulator is derived from axion electrodynamics in the quasistatic approximation. Localized modes are quantized in terms of dipolar bosonic modes, which couples dipolarly to the quantum dot. Hence, we treat the hybrid as a two-level system interacting with a single bosonic mode, where the coupling strength encodes the information concerning the nontrivial topology of the nanoparticle. The interaction of the hybrid with the environment is implemented through the coupling with a continuum reservoir of radiative output modes and a reservoir of phonon modes. In particular, we use the method of Zubarev's Green functions to derive an expression for the optical absorption spectrum of the system. We apply our results to a realistic system which consists of a topological insulator nanoparticle made of TlBiSe2 interacting with a cadmium selenide quantum dot, both immersed in a polymer layer such as poly(methyl methacrylate). The optical absorption spectrum exhibits Fano resonances with a line shape that strongly depends on the polarization of the electric field as well as on the topological magnetoelectric polarizability θ. Our results and methods can also be applied to nontopological magnetoelectric materials such as Cr2O3.

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Section: A Electrodynamics Of Topological Insulatorsmentioning

confidence: 99%

Optical response of a topological-insulator–quantum-dot hybrid interacting with a probe electric field

2020

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“…If the material body is, for example, a topological insulator, additional interactions arise due to the topological magnetoelectric effect: the charges in the atom will induce, besides image electric charges, image magnetic monopoles as well (physically induced by a vortex Hall current in the surface), which in turn will interact with the atomic via the minimal coupling prescription. This problem has been considered within the framework of quantum [46,47] and classical [59] mechanics. The aim of this work is to built up a formalism that allows us to investigate the influence of a topological WSM upon an atom nearby.…”

Section: B Model Hamiltonianmentioning

confidence: 99%

“…Some works have been done in this spirit. For example, some particular classical electrodynamics configurations both in TIs [34][35][36][37][38][39] and WSMs [40][41][42][43][44], the frequency shift induced by the Casimir-Polder interaction between atoms and TIs [45][46][47], and the optical absorption of semiconductor-TI quantum dots [48][49][50], among others. Moved by these researches, in this paper we investigate the effects of a Weyl semimetallic phase upon hydrogenlike ions near its surface, taking into account the modifications arising from the topological nontriviality of the material.…”

Section: Introductionmentioning

confidence: 99%

Ground state and polarization of an hydrogen-like atom near a Weyl semimetal

Castaño-Yepes¹,

Nader²,

Martín-Ruiz³

2022

Preprint

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In this paper we study the effects of a topological Weyl semimetal (WSM) upon the ground state and polarization of an hydrogen-like atom near its surface. The WSM is assumed to be in the equilibrium state and at the neutrality point, such that the interaction between the atomic charges and the material is fully described (in the non retarded regime) by axion electrodynamics, which is an experimentally observable signature of the anomalous Hall effect in the bulk of the WSM. The atom-WSM interaction provides additional contributions to the Casimir-Polder potential thus modifying the energy spectra and wave function, which now became distance dependent. Using variational methods, we solve the corresponding Schrödinger equation for the atomic electron. The ground state and the polarization are analyzed as a function of the atom-surface distance, and we directly observe the effects of the nontrivial topology of the material by comparing our results with that of a topologically trivial sample. We also study the impact of the medium's permittivity by assuming a hydrogen atom in vacuum and a donor impurity in gallium arsenide (GaAs). We found that the topological interaction behaves as an effective-attractive charge so that the electronic cloud tends to be polarized to the interface of materials. Moreover, the loss of wave-function normalization is interpreted as a critical location from below which the bound state is broken.

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“…The expression of these polynomials depend on two integer parameters l and m leading to the spherical harmonics. Schrödinger carried out a physical interpretation of these numbers and named them as the angular momentum number and the magnetic number, respectively [95] [98] [99]. Is it not amazing that an abstract mathematical theory developed by Sturm-Liouville could be used to make sense in the real world almost a hundred years later?…”

Section: Laplacian Domain and Incomplete Gamma Function Resolution By...mentioning

confidence: 99%

Use of mathematical methods in the resolution of chemical engineering problems

Valverde Salamanca

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This thesis consists of a compendium of five works that illustrate the utilization of selected mathematical methods to solve specific chemical engineering problems. Hence, the thesis is intended to cover both, a review of fundamental mathematical procedures for the solution of models raised from chemical phenomena, and a demonstration of their effectiveness to obtain useful novel significant results. The opening paper explores diverse global optimization algorithms to adjust both kinetic constants and the binary interaction parameters (BIPs) for the Peng-Robinson equation of state to the experimental data. Those parameters are essential to determine the model raised from the supercritical transesterification of triolein with methanol to produce biodiesel, with CO2 as cosolvent, consisting of three reversible reaction in series. Here, a novel model merging the ordinary differential equations system raised from kinetic mechanism and the time-dependent thermodynamic state of the complex mixture is presented for diverse operating conditions. Among all results obtained, novel binary interaction coefficients for the intermediate reaction species (dioleins and monooleins) highlight. The second and fourth papers included in this thesis are aimed at the study of lanolin extraction from raw wool, using 5% ethanol in CO2. The former explores solid lanolin extraction under near-critical conditions by means of a mass-transfer model based on the shrinking-core concept, while the latter is addressed at the liquid lanolin supercritical extraction. Both models result in a partial differential equations (PDEs) system determined by the solubility of multiphasic lanolin, Henry-type partition coefficient and the lanolin mass transfer coefficient. Hence, in each paper the raised PDEs system is solved through a different method: in the second paper orthogonal collocation method is employed, while in the fourth paper finite differences method is used combined with the numerical integration of an expression previously obtained by means of the Laplace transform. Finally, an optimization procedure is used in order to fit the extraction parameters to the experimental data, achieving coherent results that agree well with those previously reported. Between the cases exposed, liquid lanolin extraction is significantly complex to model because of the diffusion phenomena that may occur inside the two lanolin fraction mixture added to the diffusion of solvent in the interphase. Therefore, in the third work a nonlinear autoregressive exogenous neural network model is designed to predict the outcoming extracted fraction of lanolin at diverse temperatures, pressures, solvent mass flow rates, wool packing densities and times. The problem with the scarce data available for training of the neural network is overcome by augmenting experimental data using an empirical Weibull function, which correctly predicts the lanolin breakthrough at the extractor exit. This hybrid Weibull - Neural Network algorithm results in a low prediction error and conform a powerful tool for optimizing operating conditions, proved by the fast convergence of genetic algorithm procedure. This thesis closes with Molecular Dynamics simulations for peptide-folding studies, followed by a Principal Component Analysis (PCA) and clustering analysis to understand the Free Energy Landscape of the peptide (FEL). Those methods are aimed at assessing the conformational profile of bombesin, a peptide with interest in drug design as a possible novel agonist and/or antagonist in the fight against cancer. Results suggest that the peptide adopts mainly helical structures at the C-terminus and, to a lesser extent, hairpin turn structures at the N-terminus. Those results agree with those available from NMR in a 2,2,2-trifluoroethanol/water (30% v/v), and point out a suitable a-helix conformation for binding where Trp8 and His12 interaction has a significant role. Aquesta tesi consta d'un compendi de cinc treballs que il·lustren la utilització de mètodes matemàtics per resoldre problemes específics d'enginyeria química. Per tant, la tesi està destinada a ser una revisió dels procediments matemàtics fonamentals per a la solució de models derivats de fenòmens químics i, a més, una demostració de la seva efectivitat per obtenir resultats útils i innovadors. L'article que obre la tesi explora diferents algoritmes d'optimització global per ajustar tant les constants cinètiques com el Paràmetres d'Interacció Binària (PIB) per a l'equació d'estat de Peng Robinsos a les dades experimentals. Aquests paràmetres són essencials per determinar el model derivat de la transesterificació supercrítica de la trioleïna amb metanol per produir biodièsel, amb CO2 com a cosolvent, que consisteix en tres reaccions reversibles en sèrie. Aquí, es presenta un nou model que fusiona el sistema d'EDOs derivat del mecanisme cinètic i l'estat termodinàmic de la barreja per a condicions de funcionament diverses. Entre tots els resultats obtinguts, destaquen els nous PIBs trobats per a les espècies de reacció intermèdies. El segon i quart treball inclosos en aquesta tesi estan destinats a l'estudi de l'extracció de lanolina de llana crua amb 5% d'etanol en CO2. El primer explora l'extracció de lanolina sòlida en condicions gairebé crítiques mitjançant un model de transferència de massa basat en el concepte del nucli minvant, mentre que el segon s'adreça al cas de l'extracció supercrítica de lanolina líquida. Ambdós models donen com a resultat un sistema d'EDPs determinat per la solubilitat de la lanolina multifàsica, el coeficient de partició de Henry i el coeficient de transferències de massa. Per tant, a cada article el sistema d'EDPs obtingut es resol mitjançant un mètode diferent: en el article s'utilitza un mètode de col·laboració ortogonal, mentre que en el quart s'utilitza el mètode de diferències finites combinat amb la integració numèrica d'una expressió obtinguda mitjançant la Transformada de Laplace. Finalment, es porta a terme una optimització per ajustar els paràmetres d'extracció a les dades experimentals, aconseguint resultats coherents que coincideixen amb els reportats anteriorment. Entre els casos expotsats, l'extracció de lanolina líquida és significativament complexa de modelar a causa dels fenòmens de difusió que es poden produir a l'interior de les dues fraccions de lanolina a més de la difusió del dissolvent en la interfase. Per tant, en el tercer treball es dissenya un model de xarxa neuronal exògena no lineal autoregressiva per predir la fracció extreta de lanlina a diverses temperatures, pressions, cabals de dissolvent, densitats d'empaquetament i temps. El problema derivat de l'escassetat de dades disponibles per a l'entrenament de la xarxa neuronal es supera amb l'augment d'aquestes mitjançant una funció de Weibull empírica, que prediu correctament l'avanç de la lanolina a la sortida de l'extractor. Aquest algoritme híbrid Weibull - xarxa neuronal resulta en un baix error de predicció i conforma una potent eina per optimitzar les condicions operatives, demostrada per la ràpida convergència de l'algoritme genètic utilitzat. Aquesta tesi tanca amb simulacions de Dinàmica Molecular per a l'estudi del plegament de pèptids seguint d'un Anàlisi de Components Principals (ACP) i del "clustering" per a l'anàlisi del Paisatge d'Energia Lliure (PEL). L'objectiu és avaluar el perfil conformacional de la bombesina, un pèptid amb interès en el disseny de fàrmacs com a possible nou agonista i/o antagonista en la lluita contra el càncer. Els resultats suggereixen que el pèptid adopta estructures helicoïdals principalment al extrem C, i també en menor mesura estructures de forquilla al extrem N. Aquests resultats coincideixen amb els disponibles de RMN en 2,2-trifluoroetanol/aigua (30% v/v) i indiquen una conformació d’hèlix a adequada per a la unió on la interacció Trp8 i His12 té un paper important.

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Exact solution of the Schrödinger equation for a hydrogen atom at the interface between the vacuum and a topologically insulating surface

Cited by 5 publications

References 53 publications

Optical response of a topological-insulator–quantum-dot hybrid interacting with a probe electric field

Optical response of a topological-insulator–quantum-dot hybrid interacting with a probe electric field

Ground state and polarization of an hydrogen-like atom near a Weyl semimetal

Use of mathematical methods in the resolution of chemical engineering problems

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