Anisotropic linear and non-linear excitonic optical properties of buckled monolayer semiconductors

The optical properties of two-dimensional materials are exceptional in several respects. They are highly anisotropic and frequently dominated by excitonic effects. Dipole-allowed second order non-linear optical properties require broken inversion symmetry. Hence, several two-dimensional materials show strong in-plane (IP) non-linearity but negligible out-of-plane (OOP) response due to vertical symmetry. By considering buckled hexagonal monolayers, we analyze the critical role of broken vertical symmetry on their excitonic optical response. Both linear as well as second order shift current and second harmonic response are studied. We demonstrate that substantial OOP non-linear response can be obtained, in particular, through off-diagonal tensor elements coupling IP excitation to OOP response. Our findings are explained by excitonic selection rules for OOP response and the impact of dielectric screening on excitons is elucidated.Comment: 20 pages, 8 figure

Wannier Excitons Confined in Hexagonal Boron Nitride Triangular Quantum Dots

With the ever-growing interest in quantum computing, understanding the behaviour of excitons in monolayer quantum dots has become a topic of great relevance. In this paper, we consider a Wannier exciton confined in a triangular quantum dot of hexagonal Boron Nitride. We begin by outlining the adequate basis functions to describe a particle in a triangular enclosure, analyzing their degeneracy and symmetries. Afterwards, we discuss the excitonic hamiltonian inside the quantum dot and study the influence of the quantum dot dimensions on the excitonic states.Comment: 5 figure

Contribution to excitonic linewidth from free carrier–exciton scattering in layered materials: the example of hBN

Scattering of excitons by free carriers is a phenomenon, which is especially important when considering moderately to heavily doped semiconductors in low-temperature experiments, where the interaction of excitons with acoustic and optical phonons is reduced. In this paper, we consider the scattering of excitons by free carriers in monolayer hexagonal boron nitride encapsulated by a dielectric medium. We describe the excitonic states by variational wave functions, modeling the electrostatic interaction via the Rytova–Keldysh potential. Making the distinction between elastic and inelastic scattering, the relevance of each transition between excitonic states is also considered. Finally, we discuss the contribution of free carrier scattering to the excitonic linewidth, analyzing both its temperature and carrier density dependence.M.F.C.M.Q. acknowledges the International Nanotechnology Laboratory (INL) and the Portuguese Foundation for Science and Technology (FCT) for the Quantum Portugal Initiative (QPI) grant SFRH/BD/151114/2021. N.M.R.P. acknowledges support by the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Funding UIDB/04650/2020, COMPETE 2020, PORTUGAL 2020, FEDER, and FCT through projects PTDC/FIS-MAC/2045/2021, EXPL/FIS-MAC/0953/ 2021, and from the European Commission through the project Graphene Driven Revolutions in ICT and Beyond (Ref. No. 881603, CORE 3)

A colloquium on the variational method applied to excitons in 2D materials

In this colloquium, we review the research on excitons in van der Waals heterostructures from the point of view of variational calculations. We first make a presentation of the current and past literature, followed by a discussion on the connections between experimental and theoretical results. In particular, we focus our review of the literature on the absorption spectrum and polarizability, as well as the Stark shift and the dissociation rate. Afterwards, we begin the discussion of the use of variational methods in the study of excitons. We initially model the electron-hole interaction as a soft-Coulomb potential, which can be used to describe interlayer excitons. Using an \emph{ansatz}, based on the solution for the two-dimensional quantum harmonic oscillator, we study the Rytova-Keldysh potential, which is appropriate to describe intralayer excitons in two-dimensional (2D) materials. These variational energies are then recalculated with a different \emph{ansatz}, based on the exact wavefunction of the 2D hydrogen atom, and the obtained energy curves are compared. Afterwards, we discuss the Wannier-Mott exciton model, reviewing it briefly before focusing on an application of this model to obtain both the exciton absorption spectrum and the binding energies for certain values of the physical parameters of the materials. Finally, we briefly discuss an approximation of the electron-hole interaction in interlayer excitons as an harmonic potential and the comparison of the obtained results with the existing values from both first--principles calculations and experimental measurements.The authors thank Eduardo Castro and Joao Lopes dos Santos for comments on a preliminary version of this work, and Bruno Amorim for outlining the derivation in the Appendix A. N.M.R.P. acknowledges support from the European Commission through the project Graphene-Driven Revolutions in ICT and Beyond (Ref. No. 881603 - core 3), and the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Financing UID/FIS/04650/2019. In addition, funding from the projects POCI-01-0145-FEDER-028114, and POCI01-0145-FEDER-029265, and PTDC/NAN-OPT/29265/2017, and POCI-01-0145-FEDER-02888 is acknowledged

Optimización y revalidación del análisis de nitrógeno por el método

En el presente artículo, se ha optimizado y se ha revalidado el procedimiento de análisis de nitrógeno en muestras de taurina mediante el método Kjeldahl. La Asociación Española de Farmacéuticos de la Industria (AEFI) propone un modelo de cálculo que permite determinar el número de replicados a realizar, en función del coeficiente de variación de la repetibilidad del procedimiento (C.V.%) y el valor límite aceptado, que en el caso de la determinación de la pureza, corresponde al valor máximo o mínimo de las especificaciones de la muestra. Al aplicar dicho modelo, considerando la incertidumbre de calibración del equipo, como el mínimo valor posible para el C.V.%, y teniendo en cuenta las especificaciones establecidas para la taurina en la U.S. Pharmacopeia 30, se obtiene que el número de replicados a realizar es de cinco o seis, según las condiciones de trabajo

A Polynomial Approach to the Spectrum of Dirac-Weyl Polygonal Billiards

The Schr\"odinger equation in a square or rectangle with hard walls is solved in every introductory quantum mechanics course. Solutions for other polygonal enclosures only exist in a very restricted class of polygons, and are all based on a result obtained by Lam\'e in 1852. Any enclosure can, of course, be addressed by finite element methods for partial differential equations. In this paper, we present a variational method to approximate the low-energy spectrum and wave-functions for arbitrary convex polygonal enclosures, developed initially for the study of vibrational modes of plates. In view of the recent interest in the spectrum of quantum dots of two dimensional materials, described by effective models with massless electrons, we extend the method to the Dirac-Weyl equation for a spin-1/2 fermion confined in a quantum billiard of polygonal shape, with different types of boundary conditions. We illustrate the method's convergence in cases where the spectrum in known exactly and apply it to cases where no exact solution exists.Comment: 17 pages, 10 figure

Coexistence of Paramagnetic-Charge-Ordered and Ferromagnetic-Metallic Phases in La0.5Ca0.5MnO3 evidenced by ESR

Throughout a complete Electron Spin Resonance (ESR) and magnetization study of La0.5Ca0.5MnO3, we discuss about the nature of the complex phase-segregated state established in this compound below T~210 K. Between TN<T<TC, the ESR spectra shows two lines characteristic of two different magnetic phases. From the resonance field (Hr) derived for each line we argue that the incommensurate-charge-ordering phase (ICO) which coexists with ferromagnetic-metallic (FMM) clusters in this temperature interval, is mainly paramagnetic and not antiferromagnetic. The FMM/ICO ratio can be tuned with a relatively small field, which suggests that the internal energy associated with those phases is very similar. Below TN, there is an appreciable FM contribution to the magnetization and the ESR spectra indicates the presence of FM clusters in an antiferromagnetic matrix (canted). Our results show that ESR could be a very useful tool to investigate the nature of the phase-separated state now believed to play a fundamental role in the physics of mixed valent manganites.Comment: 6 pages, 6 figure