Exciton states in free-standing and embedded semiconductor nanocrystals

Semiconductor quantum dots (QDs), often referred to as "artificial atoms", have discrete energy levels that can be tuned by changing the QD size and shape. The existence of zero-dimensional states in QDs has been proved by high spectrally and spatially resolved photoluminescence (PL) studies Empedocles et al. (1996); Grundmann et al. (1995). Semiconductor QDs can be divided into two types, (1) epitaxially grown self-assembled dots (SAQDs) and (2) nanocrystals (NCs) surrounded by a non-semiconductor medium. Usually, SAQDs are obtained by using appropriate combinations of lattice mismatched semiconductors, taking advantage of the Stranski-Krastanov growth mode where highly strained 2D layers relax by forming 3D islands instead of generating misfit dislocations. SAQDs are robust and already integrated into a matrix appropriate for device applications Grundmann (2002). However, the size, shape and size distributions of the 3D islands are determined only by the strain related to the lattice mismatch of the specific heterojunction. Also, the density and the possibility of obtaining different nanocrystals over a given substrate have considerable limitations in this method. […] Finally, we present some calculated results concerning free-standing and embedded QDs and check them against experimental trends reported in the literature.FCT, Projeto PTDC/FIS/113199/2009; Erasmus Mundus Progra

New magneto-polaron resonances in a monolayer of a transition metal dichalcogenide

Transition metal dichalcogenide (TMD) semiconductors are two-dimensional materials with great potential for the future of nano-optics and nano-optoelectronics as well as the rich and exciting development of basic research. The influence of an external magnetic field on a TMD monolayer raises a new question: to unveil the behavior of the magneto-polaron resonances (MPRs) associated with the phonon symmetry inherent in the system. It is shown that the renormalized Landau energy levels are modified by the interplay of the long-range Pekar–Fröhlich (PF) and short-range deformation potential (DP) interactions. This leads to a new series of MPRs involving the optical phonons at the center of the Brillouin zone. The coupling of the two Landau levels with the LO and A1 optical phonon modes provokes resonant splittings of double avoided-crossing levels giving rise to three excitation branches. This effect appears as bigger energy gaps at the anticrossing points in the renormalized Landau levels. To explore the interplay between the MPRs, the electron-phonon interactions (PF and DP) and the couplings between adjacent Landau levels, a full Green’s function treatment for the evaluation of the energy and its life-time broadening is developed. A generalization of the two-level approach is performed for the description of the new MPR branches. The obtained results are a guideline for the magneto-optical experiments in TMDs, where three MPR peaks should be observable

Exciton-polaritons of a 2D semiconductor layer in a cylindrical microcavity

We describe exciton-polariton modes formed by the interaction between excitons in a 2D layer of a transition metal dichalcogenide embedded in a cylindrical microcavity and the microcavity photons. For this, an expression for the excitonic susceptibility of a semiconductor disk placed in the symmetry plane perpendicular to the axis of the microcavity is derived. Semiclassical theory provides dispersion relations for the polariton modes, while the quantum-mechanical treatment of a simplified model yields the Hopfield coefficients, measuring the degree of exciton-photon mixing in the coupled modes. The density of states (DOS) and its projection onto the photonic and the excitonic subspaces are calculated taking monolayer MoS 2 embedded in a Si 3 N 4 cylinder as an example. The calculated results demonstrate a strong enhancement, for certain frequencies, of the total and local DOS (Purcell effect) caused by the presence of the 2D layer.We are grateful to Dr. Fernando de Leon for helpful discussion. Funding from the European Commission, within the project ”Graphene-Driven Revolutions in ICT and Beyond” (Ref. No. 696656), and from the Portuguese Foundation for Science and Technology (FCT) in the framework of the PTDC/NAN-OPT/29265/2017 Towards high speed optical devices by exploiting the unique electronic properties of engineered 2D materials project the Strategic Funding UID/FIS/04650/2019 is gratefully acknowledged. C. T-G acknowledges support from the Brazilian Agency CNPq

One-dimension cubic-quintic Gross-Pitaevskii equation in Bose-Einstein condensates in a trap potential

By means of new general variational method we report a direct solution for the quintic self-focusing nonlinearity and cubic-quintic 1D Gross Pitaeskii equation (GPE) in a harmonic confined potential. We explore the influence of the 3D transversal motion generating a quintic nonlinear term on the ideal 1D pure cigar-like shape model for the attractive and repulsive atom-atom interaction in Bose Einstein condensates (BEC). Also, we offer a closed analytical expression for the evaluation of the error produced when solely the cubic nonlinear GPE is considered for the description of 1D BEC.Comment: 6 pages, 3 figure

Generating Bounds for the Ground State Energy of the Infinite Quantum Lens Potential

Moment based methods have produced efficient multiscale quantization algorithms for solving singular perturbation/strong coupling problems. One of these, the Eigenvalue Moment Method (EMM), developed by Handy et al (Phys. Rev. Lett.{\bf 55}, 931 (1985); ibid, {\bf 60}, 253 (1988b)), generates converging lower and upper bounds to a specific discrete state energy, once the signature property of the associated wavefunction is known. This method is particularly effective for multidimensional, bosonic ground state problems, since the corresponding wavefunction must be of uniform signature, and can be taken to be positive. Despite this, the vast majority of problems studied have been on unbounded domains. The important problem of an electron in an infinite quantum lens potential defines a challenging extension of EMM to systems defined on a compact domain. We investigate this here, and introduce novel modifications to the conventional EMM formalism that facilitate its adaptability to the required boundary conditions.Comment: Submitted to J. Phys.

Exciton-polaritons in 2D dichalcogenide layers placed in a planar microcavity: tuneable interaction between two Bose-Einstein condensates

Exciton-polariton modes arising from interaction between bound excitons in monolayer thin semiconductor sheets and photons in a Fabry-Perot microcavity are considered theoretically.We calculate the dispersion curves, mode lifetimes, Rabi splitting, and Hopfield coefficients of these structures for two nearly 2D semiconductor materials, MoS2 and WS2, and suggest that they are interesting for studying the rich physics associated with the Bose-Einstein condensation of exciton polaritons. The large exciton binding energy and dipole allowed exciton transitions, in addition to the relatively easily controllable distance between the semiconductor sheets, are the advantages of this system in comparison with traditional GaAs or CdTe based semiconductor microcavities. In particular, in order to mimic the rich physical properties of the quantum degenerate mixture of two bosonic species of dilute atomic gases with tunable interspecies interaction, we put forward a structure containing two semiconductor sheets separated by some atomic-scale distance (l) using a nearly 2D dielectric (e.g., h-BN), which offers the possibility of tuning the interaction between two exciton-polariton Bose-Enstein condensates. We show that thedynamics of this structure are ruled by two coupled Gross-Pitaevskii equations with the coupling parameter∼ l−1.CNPq (Brazil), FCT (Portugal), EC Graphene Flagship Project (Contract No. CNECTICT- 604391

Condensed exciton polaritons in a two-dimensional trap: elementary excitations and shaping by a Gaussian pump beam

An exciton-polariton condensate (EPC) confined in a parabolic two-dimensional trap is considered theoretically. In the realistic limit of weakly interacting polaritons, the nonlinear term in the Gross-Pitaevskii equation describing the properties of the condensate can be considered as a perturbationwith respect to the trapping potential, which allows for a convenient analytical description of the EPC ground state and Bogolyubov-type elementary excitations around it. The excitation modes with the energies and wave functions depending on the polariton-polariton coupling strength are derived for the condensate, neglecting interaction with uncondensed polaritons can be neglected. The energies of these modes are shown to be almost equidistant, even for a rather strong polariton-polariton interaction inside the condensate. This makes lateral parabolic traps promising candidates for realization of bosonic cascade lasers based on exciton polaritons. Another physical scenario is also considered where the interaction with a reservoir of uncondensed polaritons is more important than that inside the EPC. In this case, it is shown that the condensate is “reshaped” by the repulsive interaction with the reservoir, namely, pushed out from the center of the trap in real space and blue-shifted in energy, in agreement with the results obtained in a number of recent experiments.Fundação para a Ciência e a Tecnologia (FCT