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2. A Ginzburg-Landau model with topologically induced free discontinuities
- Author
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Goldman, Michael, Merlet, Benoît, Millot, Vincent, Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Reliable numerical approximations of dissipative systems (RAPSODI ), Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), We thank R. Badal, M. Cicalese, L. De Luca, and M. Ponsiglione for telling us about their result [BCLP16] and giving us an early access to a preprint version. We also thank M. Dos Santos for pointing out the paper [ILR00]. The authors have been supported by the Agence Nationale de la Recherche through the grants ANR-12-BS01-0014-01 (Geometrya), ANR-14-CE25-0009-01 (MAToS), and by the PGMO research project COCA. BM was partially supported by the INRIA team RAPSODI and the Labex CEMPI (ANR-11-LABX-0007-01)., ANR-12-BS01-0014,GEOMETRYA,Théorie géométrique de la mesure et applications(2012), ANR-14-CE25-0009,MAToS,Analyse des singularités topologiques dans quelques problèmes issus de la physique mathématique(2014), ANR-11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire Paul Painlevé (LPP), and Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe
- Subjects
Mathematics - Analysis of PDEs ,[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] ,Condensed Matter::Superconductivity ,FOS: Mathematics ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,Analysis of PDEs (math.AP) - Abstract
We study a variational model which combines features of the Ginzburg-Landau model in 2D and of the Mumford-Shah functional. As in the classical Ginzburg-Landau theory, a prescribed number of point vortices appear in the small energy regime; the model allows for discontinuities, and the energy penalizes their length. The novel phenomenon here is that the vortices have a fractional degree $1/m$ with $m\geq 2$ prescribed. Those vortices must be connected by line discontinuities to form clusters of total integer degrees. The vortices and line discontinuities are therefore coupled through a topological constraint. As in the Ginzburg-Landau model, the energy is parameterized by a small length scale $\varepsilon>0$. We perform a complete $��$-convergence analysis of the model as $\varepsilon\downarrow0$ in the small energy regime. We then study the structure of minimizers of the limit problem. In particular, we show that the line discontinuities of a minimizer solve a variant of the Steiner problem. We finally prove that for small $\varepsilon>0$, the minimizers of the original problem have the same structure away from the limiting vortices.
- Published
- 2017
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3. Narrow Linewidth Excitonic Emission in Organic-Inorganic Lead Iodide Perovskite Single Crystals
- Author
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Diab, Hiba, Trippé-Allard, Gaëlle, Lédée, Ferdinand, Jemli, Khaoula, Vilar, Christèle, Bouchez, Guillaume, Jacques, Vincent L.R., Tejeda, Antonio, Even, Jacky, Lauret, Jean-Sébastien, Deleporte, Emmanuelle, Garrot, Damien, Laboratoire Aimé Cotton (LAC), École normale supérieure - Cachan (ENS Cachan)-Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Photophysique et Photochimie Supramoléculaires et Macromoléculaires (PPSM), École normale supérieure - Cachan (ENS Cachan)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS), Groupe d'Etude de la Matière Condensée (GEMAC), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique des Solides (LPS), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Fonctions Optiques pour les Technologies de l'informatiON (FOTON), Université de Rennes (UR)-Université européenne de Bretagne - European University of Brittany (UEB)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École Nationale Supérieure des Sciences Appliquées et de Technologie (ENSSAT)-Télécom Bretagne-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Photonique Quantique et Moléculaire (LPQM), École normale supérieure - Cachan (ENS Cachan)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), This work has received funding from the European Union’s Horizon 2020 research and innovation programme under the grant agreement No 687008. The information and views set out in this paper are those of the author(s) and do not necessarily reflect the official opinion of the European Union. Neither the European Union institutions and bodies nor any person acting on their behalf may be held responsible for the use which may be made of the information contained herein. J.S. Lauret is ajunior member of the Institut Universitaire de France., Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)-École normale supérieure - Cachan (ENS Cachan), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université européenne de Bretagne - European University of Brittany (UEB)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), and Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-École Nationale Supérieure des Sciences Appliquées et de Technologie (ENSSAT)-Télécom Bretagne-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Materials science ,Photoluminescence ,Exciton ,02 engineering and technology ,010402 general chemistry ,7. Clean energy ,01 natural sciences ,Laser linewidth ,Condensed Matter::Materials Science ,Condensed Matter::Superconductivity ,General Materials Science ,Physical and Theoretical Chemistry ,Thin film ,Spectroscopy ,Perovskite (structure) ,business.industry ,Condensed Matter::Other ,021001 nanoscience & nanotechnology ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,0104 chemical sciences ,[CHIM.THEO]Chemical Sciences/Theoretical and/or physical chemistry ,Full width at half maximum ,[PHYS.COND.CM-MS]Physics [physics]/Condensed Matter [cond-mat]/Materials Science [cond-mat.mtrl-sci] ,Optoelectronics ,Crystallite ,0210 nano-technology ,business - Abstract
International audience; Hybrid perovskite thin films have demonstrated impressive performance for solar energy conversion and optoelectronic applications. However, further progress will benefit from a better knowledge of the intrinsic photophysics of materials. Here, the temperature-dependent emission properties of CH3NH3PbI3 single crystals are investigated and compared to those of thin polycrystalline films by means of steady-state and time-resolved photoluminescence spectroscopy. Single crystals photoluminescence present a sharp excitonic emission at high energy, with full width at half maximum of only 5 meV, assigned to free excitonic recombination. We highlight a strong thermal broadening of the free excitonic emission, due to exciton–LO-phonon coupling. The emission turned to be very short-lived with a subnanosecond dynamics, mainly induced by the fast trapping of the excitons. The free excitonic emission is completely absent of the thin film spectra, which are dominated by trap state bands.
- Published
- 2016
- Full Text
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