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See detailFirst-principles approaches to the description of indirect absorption and luminescence spectroscopy: exciton-phonon coupling in hexagonal boron nitride
Paleari, Fulvio UL

Doctoral thesis (2019)

The development of novel optoelectronic applications crucially depends on the detailed understanding of light--matter interaction in the candidate materials. From a theoretical point of view, this task is ... [more ▼]

The development of novel optoelectronic applications crucially depends on the detailed understanding of light--matter interaction in the candidate materials. From a theoretical point of view, this task is especially difficult in the case of quasi--2D semiconductors, since their optical response is dominated by strongly bound excitons and many--body perturbation theory (MBPT) must be employed together with first--principles computer simulations. The case of hexagonal boron nitride (hBN) is interesting because its large band gap and high absorption/emission efficiency make it amenable for the fabrication of UV emitting devices. However, the specific microscopic mechanisms that govern the appearance of complex fine structures in the optical spectra of different types of hBN samples (monolayers, few--layers, bulk samples) are poorly understood, leading to discrepancies between experimental and theoretical results. In this Thesis, we first show how the interlayer interaction in multilayers leads to a Davydov splitting of the excitonic states of single--layer hBN. We study and characterize the absorption spectra in single layer, multilayer and bulk hBN systems, focusing on the exciton symmetry and optical activity. We show that in multilayers, Davydov splitting leads to a surface localization of the lowest--lying optically active excitons. These additional spectral features still cannot explain, by themselves, the experimentally measured optical fine structure. Therefore, we calculate exciton dispersion curves in order to search for the existence of indirect excitons with lower energy than the lowest direct exciton. We find that in bilayer hBN the nature of the optical gap (direct) changes with respect to the single--particle gap (indirect). In contrast, in bulk hBN (and thicker few--layers of hBN) both optical and quasiparticle gaps are indirect, i.e., they display a pronounced minimum in the excitonic dispersion curve between $\Gamma$ and K. %in accordance with the single--particle gap. If the lowest exciton is indirect, as in bulk hBN, then phonon--assisted transitions become relevant for the description of the optical spectra. The reliable \textit{ab initio} description of exciton--phonon coupling in indirect absorption and emission is the main focus of this Thesis. We have tackled the problem with two approaches. In the static approach, we calculate the coupling of excitons with phonons in a supercell via a finite--displacement method. The supercell is commensurate with the $k$--point corresponding to the minimum of the exciton dispersion. In this way, we are able to reproduce the rich fine structure in the luminescence spectrum of bulk hBN in good agreement with experiment and to explain it in terms of exciton--phonon coupling. The finite--displacement approach is supposed to work for indirect optical spectra in any material where the minimum of the exciton dispersion gives the dominant phonon--assisted contribution. Since in the absorption case this is not always true, we have employed a second, perturbative approach for the description of indirect absorption spectra which also includes dynamical effects and a microscopic treatment of the coupling. We have implemented the required many--body quantities (namely, the exciton--phonon coupling matrix elements and self--energy) in the \texttt{Yambo} many--body code. We expect this new method to allow us to overcome many of the theoretical limitations of previous approaches to indirect absorption. [less ▲]

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See detailExciton-Phonon Coupling in the Ultraviolet Absorption and Emission Spectra of Bulk Hexagonal Boron Nitride
Paleari, Fulvio UL; Miranda, Henrique P. C.; Molina-Sanchez, Alejandro et al

in PHYSICAL REVIEW LETTERS (2019), 122(18), 187401-6

We present an ab initio method to calculate phonon-assisted absorption and emission spectra in the presence of strong excitonic effects. We apply the method to bulk hexagonal BN, which has an indirect ... [more ▼]

We present an ab initio method to calculate phonon-assisted absorption and emission spectra in the presence of strong excitonic effects. We apply the method to bulk hexagonal BN, which has an indirect band gap and is known for its strong luminescence in the UV range. We first analyze the excitons at the wave vector (q) over bar of the indirect gap. The coupling of these excitons with the various phonon modes at (q) over bar is expressed in terms of a product of the mean square displacement of the atoms and the second derivative of the optical response function with respect to atomic displacement along the phonon eigenvectors. The derivatives are calculated numerically with a finite difference scheme in a supercell commensurate with (q) over bar. We use detailed balance arguments to obtain the intensity ratio between emission and absorption processes. Our results explain recent luminescence experiments and reveal the exciton-phonon coupling channels responsible for the emission lines. [less ▲]

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See detailDirect and indirect excitons in boron nitride polymorphs: A story of atomic configuration and electronic correlation
Sponza, Lorenzo; Amara, Hakim; Attaccalite, Claudio et al

in Physical Review. B, Condensed Matter (2018), 98(12), 125206

We present a detailed discussion of the electronic band structure and excitonic dispersion of hexagonal boron nitride (hBN) in the single layer configuration and in three bulk polymorphs (usual AA′ ... [more ▼]

We present a detailed discussion of the electronic band structure and excitonic dispersion of hexagonal boron nitride (hBN) in the single layer configuration and in three bulk polymorphs (usual AA′ stacking, Bernal AB, and rhombohedral ABC). We focus on the changes in the electronic band structure and the exciton dispersion induced by the atomic configuration and the electron-hole interaction. Calculations are carried out at the level of ab initio many-body perturbation theory (GW and Bethe Salpeter equation) and of a purposely developed tight-binding model. We confirm the change from direct to indirect electronic gap when going from single layer to bulk systems and we give a detailed account of its origin by comparing the effect of different stacking sequences. We emphasize that the inclusion of the electron-hole interaction is crucial for the correct description of the momentum-dependent dispersion of the excitations. As a result the electron-hole dispersion is flatter than the one obtained from the band structure. In the AB stacking this effect is particularly important as the lowest-lying exciton is predicted to be direct despite the indirect electronic band gap. [less ▲]

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See detailExcitons in few-layer hexagonal boron nitride: Davydov splitting and surface localization
Paleari, Fulvio UL; Galvani, Thomas UL; Amara, Hakim et al

in 2D MATERIALS (2018), 5(4), 045017

Hexagonal boron nitride (hBN) has been attracting great attention because of its strong excitonic effects. Taking into account few-layer systems, we investigate theoretically the effects of the number of ... [more ▼]

Hexagonal boron nitride (hBN) has been attracting great attention because of its strong excitonic effects. Taking into account few-layer systems, we investigate theoretically the effects of the number of layers on quasiparticle energies, absorption spectra, and excitonic states, placing particular focus on the Davydov splitting of the lowest bound excitons. We describe how the inter-layer interaction as well as the variation in electronic screening as a function of layer number N affects the electronic and optical properties. Using both ab initio calculations and a tight-binding model for an effective Hamiltonian describing the excitons, we characterize in detail the symmetry of the excitonic wavefunctions and the selection rules for their coupling to incoming light. We show that for N > 2, one can distinguish between surface excitons that are mostly localized on the outer layers and inner excitons, leading to an asymmetry in the energy separation between split excitonic states. In particular, the bound surface excitons lie lower in energy than their inner counterparts. Additionally, this enables us to show how the layer thickness affects the shape of the absorption spectrum. [less ▲]

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See detailExcitons in boron nitride single layer
Galvani, Thomas; Paleari, Fulvio UL; Pereira Coutada Miranda, Henrique UL et al

in Physical Review. B : Condensed Matter (2016), 94(125303),

Boron nitride single layer belongs to the family of two-dimensional materials whose optical properties are currently receiving considerable attention. Strong excitonic effects have already been observed ... [more ▼]

Boron nitride single layer belongs to the family of two-dimensional materials whose optical properties are currently receiving considerable attention. Strong excitonic effects have already been observed in the bulk and still stronger effects are predicted for single layers. We present here a detailed study of these properties by combining ab initio calculations and a tight-binding Wannier analysis in both real and reciprocal space. Due to the simplicity of the band structure with single valence (π) and conduction (π∗) bands the tight-binding analysis becomes quasiquantitative with only two adjustable parameters and provides tools for a detailed analysis of the exciton properties. Strong deviations from the usual hydrogenic model are evidenced. The ground-state exciton is not a genuine Frenkel exciton, but a very localized tightly bound one. The other ones are similar to those found in transition-metal dichalcogenides and, although more localized, can be described within a Wannier-Mott scheme. [less ▲]

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