Tight-binding perspective on excitons in hexagonal boron nitride

Doctoral thesis (2021)

Two dimensional materials, which are systems composed of one or several angstrom-thin layers of atoms, have recently received considerable attention for their novel electronic and optical properties. In ... [more ▼]

Two dimensional materials, which are systems composed of one or several angstrom-thin layers of atoms, have recently received considerable attention for their novel electronic and optical properties. In such systems, the quasi two dimensional confinement of electrons as well as the reduced dielectric screening lead to a strong binding of electrons and holes. These bound electron-hole excitations, termed excitons, control many of the peculiar opto-electronic properties of 2D materials. In this context we study hexagonal Boron Nitride (hBN) as a prototypical 2D system. hBN layers crystallize in a honeycomb lattice similar to graphene, with carbon atoms replaced by boron and nitrogen. Contrary to its carbon cousin, hBN is a wide band gap semiconductor, well know for its UV luminescence properties and its particularly strong excitons. We investigate theoretically the excitonic properties of single and multilayer hBN. To describe excitons, we make use of the Bethe-Salpeter equation, which provides an effective hamiltonian for electron-hole pairs. We show that, owing to the relatively simple electronic structure of BN systems, it is possible there to construct a model that approximately maps the Bethe-Salpeter equation onto an effective tight-binding Hamiltonian with few parameters, which are in turn fitted to ab initio calculations. Using this technique, we are able to study in detail the excitonic series in single layer hBN. We classify its excitons according to the symmetries of the point group of the crystal lattice, and thus provide precise optical selection rules. Because our model naturally preserves the crystal geometry, we are able to characterize the effects of the lattice, and show how their inclusion affects the excitonic and, in turn, optical properties of hBN compared to a continuum hydrogenoid model. Further, we can access exciton dispersion, which is a crucial component for the understanding of indirect processes. We thus examine the dispersion of the lowest bound state. Having established the properties of the single layer, we turn our attention to multilayers. The interaction of several layers leads to a phenomenon known as Davydov splitting. Under this lens, we investigate how the number of layers affects the excitonic properties of hBN, with particular focus on the Davydov splitting of the lowest bound exciton, which is responsible for the main feature of the absorption spectra. We discuss the effects responsible for the splitting of excitons in multilayers, and construct a simple one-dimensional model to provide a qualitative understanding of their absorption spectra as a function of the number of layers. In particular, we show that, from trilayers onwards, we can distinguish inner excitons, which are localized in the inner layers, and surface excitons, which are localized on the outer layers. Remarkably, the lowest bound bright state is found to be a surface exciton. Finally, we briefly present a comparison of tight-binding calculations with ab initio calculations of the absorption spectrum of bulk hBN. We discuss its first peaks, and how they are related to the excitons of single-layer hBN. [less ▲]

Direct and indirect excitons in boron nitride polymorphs: A story of atomic configuration and electronic correlation

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 ▲]