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 known 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 hydrogenoïd 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.
Dissertation defence committee:
Chairman: Professor, Dr. Thomas Schmidt, Université du Luxembourg
Vice Chairman: Professor, Dr Gabriel Bester, Universität Hamburg
Dr.Christophe Delerue, CNRS Institute
Dr. Hakim Amara,ONERA Institute