On the physics of excitons and trions in 2D quantum materials

<p dir="ltr">Quantum materials are a fascinating set of materials which exhibit exotic quantum phenomena that can be used in many modern technologies, such as electronics and photonics. An important consideration for these materials is how they interact with light. As a result, the study of excitons and trions (charged excitons), which are bound states which can form after the absorption of a photon, is of ever-growing interest. For these states, there are two main considerations: the binding energy and the state's lifetime. The ability to investigate and control these factors can lead to greater potential applications for such systems, from quantum information processing to optoelectronic devices such as solar cells.</p><p dir="ltr">In this thesis, we investigate the properties of momentum-dark excitons and trions formed in two-dimensional (2D) materials that exhibit an inverted Mexican-hat shaped dispersion relation, taking monolayer InSe as an example. We employ variational techniques to obtain the momentum-dark and bright ground-states (non-zero and zero quasiparticle momenta, respectively). These states are of particular interest due to their peaks in the quasiparticle density of states. The largest contribution comes from the momentum-dark ground state due to the presence of a van Hove singularity (VHS). These momentum-dark systems require a physical process to provide the necessary momentum to become bright, and thus have longer lifetimes than the bright states. We study the brightening of this state due to coupling with phonons and compute the resulting photoluminescence spectrum.</p><p dir="ltr">We extend this investigation of these bound states to more general cases of Mexican-hat shaped systems, from which we are able to investigate how sensitive these bound states are to changes in the band structure. In particular, we study the effect of the Mexican-hat depth (difference in energy between the $\Gamma$-point and the valence band maximum (VBM)) and the Mexican-hat width (how far away the VBM is from the $\Gamma$-point). We further consider the influence of higher-order van Hove singularities (HOVHS) on these bound states. In addition, we are able to see how a HOVHS can be added to a previously bright excitonic system as a perturbation to generate a momentum-dark state.</p><p dir="ltr">To conclude this work, we begin to develop a way to generalise the sensitivities of changing the Mexican-hat depths on the bound states. This includes comparing directly between the exciton and trion systems and the role the radius (distance between electron-hole pairs) values have on the system.</p>