Group VI elemental 2D materials have been predicted to possess promising properties in electronics, optoelectronics, thermoelectricity, sensors, and detectors[1–5]. In this thesis, we present the electronic and optical properties of square selenene (s-Se), a 2D allotrope of selenium. We start by calculating the electronic properties using Density Functional Theory (DFT). These ab initio calculations show the formation of an anisotropic cone with semi-Dirac dispersion in a non-symmetric point, denoted P1, in the Brillouin zone, which forms a narrow gap (∼0.1 eV) due to spin-orbit coupling (SOC). Then, we uncover an intricate reciprocal space spin texture along the Brillouin zone, with spin-momentum locking around P1. To conclude the DFT calculations, we show the existence of edge states in two types of s-Se nanoribbons, with one of them presenting topologically non-trivial features, which are confirmed in other works[1,6]. We then replicate a k⋅p Hamiltonian, for the band structure around P1, from the literature[1] and add various SOC terms to obtain an effective model that describes the band structure data from fully relativistic DFT calculations and qualitatively reproduces the spin texture in reciprocal space. Using this effective model, we describe the exciton formation in the Dirac-like cone gap using the variational method while considering an anisotropic version of the Rytova-Keldysh potential[7]. This analysis provides a first characterisation of the exciton ground-state in square selenene, describing its binding energy (Eb=-24 meV) and wavefunction, which, to the best of our knowledge, have not been previously reported.

Nesta dissertação são exploradas algumas das principais propriedades óticas de dicalcogenetos de metais de transição (TMDs) devido a efeitos excitónicos. Na primeira parte do texto dedicamo-nos ao estudo do caso de uma camada de MoS2 perto de um material magnético. Aí, vimos que, devido à proximidade com o material magnético, a simetria de inversão temporal do TMD é quebrada, originando uma resposta de Hall finita mesmo na ausência de um campo magnético externo. Nessa mesma secção, calculamos a condutividade ótica do sistema quer no regime de partícula única, quer no excitónico, estudando o efeito da polarização da luz incidiente. Em ambos os casos verificou-se a excitação seletiva do vale K ou K’ quando luz circularmente polarizada é usada. Na secção seguinte dedicamo-nos ao estudo dos estados-, uma classe de excitões que, devido a regras de seleção, não aparece em espetros óticos resultantes de excitações interbanda, mas que pode ser estudada em experiências do tipo pump-probe. Partindo de uma expressão microscópica para a polarizabilidade, estudamos como o laser pump pode povoar o estado 1, enquanto que o probe induz transições do 1 para a série-. As duas secções finais são dedicadas ao estudo da interação de excitões com fonões Aí, calculamos a largura espetral da ressonância 1 em vários TMDs e observamos que naqueles com molibdénio a largura cresce linearmente com a temperatura, com uma correção exponencial a temperaturas elevadas, enquanto que para TMDs com tungsténio esta rapidamente se afasta da dependência linear. Nessas secções estudamos ainda como o acoplamento com fonões produz um desvio para o vermelho da ressonância do estado 1, e como esta adquire uma forma assimétrica.

In this thesis, we study the emission of excitons via inelastic tunneling in mesoscopic devices with two electrodes separated by a non-conductive material, subjected to a biased electrostatic potential. We study this problem applying both a simplified toy model and a detailed model for a graphene/hexagonal boron nitride/graphene (gr-hBN-gr) van der Waals (vdW) heterostructure. Specifically, we focus on the corrections to the current arising from the interaction between the tunneling electrons and the two-dimensional excitons hosted by a transition metal dichalcogenide (TMD) layer placed a few nanometers apart. To this end, we start by applying the non-equilibrium Green’s function (NEGF) technique to a generalized transport problem for a two-contact mesoscopic system with general electron-boson interactions, thus obtaining analytic expressions for the non-interacting elastic current - the Landauer formula - written as the energy integral of the contact’s occupied levels and the transmission function, which is related to the probability of an electron with a given energy to tunnel through the device. Treating the electron-boson interaction as a perturbation, we also obtain the second order corrections that these interactions introduce, separating the cases of elastic and inelastic processes. In order to gain insight about the general features that arise in the electron tunneling problem, we apply these generic results to a one-dimensional toy-model at zero temperature and calculate both the transmission functions and the I-V curves for this idealized system. Although simple in its nature, it is sufficient to capture the phenomena of inelastic tunneling assisted by the emission of a bosonic excitation. As such, it captures some of the essential features of the more complex vdW device. We are able to show that, when accounting for interactions up to the second order, there is an increase in the total current for bias voltages in resonance with the model sample, while for voltages exceeding this threshold there is a suppression in the total current dominated by the elastic correction, even though its inelastic counterpart contributes with a small increase. Additionally, we also show that these interactions open new tunneling channels that depend on boson’s energy. Finally, we tackle the problem of finding the exciton-assisted inelastic tunneling current flowing in the vdW heterostructure, electromagnetically coupled to the excitonic layer (TMD). To do so, we calculate the matrix element for the electron-exciton interaction, mediated by the emission and absorption of virtual photons, in a second order perturbation theory and use it to obtain the transition rate from Fermi’s golden rule, from which we are able to find the inelastic current flowing through the system and the corresponding rate of generation of excitons in the TMD layer.