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.

We reviewed the tools of quantum physics used in modeling of quantum coherence (QC) effects in different systems, including biological systems, which behave as quantum objects in some of their degrees of freedom. In particular, we considered the usage of the effective Hamiltonian (EH), Green's function (GF) and density matrix (DM) methods in the analysis of QC, focusing on QC in biological systems. We discussed the two main mechanisms of loss of quantum state coherence: (i) dephasing of the originally prepared coherent wave package and (ii) population relaxation in the same wave package. Dephasing does not affect the quantum state population, e.g. as in spin-spin relaxation, where dephasing is described by the tau(2) relaxation time. On the other hand, the state population relaxation of the spin wavepackage is attributed to spin-lattice relaxation and is described by the tau(1) relaxation time. Presently we discussed EH and GF formalisms in terms of the complex energy, dependent on intra- and intersystem interactions that induce state population relaxation. We provided a detailed analysis of these approaches for the exciton relaxation dynamics in a glycine polypeptide chain. The same phenomena were described in the DM formalism using the relaxation matrix. We discussed QC in different biological systems, showing that QC is conserved when the interactions of the coherent wavepackage with other degrees of freedom are weak, as otherwise population relaxation causes loss of QC. We believe that our results will be useful for the researchers in the area of quantum biology.