In this thesis, we have explored the electronic structures of materials for specific applications by investigating controllable competing interactions, a forefront in condensed matter physics and materials science. Utilizing density functional theory (DFT) and parametric tight-binding (TB) model Hamiltonians, our study focuses on halide perovskites (HPs) and 2D transition metal dichalcogenides (TMDs). For HPs, the research develops effective model Hamiltonians for centrosymmetric and non-centrosymmetric halide single perovskites, revealing the impact of inversion symmetry breaking (ISB) on Rashba and/or Dresselhaus spin-orbit coupling (SOC). The exploration extends to halide double perovskites (HDPs), demonstrating the tunability of optoelectronic properties through functionalization, dopings, and defects. A theoretical framework, including a band-projected molecular orbital picture (B-MOP) and momentum matrix elements (MME) from a TB model, is proposed for detailed analysis and tailoring of electronic and optoelectronic properties in HDPs.

We further delve into defect engineering techniques for transition metal dichalcogenides, highlighting chain-doped monolayer TMDs exhibiting one-dimensional (1D) bands with unique physics, including Tomonaga-Luttinger liquid behavior and Rashba spin splitting. Point magnetic defects in metallic hosts like NbSe2 have been explored, revealing spin and orbital polarization characteristics near the impurity site. Overall, the thesis provides comprehensive insights into the role of spin-orbit coupling, symmetry-breaking effects, and defect engineering in inducing non-trivial quantum phases and altering optoelectronic properties in diverse materials.