Executive Summary : | The escalating research in the field of topology necessitates an understanding of the underlying rich physics behind the materials possessing unique features of non-trivial topology in both electronic and phononic states. The fundamental focus of the proposal is to leverage their utility in the domains of superconductivity, thermoelectric materials, and transport phenomena. The current proposal aims at a detailed theoretical investigation of potential quantum materials which are expected to provide opportunities for realising the topological superconductors that host Majorana Fermions - a cornerstone of Quantum computing, as well as efficient thermoelectric (magnetic or non-magnetic) materials and materials with excellent transverse effects. Our proposal mainly focuses on three families of compounds as 111-series, ABCD-type oxy - chalcogenides, (i.e A → heavy metal, B → transition metal elements, C → chalcogenides and D → oxides) and XY-type compounds (X being transition metal elements and Y = Pnictides) and related materials. With the challenging aspects involved in detecting the phonon surface states of materials and topological superconductivity experimentally, we strongly believe that our primary objective of exploring the quantum materials through first-principles modelling will provide a roadmap for experimentalists working in these areas and will make a significant contribution to human resource development |