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We start by describing a symmetry enforced nodal line semi-metal (NLSM) inthe 2D flat form of honeycomb Group - V and its non trivial thermo-electricresponse. We will then proceed to show that, upon buckling, the systemundergoes its dirac-merging phase transitions. Further buckling leads to theseunpinned Dirac cones annihilating in pairs at two distinct critical angleleading to a second topological phase transition to an insulating state. Wethen show that this seemingly innocuous insulating state is indeed a weaktopological crystalline insulator. Furthermore, upon closer look, thisinsulating state turns out to be a Higher Order Topological Insulator (HOTI)that is protected by $\mathcal{S}_6$ symmetry. In a broader context, we willsee that the the topological properties of buckled Group - $V$ stem from thefact that they topologically belong to the class of Obstructed Atomic Limit(OAL) insulators. Combining all these, we will prove that annihilating pairs ofDirac fermions necessitate a topological phase transition from the criticalsemi-metallic phase to an OAL insulator phase. We also uncover the rich set ofphases in the phase diagram in case of annihilating Dirac fermions and studytheir entanglement properties using entanglement entropy. Finally, based on thenon-trivial topology of these systems, we propose the conceptual design of aquantized switch that is protected by topology. Last part of the thesisinvolves the remarkable discovery of a spin polarized 2D electron/hole gas atthe surfaces of a well known system - LiCoO2.

Knitting quantum knots: Topological phase transitions in Two-Dimensional systems