Sharma, Shivam2025-03-212025-03-212024-10https://hdl.handle.net/11299/270614University of Minnesota Ph.D. dissertation. October 2024. Major: Aerospace Engineering and Mechanics. Advisor: Richard James. 1 computer file (PDF); x, 173 pages.The design, discovery, synthesis and characterization of novel nanomaterials and nanostructures with intriguing electronic and functional properties are central to contemporary scientific research. Symmetries of quantum mechanics such as time-reversal, spatial, and particle-hole symmetry govern the range of remarkable phenomena including superconductivity, ferromagnetism, electron transport, spin dynamics and emergence of topological states. The exploitation of these symmetries plays a pivotal role in understanding and controlling the behavior of quantum systems at nanoscale. Following this line of thought, this thesis first deals with quasi-one-dimensional (1D) materials with helical and cyclic symmetries such as nanotubes, nanowires and nanoribbons. The emergent forms of such matter can exhibit strongly correlated phases and collective electronic phases such as superconductivity, ferromagnetism, Wignercrystallization and Mott insulating states. Due to the unique morphology of these materials, they are expected to exhibit these properties significantly different from bulk phase materials. Moreover, its 1D geometry offers excellent opportunities for incorporating them in novel quantum, electromagnetic and photonic device applications. In this work, we use specialized symmetry-adapted first principles calculations to investigate the electromechanical properties of a set of 1D materials featuring flat bands. Specifically, two prototypical nanotubes based on Kagome and hexagonal lattice geometries of carbon and phosphorus are studied. All types of nanotubes explored here display flat bands degenerate with either parabolic or Dirac bands, which makes them multifunctional. Our findings unveil a range of noteworthy phase transitions, electronic, structural, and magnetic characteristics unique to these nanotubes. The thesis further leverages a graph theoretic framework to systematically generate a variety of 2D lattices which feature fascinating electronic states including flat bands and Dirac cone. Specifically, the split and line graphs of a bipartite lattices exhibit a degenerate combination of flat and dispersive bands in their band diagram. These bands are usually topologically trivial but by introducing spin-orbit coupling, the flatband transforms into a quasi-flat, become gapped and show topologically non-trivial state. Remarkably, tuning system parameters and applying external strain trigger qauntum and topological phase transition transitions between trivial insulator, semimetallic, and topological phases across different lattices. These findings highlight the potential of strain engineering as a powerful tool for manipulating quantum phases. Finally, we have extended the objective molecular dynamics (OMD) framework to nonadiabatic quantum dynamics. In the nonadiabatic regime, the system's characteristics are influenced by the coupled electron-nuclei dynamics. The nuclei follow the classical description of OMD, and the electronic motion is described by the time-dependent Schrödinger equation. Using the time-dependent symmetry groups, we derived the exact simplification of time-dependent Schrödinger equation. Such phenomena break Born-Oppenheimer approximation and offer opportunity to investigate non-equilibrium electron transport, photoexcitation and superfluidity.enFlat band physicsNondiabatic quantum dynamicsStrongly correlated quantum mechanicsTopological insulatorsThesis or Dissertation