Oral: Strain induced topological phase transitions in split and line graphs of bipartite lattices featuring flat bands

Materials featuring topological flat bands are gaining significant attention owing to their association with remarkable transport and strongly correlated electronic properties such as high-temperature superconductivity, magnetism, Wigner crystallization and Mott-insulating states. Of particular interest are two-dimensional (2D) materials which provide the good set up for observing fascinating electronic states including flat bands and Dirac cones. In this work, we use unifying graph-theoretic framework to systematically generate a variety of 2D lattices that exhibit dispersionless states and investigate the effect of strain on their electronic and topological properties. Specifically, combinations of split and line graph operations applied to root graphs (square and hexagonal honeycomb lattices) create lattices possessing degenerate combinations of flat and dispersive bands. By introducing spin-orbit coupling, the flatband transforms into a quasi-flat, become gapped and topologically non-trivial. Interestingly, tuning system parameters and applying external strain trigger transitions between trivial insulator, semimetallic, and topological phases. These findings highlight the potential of strain engineering as a powerful tool for manipulating quantum phases.