Identifying and Isolating a Flat Band in 2D Systems

Flat band systems are gaining popularity due to special properties. For instance, the strong correlation of electrons in flat bands leads to realization of unconventional superconductivity. Typically, such bands are only approximately flat and are engineered by fine tuning Vanderwaal’s structures. On the other hand, systems with perfectly flat bands provide a ground for studying exotic quasi-particles such as composite fermions in the fractional quantum Hall state. These flat bands, however, are induced by an external field. Here we explore other systems that host perfectly flat bands, namely the Kagome lattice and the Lieb lattice. One issue with these lattices, however, is that their flat bands are degenerate with other bands. This thesis will explore means to lift the degeneracy while preserving the flatness of the band. It will also demonstrate that the flatness is robust under certain modifications to the lattice and that, unlike suggested by past studies, breaking time-reversal symmetry is not sufficient to isolate the flat band. Instead, we will show that modulating the flux arising from a Chern-Simons type field gaps out the band without disturbing its flatness