Electronic structures of a diagonally striped lattice: Multiple (N−1) -fold degenerate flat bands

We investigate the electronic structure of an interesting two-dimensional (2D) diagonally striped lattice (DSL). It consists of arrays of N different types of ``atoms'' or ``molecules'' with a fixed sequence in both horizontal and vertical directions. Using a tight-binding model, we show that the DSL $(N>2)$ has the symmetry group Amm2 and Pmm2, and exhibits an oscillatory metallic and insulating phases for the odd- and even- N number, respectively. Some conventional 2D lattices, such as the Lieb lattice, can be related to the derivative DSL via vacancy formation by removing one type of atom in every other $(N\ensuremath{-}1)$ row of the original DSL. Interestingly, there are multiple $(N\ensuremath{-}1)$-fold degenerate flat bands in one group of the derivative DSLs, which affords a unique platform for studying many-body physics. In addition to atomic and molecular lattices, we suggest other artificial DSLs, such as photonic and phononic, to be also constructed with possibly interesting properties.