Isolated flat band in artificially designed Lieb lattice based on macrocycle supramolecular crystal

Abstract

Abstract Isolated flat bands are known to host various strongly correlated phases due to the enhanced Coulomb interactions when the flat bands are gapped from dispersive bands. One way to achieve an isolated flat band is by breaking the on-site energy symmetry in a Lieb lattice. In this study, we demonstrate the design of such a Lieb lattice. The self-assembly of square-shaped macrocycle molecules on a Ag(111) surface forms a two-dimensional supramolecular crystal, comprising three types of nanopores with different sizes arranged in a Lieb lattice. The surface-state electrons of the Ag(111) substrate confined by these nanopores behave as quantum dots with specific energies depending on the pore size. Using scanning tunneling spectroscopy and plane-wave quantum simulation, we reveal that this artificial Lieb lattice exhibits an isolated flat band gapped at 0.16 eV from the nearest band. The supramolecular crystal is nearly defect-free and extends to sub-micrometer size, making it a practical platform for exploring the exotic properties of the isolated flat band.