Designer flat bands in quasi-one-dimensional atomic lattices

Certain lattices with specific geometries have one or more spectral bands that are strictly flat, i.e., the electron energy is independent of the momentum. This can occur robustly irrespective of the specific couplings between the lattices sites due to the lattice symmetry, or it can result from fine-tuned couplings between the lattice sites. While the theoretical picture behind flat electronic bands is well developed, experimental realization of these lattices has proven challenging. Utilizing scanning tunneling microscopy (STM) and spectroscopy (STS), we manipulate individual vacancies in a chlorine monolayer on Cu(100) to construct various atomically precise one-dimensional (1D) lattices with engineered flat bands. We realize experimentally both gapped and gapless flat band systems with single or multiple flat bands. We also demonstrate tunability of the energy of the flat bands and how they can be switched on and off by breaking and restoring the symmetry of the lattice geometry. The experimental findings are corroborated by tight-binding calculations. Our results constitute the first experimental realizations of engineered flat bands in a 1D solid-state system and pave the way toward the construction of, e.g., topological flat band systems and experimental tests of flat-band-assisted superconductivity in a fully controlled system.