Abstract
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 tunnelling microscopy (STM) and spectroscopy (STS), we manipulate individual vacancies in a chlorine monolayer on Cu(100) to construct various atomically precise 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 tuneability 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 towards the construction of e.g. topological flat band systems and experimental tests of flat-band-assisted superconductivity in a fully controlled system.
Highlights
There has been a surge of interest in systems exhibiting flat electronic bands, i.e., structures where one of the bands are completely dispersionless throughout the Brillouin zone [1,2,3,4]
The zero kinetic energy means that any other energy scale can be the dominant one: Flat bands are not stable against perturbations and even weak interactions can induce the formation of broken symmetry ground states, such as ferromagnetism [6,10,12,14,15], Wigner crystals [16], superconductivity [17,18,19,20], or fractional quantum Hall, quantum anomalous Hall, and fractional Chern insulator states [21,22,23,24]
We will focus experimentally on the effects of the next nearest neighbor (NNN) hoppings to test the robustness of the engineered bands, how to engineer both gapped and metallic flat-band systems, and to demonstrate how by breaking the symmetry of the chain geometry, we can control the dispersion of the flat bands
Summary
There has been a surge of interest in systems exhibiting flat electronic bands, i.e., structures where one (or more) of the bands are completely dispersionless throughout the Brillouin zone [1,2,3,4]. We will focus experimentally on the effects of the NNN hoppings to test the robustness of the engineered bands, how to engineer both gapped and metallic flat-band systems, and to demonstrate how by breaking the symmetry of the chain geometry, we can control the dispersion of the flat bands. These 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 [49,60,61,62]
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