Thus far, a 2D electronic Lieb lattice has not been realized. Hence, the local density of states (LDOS) exhibits a characteristic spatial variation, see Fig. 1c. In contrast, all sites contribute to the dispersing bands converging to the Dirac cone. The flat band exclusively contains electronic states which are localized on edge sites. Taking only nearest-neighbour hopping into account and using the same on-site energy for the three sites results in the band structure shown in Fig. 1b. Where ε i and t ( t′) indicate the on-site energy of site i and the (next-)nearest-neighbour hopping constants, respectively. At higher energies, second-order electronic patterns are observed, which are equivalent to a super-Lieb lattice. The experimental findings are corroborated by muffin-tin and tight-binding calculations.
Using scanning tunnelling microscopy, spectroscopy and wavefunction mapping, we confirm the predicted characteristic electronic structure of the Lieb lattice. Here, we report an electronic Lieb lattice formed by the surface state electrons of Cu(111) confined by an array of carbon monoxide molecules positioned with a scanning tunnelling microscope. Whereas photonic and cold-atom Lieb lattices have been demonstrated 11, 12, 13, 14, 15, 16, 17, an electronic equivalent in 2D is difficult to realize in an existing material. The Lieb lattice is the 2D analogue of the 3D lattice exhibited by perovskites 2 it is a square-depleted lattice, which is characterized by a band structure featuring Dirac cones intersected by a flat band. Theoretical predictions are triggering the exploration of novel two-dimensional (2D) geometries 2, 3, 4, 5, 6, 7, 8, 9, 10, such as graphynes and the kagomé and Lieb lattices. For example, a honeycomb lattice leads to Dirac-type bands where the charge carriers behave as massless particles 1.
Some specific geometries give rise to novel and potentially useful electronic bands.
Geometry, whether on the atomic or nanoscale, is a key factor for the electronic band structure of materials.
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