Experimental realization and characterization of an electronic Lieb lattice

Abstract

Geometry, whether on the atomic or nanoscale, is a key factor for the electronic band structure of materials. Some specific geometries give rise to novel and potentially useful electronic bands. For example, a honeycomb lattice leads to Dirac-type bands where the charge carriers behave as massless particles¹. 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. The Lieb lattice is the 2D analogue of the 3D lattice exhibited by perovskites²; it is a square-depleted lattice, which is characterized by a band structure featuring Dirac cones intersected by a flat band. 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. 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. Using scanning tunnelling microscopy, spectroscopy and wavefunction mapping, we confirm the predicted characteristic electronic structure of the Lieb lattice. The experimental findings are corroborated by muffin-tin and tight-binding calculations. At higher energies, second-order electronic patterns are observed, which are equivalent to a super-Lieb lattice.