Experimental realization and characterization of an electronic Lieb lattice

TL;DR

This paper reports the experimental creation and analysis of an electronic Lieb lattice on a Cu(111) surface, confirming theoretical predictions with STM techniques and computational models, and revealing complex electronic patterns at higher energies.

Contribution

First realization of an electronic Lieb lattice in a 2D material using STM-confined surface state electrons, validated by experimental and computational methods.

Findings

Confirmed the characteristic band structure of the Lieb lattice

Observed second-order electronic patterns resembling a super-Lieb lattice

Validated experimental results with muffin-tin and tight-binding calculations

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 particles. Theoretical predictions are triggering the exploration of novel 2D geometries, such as graphynes, Kagom\'{e} and the Lieb lattice. The latter is the 2D analogue of the 3D lattice exhibited by perovskites; it is a square-depleted lattice, which is characterised by a band structure featuring Dirac cones intersected by a topological flat band. Whereas photonic and cold-atom Lieb lattices have been demonstrated, 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 CO molecules positioned with a scanning tunneling microscope (STM). Using scanning tunneling microscopy, spectroscopy and wave-function 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 energy, second-order electronic patterns are observed, which are equivalent to a super-Lieb lattice.