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 particles [1]. Theoretical predictions are triggering the exploration of novel 2D geometries [2–10], such as graphynes, Kagomé and the Lieb lattice. The latter is the 2D analogue of the 3D lattice exhibited by perovskites [2]; it is a square-depleted lattice, which is characterised by a band structure featuring Dirac cones intersected by a flat band. Whereas photonic and cold-atom Lieb lattices have been demonstrated [11–17], 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 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 energies, second-order electronic patterns are observed, which are equivalent to a super-Lieb lattice.

Localized gap modes in nonlinear dimerized Lieb lattices

“…Our findings might open a new pathway in the attempts to realize the most suitable environment and conditions for full control of the light propagation in photonics. Some experimental realizations of electronic Lieb lattices have also been done recently using CO molecules on Cu(111) [50]. The proposed system may be a good candidate for our predictions, since it allows one to tune parameters that cannot be easily varied in a real solidstate material.…”

Disorder-induced topological phase transitions on Lieb lattices

“…Recently, Qiu et al showed that the artificial Lieb lattices can be realized on the metallic copper surface 13 . The artificial Lieb Lattice was rapidly confirmed in experiments 14,15 , providing a realistic electronic Lieb lattice system to explore the above-mentioned physics.…”

Temperature and doping induced instabilities of the repulsive Hubbard model on the Lieb lattice

“…1. The noninteracting 2D Lieb lattice has been realized using ultracold atoms [17,26], photonic lattices [27,28], and also electronically [29,30]. To explore flat-band ferromagnetism, the repulsive Hubbard model on the 2D Lieb lattice has previously been studied using real-space dynamical mean theory (R-DMFT) combined with a numerical renormalization group (NRG) impurity solver at half-filling and zero temperature [6].…”