p Orbital Flat Band and Dirac Cone in the Electronic Honeycomb Lattice

Abstract

Theory anticipates that the in-plane p x , p y orbitals in a honeycomb lattice lead to potentially useful quantum electronic phases. So far, p orbital bands were only realized for cold atoms in optical lattices and for light and exciton-polaritons in photonic crystals. For electrons, in-plane p orbital physics is difficult to access since natural electronic honeycomb lattices, such as graphene and silicene, show strong s–p hybridization. Here, we report on electronic honeycomb lattices prepared on a Cu(111) surface in a scanning tunneling microscope that, by design, show (nearly) pure orbital bands, including the p orbital flat band and Dirac cone.

Topological superconductivity in a van der Waals heterostructure

“…While flat band (FB) systems have existed in theoretical proposals for a long time [75][76][77][78][79][80][81][82][83], their experimental realization has been challenging. Flat bands have been recently realized experimentally in optical systems and ultracold atomic gases [84][85][86][87][88][89], in electronic systems arising in real materials (notably twisted bilayer graphene) [90][91][92][93], and recently, in artificial materials fabricated through atom manipulation with the STM [15,28,94,95]. Using the very highly controlled artificial lattices with chlorine vacancies, in PII, we have investigated flat band engineering in quasi-one-dimensional chains.…”

Engineering a Robust Flat Band in III–V Semiconductor Heterostructures

“…While such a ratio is suitable for the creation of a FB, it also renders the s-DC bandwidth to 7 meV at the M points of the Brillouin zone (Figure S4). Direct access to the local density of states (LDOS) in the lattice is obtained with scanning tunnelling spectroscopy (STS), which has beautifully revealed the existence of FBs in 2D atomic crystals 21,22,23 or atomic and molecular lattices on metal surfaces 7,8,9 .…”

Topology, flat bands and magnetic fields in artificial electronic lattices

“…We show that by playing with the size of the artificial sites and their coupling, the p orbitals of the system can be brought in the experimentally observable energy window. Additionally, we show that by introducing clusters of CO scatterers, the hopping parameters in the system can be manipulated to obtain a system with separated s and p orbitals and a flat p orbital band [28,29].…”

“…the bands derived from the 2p z orbitals in graphene). Later, Gardenier et al [28] extended the method: The size of the atomic sites was increased to bring the p band system in the accessible energy window of the Cu (111) surface state [53]. Additionally, by using CO rosettes instead of single COs s-p hybridization could be avoided to a large extent, resulting in two sand four p orbital bands.…”

“…Additionally, by using CO rosettes instead of single COs s-p hybridization could be avoided to a large extent, resulting in two sand four p orbital bands. The p orbital bands include a Dirac cone and a flat band [28], which was considered by tight-binding methods [24,70,71,77,99,101].…”