Origin of the Flat Band in Heavily Cs-Doped Graphene

Abstract

A flat energy dispersion of electrons at the Fermi level of a material leads to instabilities in the electronic system and can drive phase transitions. Here we introduce a method to induce a flat band in two-dimensional (2D) materials. We show that the flat band can be achieved by sandwiching the 2D material by two cesium (Cs) layers. We apply this method to monolayer graphene and investigate the flat band by a combination of angle-resolved photoemission spectroscopy experiment and the calculation. Our work highlights that charge transfer, zone folding of graphene bands and the covalent bonding between C and Cs atoms are at the origin of the flat energy 1 arXiv:1903.09038v2 [cond-mat.mes-hall] 30 May 2019 band formation. The presented approach is an alternative route for obtaining flat band materials to twisting bilayer graphene which yields thermodynamically stable flat band materials in large areas.

Massive and massless charge carriers in an epitaxially strained alkali metal quantum well on graphene

“…1h were taken). The Raman G band of Cs-doped bilayer graphene has a large downshift and a Fano asymmetric shape which arises from electron doping and is in agreement to previous works on monolayer graphene 15,16 . Performing a fit with one Fano line and one line for the feature at 1632 cm −1 that we identified already in the pristine bilayer samples (see Fig.…”

“…Third, the zone folding of the band structure is caused by the Coulomb potential of the Cs 2 × 2 superstructure. The zone folding of the electronic structure of graphene is similar to what we have observed recently for Csfunctionalized monolayer graphene/Ir(111) 16 and what has been reported for oxygen intercalated graphene 48 . Zone folding causes the appearance of a new BZ with new high-symmetry points that are labeled by Γ 0 , K 0 , K 0 Ã , and M 0 that are indicated in Fig.…”

“…Quantum well state 3 comes from Cs orbitals that belong to the first layer of Cs atoms grown on top of the bilayer and quantum well state 4 is from Cs orbitals of intercalated Cs atoms. The proximity of C and Cs orbitals can cause hybridization between them 16 which is clearly visible from Fig. 2b.…”

“…1e of ref. 16 for a sketch of the zone-folded BZ). The broadening of the π conduction band of graphene along the Γ 0 K 0 Ã (KM) direction is a result of covalent bonding of C to Cs and also present in the calculations that we will show later.…”

“…The mechanism which dictates the alkali-metal order is the Coulomb repulsion between ionized alkali atoms. For cesium (Cs) adsorbed on or intercalated underneath monolayer graphene, a perfect order in a (2 × 2) or a ( ffiffi ffi 3 p ffiffi ffi 3 p )R30°superlattice has been observed 11,[14][15][16] . The interaction of epitaxial bilayer graphene with Cs has revealed that, at low Cs coverages, the energetically favorable position of Cs is below the bilayer 14 .…”