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Extremely flat band in bilayer graphene

DISCUSSION

The experimental high photoemission intensity of the flat band can be partially explained by the 2D extent and broadening in kx and ky. This broadening, however, is not the reason for the flatness and the observed features of the band. If this broadening were to play a significant role, we would see the narrowing and intensity enhancement effects also at other BLG bands around the Embedded Image point where their dE/dk becomes locally zero. The experiments do not show these effects.

In Fig. 1C, we see, unusual for graphene, the disappearance of the interference pattern in the region of the flat band, resulting (Fig. 1D) in a disk-like image of the constant energy cut at 255-meV binding energy. The destructive interference arises because of localization of the wave function on different graphene sublattices (24, 25); however, for the flat band, the wave function is localized on one sublattice only, and preconditions for the destructive interference disappear (fig. S3).

In the ARPES data, there are, in addition to the pronounced flat band, a kink and a second flat band, faintly visible around 150-meV binding energy (Fig. 1, B and G, and fig. S1). The nature of this kink is not unambiguous as two different reasons could produce a similar result. First, it could be due to overlap of intensities from regions with different numbers of graphene layers, particularly TLG.

Calculations of TLG on 6H-SiC in two possible stackings (ABA and ABC) are presented in fig. S2. In fig. S4, they are shown taking into account the contribution of the wave function to the top graphene layer and overlapped with the BLG for comparison. From these figures, we see that the rhombohedral (ABC) TLG on SiC has its own flat band structure with specific electron localization at a binding energy lower than that of BLG. This TLG coverage may actually be negligibly small, especially in the case of an extremely sharp and intense photoemission feature. For undoped TLG, the band structure was studied experimentally by Nanospot ARPES and shows cubic band dispersion at the Fermi level (30) for rhombohedral stacking. An example of MLG, BLG, and TLG on another substrate, Ir(111), is presented in fig. S5. There are characteristic double- and triple-split Dirac cones without flat bands. Because of the absence of n-doping, only the bottom bands are visible.

Another possible explanation for the observed kinks is renormalization due to many-body effects as known from MLG (20, 31). The enhanced electron-phonon coupling in superconducting CaC6 produces in ARPES a very similar renormalization around 160 meV below the Fermi level (32). Thus, we want to address at this point again the relevance for superconductivity. There are various possible pairing mechanisms for intrinsic superconductivity in graphene. Besides conventional s-wave pairing (33), p + ip (33), d (34), d + id (16), and f (16) have also been considered for graphene. It should also be mentioned that the extra layer degree of freedom in bilayer systems leads to more possibilities in pairing. In this way, e.g., the possibility of interlayer pairing arises (35). Since the pairing mechanism is not established despite the strong indication for electron-phonon coupling, we want to briefly assess the role of strong electron correlation (36). It is possible that electron correlation contributes to the flatness of the band. For graphene, this has been predicted (31). We have performed model calculations to simulate complete photoemission spectra. As a result, the small broadening in the experiment at higher energies is incompatible with a significant role of electron correlation for the flat band dispersion.

Returning to the question of electron-phonon coupling, we note that the disk-like constant energy surface around the Embedded Image and Embedded Image points of the graphene Brillouin zone favors enhanced intravalley and Embedded Image intervalley scattering processes when the flat band is shifted to the Fermi level. With small doping/gating of only a few milli–electron volts, the Fermi surface can be changed between circle and disk shapes, strongly affecting the number of possible scattering channels.

The measured band structure shows n-doping due to the substrate influence; therefore, the Dirac cone and the flat band in discussion are located significantly below the Fermi level. This means that it is necessary to bring the flat band to the Fermi energy to examine possible superconductivity. This is possible by doping (21) and gating (37). We recall that the possibility of doping large amounts of charge carriers to the graphene layer was realized by combined Ca intercalation and K deposition, resulting in bringing a 1D extended van Hove singularity along the Embedded Image direction from more than 1 eV above down to the Fermi level (17). In the present case, four times less doping but of the p-type must be accomplished. Fortunately, p-doping of BLG on SiC has been demonstrated as well (21). It was shown that F4-TCNQ molecules compensate n-doping of BLG on SiC and make it charge neutral (21).

Based on the proposed model, n-doping of only one graphene sublattice (either B or C) of initially undoped BLG leads to gap opening along with an instant flattening of the dispersion at Embedded Image. With increased doping, the flat band area increases, but the energy position remains fixed (fig. S6). In a device, however, single-sublattice doping is difficult to control. Thus, the main approach of modification of the band dispersion is supposed to be the gate biasing with corresponding change of interlayer asymmetry until both interlayer and sublattice asymmetries compensate each other at the A sublattice of the bottom layer. By using a double-gate device configuration (37), it should become possible to control both the doping and the interlayer asymmetries independently and in operando.