Fig. 4: Visualization of multiple vHSs and flat bands.

a Experimental photoelectron intensity plot of the band structure along the \(\overline{\Gamma }\)–\(\overline{\,{\mbox{M}}\,}\)–\(\overline{\,{\mbox{K}}\,}\)–\(\overline{\Gamma }\) line with 90 eV photons. The white-dashed curves serve as guides to the eye to help visualize the two vHSs. Purple and black arrows in (a) and (b) point to the vHSs and flat bands, respectively. b DFT-based bulk band structure along the \(\overline{\Gamma }\)–\(\overline{\,{\mbox{M}}\,}\)–\(\overline{\,{\mbox{K}}\,}\)–\(\overline{\Gamma }\) line. c Experimental band dispersion and the associated integrated energy distribution curves (EDCs) along the \(\overline{\Gamma }\)–\(\overline{\,{\mbox{K}}\,}\)–\(\overline{\,{\mbox{M}}\,}\)–\(\overline{\,{\mbox{K}}\,}\)–\(\overline{\Gamma }\) line measured using 58 eV photons. Peak positions in the EDCs (black arrows) denote flat bands at  ~ −0.3 eV,  ~ −0.5 eV, and  ~ −0.7 eV, with the most intense peak lying at around ~ − 1.1 eV. d Same as (c) except these results are for measurements using 55 eV photons. e Integrated intensity of the EDCs (over the momentum range of −0.8 Å⁻¹ to 0.8 Å⁻¹) along the \(\overline{\Gamma }\)–\(\overline{\,{\mbox{K}}\,}\)–\(\overline{\,{\mbox{M}}\,}\)–\(\overline{\,{\mbox{K}}\,}\)–\(\overline{\Gamma }\) line. The EDCs used to obtain integrated intensities plotted were taken at photon energies ranging from 40 to 60 eV as indicated by the color bars on the right side of (f). Peak positions in the EDCs (black arrows) correspond to flat bands. f Same as (e) except that here the integration involves EDCs along the \(\overline{\,{\mbox{K}}\,}\)–\(\overline{\Gamma }\)–\(\overline{\,{\mbox{K}}\,}\) line.