Fig. 3: Determination of the orbital nature the kagome bands in CsV₃Sb₅.

a Experimental geometry of our polarization-dependent ARPES. b The two-dimensional projection of the Brillouin zone and the high-symmetry directions. c, d Band dispersions along the \(\bar{\varGamma }\)-\(\bar{{{{{{\rm{K}}}}}}}\) -\(\bar{{{{{{\rm{M}}}}}}}\) -\(\bar{{{{{{\rm{K}}}}}}}\) [Cut#1, (c)] and \(\bar{\varGamma }\) -\(\bar{{{{{{\rm{K}}}}}}}\) -\(\bar{\varGamma }\) [Cut#2, (d)] directions, respectively. The momentum directions of the cuts are indicated by the red arrows in (b). The bands were measured with circularly polarized light, at 200 K. e, f and g, h Same as (c, d), but probed with linear horizontal (LH) (e, f) and linear vertical (LV) (g, h) polarizations, respectively. We note that the intensity of the flat-top dispersion around the \(\bar{{{{{{\rm{M}}}}}}}\) point is weakened in (e), which may be due to the matrix element effects (see Supplementary Fig. 7 for the details of the matrix element analysis for the higher-order VHS band). i Experimental band structure along the \(\bar{\varGamma }\)-\(\bar{{{{{{\rm{K}}}}}}}\)-\(\bar{{{{{{\rm{M}}}}}}}\)-\(\bar{\varGamma }\) direction, with orbital characters marked. The momentum range is equal to the sum of the region I in (c) and region II in (d) selected by the red box. The dispersion is the same as the cut shown in Fig. 2c. j Orbital character resolved band structure from the A sublattice in the calculations, with irreducible band representations labeled. k The sign structure (blue/red) and spatial orientation of the \(d_{{{x}^{2}}-{{y}^{2}}}\)-orbital A_g p-type (inversion-even) and d_xz-orbital B_1u m-type type (inversion-odd) VHS. The phase orbitals are plotted in the positive k_z plane. The black dots in the center of the hexagons indicate the inversion centers.