Hidden kagome-lattice picture and origin of high conductivity in delafossite PtCoO$_2$

We study the electronic structure of delafossite PtCoO$_2$ to elucidate its extremely small resistivity and high mobility. The band exhibits steep dispersion near the Fermi level despite the fact that it is formed mainly by Pt $d$ orbitals that are typically localized. We propose a picture based on two hidden kagome-lattice-like electronic structure: one originating from Pt $s+p_x/p_y$ orbitals, and the other from Pt $d_{3z^2-r^2}+d_{xy}/d_{x^2-y^2}$ orbitals, each placed on the bonds of the triangular lattice. In particular, we find that the underlying Pt $s+p_x/p_y$ bands actually determine the steepness of the original dispersion, so that the large Fermi velocity can be attributed to the large width of the Pt $s+p_x/p_y$ band. More importantly, the kagome-like electronic structure gives rise to "orbital-momentum locking" on the Fermi surface, which reduces the electron scattering by impurities. We conclude that the combination of the large Fermi velocity and the orbital-momentum locking is likely to be the origin of the extremely small resistivity in PtCoO$_2$.