Wannier orbital theory and angle-resolved photoemission spectroscopy for the quasi-one-dimensional conductor LiMo6O17 . III. The two metallic bands in the gap

This is the third paper of a series of three papers presenting a combined study by band theory and angle-resolved photoemission spectroscopy (ARPES) of lithium purple bronze. The first paper laid the foundation for the theory, and the second paper discussed a general comparison between theory and experiment, including deriving an ARPES selection rule. The present paper III focuses in detail on the two metallic, quasi-one-dimensional (quasi-1D) $xy$-like bands left in the 0.4 eV dimerization gap between the $xz$ and $yz$ valence and conduction (V) bands. The hybridizations with the latter change the perpendicular dispersions of --- and splitting between --- the resulting ̃ \~xy bands. The edges of the V (C) bands, in particular, push resonance peaks up (down) in the ̃ \~xy bands which are now described by a two-band Hamiltonian whose two first terms consist of the pure $xy$ block of the six-band tight-binding (TB) Hamiltonian and whose four following terms describe the resonant coupling to (i.e., indirect hopping via) the V bands. The two-band Hamiltonian extends the selection rule derived in the previous paper to the hybridized ̃ \~xy bands, which enables extracting the split quasi-1D Fermi surface (FS) from the raw ARPES data. The complex shape of the FS, verified in detail by our ARPES, depends strongly on the Fermi-energy position in the gap, implying a great sensitivity to Li stoichiometry of properties dependent on the FS, such as FS nesting or superconductivity. The strong resonances prevent either a two-band TB model or a related real-space ladder picture from giving a valid description of the low-energy electronic structure. Down to a temperature of 64pt0exK, we find no evidence for a theoretically expected downward renormalization of perpendicular single-particle hopping due to LL fluctuations in the quasi-1D chains.