  The title material has a quasi-one-dimensional electronic structure and is of
considerable interest because it has a metallic phase with properties different
from a simple Fermi liquid, a poorly understood "insulating" phase, and a
superconducting phase which may involve spin triplet Cooper pairs. Using the
Slater-Koster approach and comparison with published band structure
calculations we present the simplest possible tight-binding model for the
electronic band structure near the Fermi energy. This describes a set of
ladders with weak (and frustrated) inter-ladder hopping. In the corresponding
lattice model the system is actually close to one-quarter filling (i.e., one
electron per pair of sites) rather than half-filling, as has often been
claimed. We consider the simplest possible effective Hamiltonian that may
capture the subtle competition between unconventional superconducting, charge
ordered, and non-Fermi liquid metal phases. We argue that this is an extended
Hubbard model with long-range Coulomb interactions. Estimates of the relevant
values of the parameters in the Hamiltonian are given. NMR relaxation rate
experiments should be performed to clarify the role of charge fluctuations in
Li0.9Mo6O17 associated with the proximity to a Coulomb driven charge ordering
transition.
