Density-functional study of the Luttinger liquid behavior of the lithium molybdenum purple bronzeLi0.9Mo6O17

Abstract

Using density-functional calculations, we study the electronic structure of the purple bronze ${\mathrm{Li}}_{0.9}{\mathrm{Mo}}_{6}{\mathrm{O}}_{17}$, which has been proposed to be a paradigm system for the Luttinger liquid behavior. Our results show that the quasi-one-dimensional (1D) electron bands crossing the Fermi energy originate from the Mo atoms on the double zigzag chains with predominant Mo $({d}_{xy})$ character and a Fermi surface that consists of two slightly warped planes, normal to the direction of the zigzag chains. The overall shape and dispersion of the bands as well as the calculated Fermi surface nesting vector are in excellent agreement with recent photoemission measurements. From constrained density-functional calculations of the Coulomb interactions and the calculated Fermi velocity, we estimate the values for the characteristic parameters of the Luttinger liquid, viz., the ratio of the spin-charge velocities to be ${v}_{\ensuremath{\rho}}∕{v}_{s}\ensuremath{\approx}1.8$ and the anomalous dimension characterizing the Fermi surface discontinuity to be $\ensuremath{\alpha}\ensuremath{\approx}0.6$. The general agreement of these values with experiments further strengthens the case for the lithium molybdenum purple bronze as a Luttinger liquid.