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 Li 0.9 Mo 6 O 17 , which has been proposed to be a paradigm system for the Luttinger liquid behavior. Our results show that the quasi-one-dimensional ͑1D͒ 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 / v s Ϸ 1.8 and the anomalous dimension characterizing the Fermi surface discontinuity to be ␣ Ϸ 0.6. The general agreement of these values with experiments further strengthens the case for the lithium molybdenum purple bronze as a Luttinger liquid.

Luttinger-liquid theory of purple bronze Li0.9Mo6O17in the charge regime

“…in the local density approximation (LDA). Recent calculations [17] lead to results which are globally consistent with several previous computations [18,19]. Overall the band dispersions agree well with the measured results obtained by angle resolved photoemission spectroscopy (ARPES) [20].…”

“…A fully self-consistent calculation has been performed in [18] and a value U = 6.4eV was found. This value seems at first sight surprisingly large (for 4d electrons), but a recent study using constrained-RPA [23] allows to understand this result.…”

“…[18]. Those authors gave estimate for a value of interaction from standard electrostatic Coulomb law (with the simplest static screening):…”

“…A more fundamental problem is the value of the dielectric permittivity κ. In the previous work [18] the bulkκ ≈ 10 was used, which is typical for bulk semiconductors with similar value of a gap for oxygen states(∆ O ≈ 2eV ). Taking into account the very weak metallic character along the c-axis the semiconductor approximation is correct.…”

“…The band gap seems to be quite small, however the presence the hybridization makes the estimate quite difficult. In the following we assume that it is ≤ 10%t.Along the c−axis the dispersion relation is quite unusual (there is a node at zero momenta along this axis) and this peculiar feature appears within all independent DFT calculations [17][18][19]. Here we are also dealing with the reduced Brillouin zone, but the presence of the node means that the standard back-folding does not apply at all.…”