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

Abstract

arXiv:1205.0239v1 [cond-mat.str-el] 1 May 2012Luttinger liquid theory of purple bronze Li 0.9 Mo 6 O 17 in the charge regime.P. Chudzinski, T. Jarlborg, and T. Giamarchi DPMC, University of Geneva, 24 Quai Ernest-Ansermet, CH-1211 Geneva 4, Switzerland (Dated: March 4, 2018 Molybdenum purple bronze Li0.9Mo6O17 is an exceptional material known to exhibit one dimensional (1D) properties for energies down to a few meV. This fact seems to be well established both in experiments and in band structure theory. We use the unusual, very 1-dimensional band dispersion obtained in ab-initio DFT-LMTO band calculations as our starting point to study the physics emerging below 300meV. A dispersion perpendicular to the main dispersive direction is obtained and investigated in detail. Based on this, we derive an effective low energy theory within the Tomonaga Luttinger liquid (TLL) framework. We estimate the strength of the possible interactions and from this deduce the values of the TLL parameters for charge modes. Finally we investigate possible instabilities of TLL by deriving renormalization group (RG) equations which allow us to predict the size of potential gaps in the spectrum. While 2kF instabilities strongly suppress each other, the 4kF instabilities cooperate, which paves the way for a possible CDW at the lowest energies. The aim of this work is to understand the experimental findings, in particular the ones which are certainly lying within the 1D regime. We discuss the validity of our 1D approach and further perspectives for the lower energy phases. [12]. Although the main effort of those investigations was focused on the nature of a mysterious phase transition at around 25K, interesting knowledge about higher energy phase was also gathered. Certain properties of the one dimensional (1D) metal, the Luttinger liquid (TLL), have been invoked to explain the measured data [2,3,13,14] and nowadays the presence of the 1D physics is well established experimentally [15,16], at least in some energy range.On the theoretical side, band structure calculations have shown a quasi-1D character of molybdenum purple bronze. A remarkably simple band structure emerges from rather complex crystal structure. At the Fermi surface there are only two bands, lying very close to each other, in the form of flat sheets dispersing well only along the b-axis. This gives a hope that purple bronze can indeed be a rare realization of the 1D physics.The key problem is that several possible mechanisms has been invoked to explain the observed properties, which made the subject quite unclear and controversial. In our opinion the reason for this situation is that each of previous attempts was focused only on one out of many peculiar properties of Li 0.9 M o 6 O 17 and most of them searched for an explanation in the low energy regime (below 5meV ), where indeed the properties of Li 0.9 M o 6 O 17 are the most spectacular. By now, not enough attention has been paid even to the parameters of the 1D state. It is only agreed that it emerges at energies as hi...

Multi-orbital physics in lithium-molybdenum purple-bronze: going beyond paradigm

“…This constitutes a very complicated problem, whose solution is not accessible neither in analytic nor in numerical way, but even the H bs does not exhaust entire problem we face in the LMO. Since the LMO is likely to be very close to the quantum phase transition [21], and we are interested in the low energy phenomena, we must incorporate further perturbations to obtain the full hamiltonian:…”

“…The last three terms are the strong correlations in the form of Hubbard term between electrons on the same orbital (U + J H ), on different orbitals U, (U − J H ), orbital exchange J H and the long range interactions term V αβ γδ (r − r ) (the 1D system itself is unable to fully screen Coulomb interactions [23]). The Hubbard terms are the largest energy scale in the problem [18,21,22], the value of U computed for a sparse LMO lattice [18] is 6.4 eV, while cRPA calculations on atomic Mo, within t 2g manifold (with all other orbitals contributing to screening), for a dense fcc lattice [34] give U = 3.7 eV and J = 0.55 eV while for a dense oxide lattice [35] U = 3.8 and J = 0.5 eV. The long-range part V αβ γδ (r − r ) is also substantial due to poor screening in LMO and furthermore does depend on the orbital index because of an extended nature of eigenwavefunctions.…”

“…Moreover, most recent measurements showed intriguing deviations from a standard 1D physics already at higher temperatures T ∼ 150 K: anomalous ARPES scaling [15] and broadening [16] below energy scales of order 150 K and breaking of WiedmanFranz law at the same energy scales [17] (again with no influence of phonons). On the theory side it has been established that the system can be considered as 1D two leg ladder [18][19][20] very close to the (quarter-filled) Mott transition [21,22]. Hence, from a very fundamental perspective, we face not only the problem of dimensional cross-over [23][24][25] but also a weakly doped (quarter-filled) Mott-insulator.…”

“…The characteristic energy scale detected in this work, associated with a characteristic magnetic field when the LMO's color changes, falls quite close to T * . Authors' of reference [30] concluded that this must be manifestation of some electronic re-organization within the d-manifold, an effect inaccessible in a purely 1D model, where only one, the d xy -orbital, was taken into account [21]. Extending the model by including an orbital degree of freedom makes a lot of sense also if one realizes [31] that in LMO any perpendicular hopping must be transferred through d-orbitals other than d xy , so any out-of-1D processes, any dimensional cross-over, must involve excitations involving orbital-swap processes.…”

“…In Section 2 we first introduce in detail a possibility for excitonic states and their interactions in LMO, then we write down the hamiltonian of the problem and explain physics covered by each of its constituents. To be precise, in our construction we start with a robust TLL, as found in reference [21], and then introduce a new "UV" cut-off at energy scale that is slightly larger than the spin-orbit coupling. The orbital-fluctuation effects enter into problem (as e.g.…”