Luttinger liquid theory of purple bronze Li0.9Mo6O17Li_{0.9}Mo_6O_{17} in the charge regime

Molybdenum purple bronze Li$_{0.9}$Mo$_{6}$O$_{17}$ 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 \emph{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 $2k_F$ instabilities strongly suppress each other, the $4k_F$ 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.Comment: We wish to acknowledge financial support of MaNEP, SectionI

Spin rotational symmetry breaking by orbital current patterns in two-leg ladders.

We investigate the physical consequences of orbital current patterns (OCP) in doped two-leg Cu-O Hubbard ladders. The internal symmetry of the pattern, in the case of the ladder structure, differs slightly from that suggested so far for cuprates. We focus on this OCP and look for measurable signatures of its existence. We compute the magnetic field produced by the OCP at each lattice site, and estimate its value in view of a possible experimental detection. Using a renormalization group (RG) analysis, we determine the changes that are caused by the SU(2) spin-rotational symmetry breaking which occurs when the OCP is present in the ground state phase diagram. The most signifcant one is an in-plane SDW gap opening in an otherwise critical phase, at intermediate dopings. We estimate the value of this gap, give an analytic expression for the correlation functions and examine some of the magnetic properties of this new phase which can be revealed in measurements. We compute the conductance in the presence of a single impurity, using an RG analysis. A discussion of the various sources of SU(2) symmetry breaking underscores the specificity of the OCP induced effects.Comment: 12 pages, 3 figures, submitted to PR

Bragg- and Moving-glasses: a theory of disordered vortex lattices

We study periodic lattices, such as vortex lattices in type II superconductors in a random pinning potential. For the static case we review the prediction that the phase diagram of such systems consists of a topologically ordered Bragg glass phase, with quasi long range translational order, at low fields. This Bragg glass phase undergoes a transition at higher fields into another glassy phase, with dislocations, or a liquid. This proposition is compatible with a large number of experimental results on BSCCO or Thalium compounds. Further experimental consequences of our results and relevance to other systems will be discussed. When such vortex systems are driven by an external force, we show that, due to periodicity in the direction transverse to motion, the effects of static disorder persist even at large velocity. In $d=3$, at weak disorder, or large velocity the lattice forms a topologically ordered glass state, the ``moving Bragg glass'', an anisotropic version of the static Bragg glass. The lattice flows through well-defined, elastically coupled, static channels. We determine the roughness of the manifold of channels and the positional correlation functions. The channel structure also provides a natural starting point to study the influence of topological defects such as dislocations. In $d=2$ or at strong disorder the channels can decouple along the direction of motion leading to a ``smectic'' like flow. We also show that such a structure exhibits an effective transverse critical pinning force due to barriers to transverse motion, and discuss the experimental consequences of this effect.Comment: Proceedings of M2S-HTSC-V conference (Beijing, Feb 97) to be published in Physica C; 4 pages, 3 figures, uses espcrc2.st

Hall effect in strongly correlated low dimensional systems

We investigate the Hall effect in a quasi one-dimensional system made of weakly coupled Luttinger Liquids at half filling. Using a memory function approach, we compute the Hall coefficient as a function of temperature and frequency in the presence of umklapp scattering. We find a power-law correction to the free-fermion value (band value), with an exponent depending on the Luttinger parameter $K_{\rho}$. At high enough temperature or frequency the Hall coefficient approaches the band value.Comment: 7 pages, 3 figure

Phase diagram of hole doped two-leg Cu-O ladders

In the weak coupling limit, we establish the phase diagram of a two-leg ladder with a unit cell containing both Cu and O atoms, as a function of doping. We use bosonization and design a specific RG procedure to handle the additional degrees of freedom. Significant differences are found with the single orbital case; for purely repulsive interactions, a completely massless quantum critical region is obtained at intermediate carrier concentrations (well inside the bands) where the ground state consists of an incommensurate pattern of orbital currents plus a spin density wave (SDW) structure.Comment: 4 pages, 2 figures, accepted to Phys. Rev. B, Rapid Com

Specific heat of the quantum Bragg Glass

We study the thermodynamics of the vibrational modes of a lattice pinned by impurity disorder in the absence of topological defects (Bragg glass phase). Using a replica variational method we compute the specific heat $C_v$ in the quantum regime and find $C_v \propto T^3$ at low temperatures in dimension three and two. The prefactor is controlled by the pinning length. The non trivial cancellation of the linear term in $C_v$ arises from the so-called marginality condition and has important consequences for other mean field models.Comment: 5 pages, RevTex, strongly revised versio

Phase transitions for a collective coordinate coupled to Luttinger liquids

We study various realizations of collective coordinates, e.g. the position of a particle, the charge of a Coulomb box or the phase of a Bose or a superconducting condensate, coupled to Luttinger liquids (LL) with N flavors. We find that for Luttinger parameter 1/2<K<1 there is a phase transition from a delocalized phase into a phase with a periodic potential at strong coupling. In the delocalized phase the dynamics is dominated by an effective mass, i.e. diffusive in imaginary time, while on the transition line it becomes dissipative. At K=1/2 there is an additional transition into a localized phase with no diffusion at zero temperature.Comment: 5 pages, 2 figures, 1 table, Phys. Rev. Lett. (in press

Impurity and soliton dynamics in a Fermi gas with nearest-neighbor interactions

We study spinless fermions with repulsive nearest-neighbor interactions perturbed by an impurity particle or a local potential quench. Using the numerical time-evolving block decimation method and a simplified analytic model, we show that the pertubations create a soliton-antisoliton pair. If solitons are already present in the bath, the two excitations have a drastically different dynamics: The antisoliton does not annihilate with the solitons and is therefore confined close to its origin while the soliton excitation propagates. We discuss the consequences for experiments with ultracold gases.Comment: 12 pages, 16 figure