Electronic Glasses
A short introduction to the physics and the method to treat quantum crystals of electrons (Wigner crystal) and the related disordered elastic systems.
cond-mat.mes-hall↗
arXiv subjects
T. Giamarchi
Publications and source records attributed to T. Giamarchi.
Transport in Luttinger Liquids
We compute the transport properties of one dimensional interacting electrons, also known as a Luttinger liquid. We show that a renormalization group study allows to obtain the temperature dependence of the conductivity in an intermediate temperature range. In this range the conductivity has a power-law like dependence in temperature. At low temperatures, the motion proceed by tunnelling between localized configurations. We compute this tunnelling rate using a bosonization representation and an instanton technique. We find a conductivity $σ(T) \propto e^{-β^{1/2}}$, where $β$ is the temperature. We compare this results with the standard variable range hopping (VRH) formula.
cond-mat.str-el↗
Point-contact tunneling involving low-dimensional spin-triplet superconductors
We modify and extend previous microscopic calculations of tunneling in superconducting junctions based on a non-equilibrium Green function formalism to include the case of spin-triplet pairing. We show that distinctive features are present in the I-V characteristics of different kinds of junctions, in particular when the effects of magnetic fields are taken into account, that permit to identify the type of pairing. We discuss the relevance of these results in the context of quasi one-dimensional organic superconductors like (TMTSF)_2(PF_6) and layered compounds like Sr_2RuO_4.
cond-mat.supr-con↗
Dimensional crossover and deconfinement in Bechgaard salts
The Bechgaard salts are made of weakly coupled one dimensional chains. This particular structure gives the possibility to observe in these systems a dimensional crossover between a high temperature (or high energy) one dimensional phase and a two or three dimensional system. Since the filling of the chains is commensurate the system thus undergoes a deconfinement transition from a one dimensional Mott insulator to a two (or three) dimensional metal. Such a transition has of course a strong impact on the physical properties of these compounds, and is directly seen in transport measurements. In order to describe such a transition a dynamical mean field method has been introduced (chain-DMFT). Using this method we investigate a system of coupled Hubbard chains and show that we can indeed reproduce the deconfinement transition. This allows to determine physical quantities such as the transport transverse to the chains and the shape of the Fermi surface and quasiparticle residues in the low temperature phase.
cond-mat.str-el↗
Numerical simulation evidence of dynamical transverse Meissner effect and moving Bose glass phase
We present 3D numerical simulation results of moving vortex lattices in presence of 1D correlated disorder at zero temperature. Our results with field tilting confirm the theoritical predictions of a moving Bose glass phase, characterized by transverse pinning and dynamical transverse Meissner effect, the moving flux lines being localized along the correlated disorder direction. Beyond a critical transverse field, vortex lines exhibit along all their length a "kink" structure resulting from an effective static "tin roof" pinning potential in the transverse direction.
cond-mat.supr-con↗
Disordered Wigner crystals
I review some of the properties of a Wigner crystal of electrons in two dimensional systems. The effect of disorder on such quantum crystals is discussed. The question of compressibility of such systems as obtained from capacitance measurements is examined in details.
cond-mat.mes-hall↗
Domain wall creep in epitaxial ferroelectric Pb(Zr0.2Ti0.8)O3 thin films
Ferroelectric switching and nanoscale domain dynamics were investigated using atomic force microscopy on monocrystalline Pb(Zr0.2Ti0.8)O3 thin films. Measurements of domain size versus writing time reveal a two-step domain growth mechanism, in which initial nucleation is followed by radial domain wall motion perpendicular to the polarization direction. The electric field dependence of the domain wall velocity demonstrates that domain wall motion in ferroelectric thin films is a creep process, with the critical exponent mu close to 1. The dimensionality of the films suggests that disorder is at the origin of the observed creep behavior.
cond-mat.dis-nn↗
Quasi-one-dimensional organic conductors: dimensional crossover and some puzzles
We review some properties of quasi-one-dimensional organic conductors, such as the Bechgaard salts, with an emphasis on aspects related to the crossovers between a Mott insulating state to a metallic state, and crossovers between different metallic behaviors. We discuss why a theoretical description of these issues is a particularly challenging problem, and describe a recent non-perturbative approach designed to deal with systems of coupled chains. This method, dubbed "chain-DMFT", is a generalization of dynamical mean field theory that treats both, one-dimensional and higher dimensional physics, in a unified manner. We present numerical results for a system of coupled Hubbard chains. Chain-DMFT indeed captures the metal-insulator transition and the dimensional crossover from a high temperature Luttinger liquid to a low temperature Fermi liquid phase, and allows to access the properties of these phases. Based on these results perspectives for a theoretical understanding of the physics of the Bechgaard salts are discussed.
cond-mat.str-el↗
Vortex phases
These lecture notes are meant to provide a pedagogical introduction, and present the latest theoretical and experimental developments on the physics of vortices in type II superconductors.
cond-mat.supr-con↗
A Bragg glass phase in the vortex lattice of a type II superconductor
Although crystals are usually quite stable, they are sensitive to a disordered environment: even an infinitesimal amount of impurities can lead to the destruction of the crystalline order. The resulting state of matter has been a longstanding puzzle. Until recently it was believed to be an amorphous state in which the crystal would break into crystallites. But a different theory predicts the existence of a novel phase of matter: the so-called Bragg glass, which is a glass and yet nearly as ordered as a perfect crystal. The lattice of vortices that can contain magnetic flux in type II superconductors provide a good system to investigate these ideas. Here we show that neutron diffraction data of the vortex lattice in type II superconductors provides unambiguous evidence for a weak, power-law decay of the crystalline order characteristic of a Bragg glass. The theory also predicts accurately the electrical transport properties of superconductors; it naturally explains the observed phase transition and the dramatic jumps in the critical current associated with the melting of the Bragg glass. Moreover the model explains experiments as diverse as X-ray scattering in disordered liquid crystals and conductivity of electronic crystals.
cond-mat.supr-con↗
Deconfinement transition and Luttinger to Fermi Liquid crossover in quasi one-dimensional systems
We investigate a system of one dimensional Hubbard chains of interacting fermions coupled by inter-chain hopping. Using a generalization of the Dynamical Mean Field Theory we study the deconfinement transition from a Mott insulator to a metal and the crossover between Luttinger and Fermi liquid phases. One-particle properties, local spin response and inter-chain optical conductivity are calculated. Possible applications to organic conductors are discussed.
cond-mat.str-el↗
Competition of random and periodic potentials in interacting fermionic systems and classical equivalents: the Mott Glass
We study the competition between a random potential and a commensurate potential on interacting fermionic and bosonic systems using a variety of methods. We focus on one dimensional interacting fermionic systems but higher dimensional bosonic and fermionic extensions, as well as classical equivalents are also discussed. Our methods which include bosonization, replica variational method, functional renormalization group (RG) and perturbation around the atomic limit, go beyond conventional perturbative expansions around the Luttinger liquid in one dimension. All these methods agree on the prediction in these systems of a phase, the Mott glass, intermediate between the Anderson Insulator (compressible, with a pseudogap in the optical conductivity) and the Mott Insulator (incompressible with a gap in the optical conductivity). The Mott glass, which was unexpected from a perturbative renormalization group point of view has a pseudogap in the conductivity while remaining incompressible. Having derived the existence of the Mott Glass phase in one dimension, we show qualitatively that its existence can also be expected in higher dimension. We discuss the relevance of this phase to experimental systems such as disordered classical elastic systems and dirty bosons.
cond-mat.str-el↗
Interacting fermions in self-similar potentials
We consider interacting spinless fermions in one dimension embedded in self-similar quasiperiodic potentials. We examine generalizations of the Fibonacci potential known as precious mean potentials. Using a bosonization technique and a renormalization group analysis, we study the low-energy physics of the system. We show that it undergoes a metal-insulator transition for any filling factor, with a critical interaction that strongly depends on the position of the Fermi level in the Fourier spectrum of the potential. For some positions of the Fermi level the metal-insulator transition occurs at the non interacting point. The repulsive side is an insulator with a gapped spectrum whereas in the attractive side the spectrum is gapless and the properties of the system are described by a Luttinger liquid. We compute the transport properties and give the characteristic exponents associated to the frequency and temperature dependence of the conductivity.
cond-mat.str-el↗
Meissner effect in a bosonic ladder
We investigate the effect of a magnetic field on a bosonic ladder. We show that such a system leads to the one dimensional equivalent of a vortex lattice in a superconductor. We investigate the physical properties of the vortex phase, such as vortex density and vortex correlation functions and show that magnetization has plateaus for some commensurate values of the mag netic field. The lowest plateau corresponds to a true Meissner to vortex transition at a critical field $H_{c1}$ that exists although the system has no long range superconducting order. Implications for experimental realizations such as Josephson junction arrays are discussed.
cond-mat.str-el↗
Pinned Wigner Crystals
We study the effects of weak disorder on a Wigner crystal in a magnetic field. We show that an elastic description of the pinned Wigner crystal provides an excellent framework to obtain most of the physically relevant observables. Using such a description, we compute the static and dynamical properties. We find that, akin to the Bragg glass phase, a good degree of translational order survives (up to a large lengthscale in $d=2$, infinite in $d=3$). Using a gaussian variational method, we obtain the full frequency dependence of the conductivity tensor. The zero temperature Hall resistivity is independent of frequency and remains unaffected by disorder at its classical value. We show that the characteristic features of the conductivity in the pinned Wigner crystal are dramatically different from those arising from the naive extrapolations of Fukuyama-Lee type theories for charge density waves. We determine the relevant scales and find that the physical properties depend crucially on whether the disorder correlation length is larger than the cyclotron length or not. We analyse, in particular, the magnetic field and density dependence of the optical conductivity. Within our approach the pinning frequency can increase with increasing magnetic field and varies as $n^{-3/2}$ with the density $n$. We compare our predictions with recent experiments on transport in two dimensional electron gases under strong magnetic fields. Our theory allows for a consistent interpretation of these experiments in terms of a pinned WC.
cond-mat.str-el↗
Mott-Superfluid transition in bosonic ladders
We show that in a commensurate bosonic ladder, a quantum phase transition occurs between a Mott insulator and a superfluid when interchain hopping increases. We analyse the properties of such a transition as well as the physical properties of the two phases. We discuss the physical consequences for experimental systems such as Josephson Junction arrays.
cond-mat.str-el↗
Commensurate-incommensurate transition in two-coupled chains of nearly half-filled electrons
We investigate the physical properties of two coupled chains of electrons, with a nearly half-filled band, as a function of the interchain hopping t_\perp and the doping. We show that upon doping, the system undergoes a metal-insulator transition well described by a commensurate-incommensurate transition. By using bosonization and renormalization we determine the full phase diagram of the system, and the physical quantities such as the charge gap. In the commensurate phase two different regions, for which the interchain hopping is relevant and irrelevant exist, leading to a confinement-deconfinement crossover in this phase. A minimum of the charge gap is observed for values of t_\perp close to this crossover. At large t_\perp the region of the commensurate phase is enhanced, compared to a single chain. At the metal-insulator transition the Luttinger parameter takes the universal value K_ρ^*=1, in agreement with previous results on special limits of this model.
cond-mat.str-el↗
Hall effect and inter-chain magneto-optical properties of coupled Luttinger liquids
We consider the Hall effect in a system of weakly coupled Luttinger chains. We obtain the full conductivity tensor in the absence of dissipation along the chains. We show that while the dependence of the Hall and transverse conductivities on temperature and frequency are affected by the Luttinger interaction very strongly, the Hall resistivity is given by a simple formula corresponding to the noninteracting fermions. We compute the frequency, temperature and field dependence of the transverse conductivity. Consequences for the quasi-one-dimensional organic conductors are discussed.
cond-mat.str-el↗