arXiv subjects

Thierry Giamarchi

Publications and source records attributed to Thierry Giamarchi.

At least 163 records · Page 9Linked to original sources

arXiv2005

Non-equilibrium relaxation of an elastic string in a random potential

We study the non--equilibrium motion of an elastic string in a two dimensional pinning landscape using Langevin dynamics simulations. The relaxation of a line, initially flat, is characterized by a growing length, $L(t)$, separating the equilibrated short length scales from the flat long distance geometry that keep memory of the initial condition. We show that, in the long time limit, $L(t)$ has a non--algebraic growth with a universal distribution function. The distribution function of waiting times is also calculated, and related to the previous distribution. The barrier distribution is narrow enough to justify arguments based on scaling of the typical barrier.

cond-mat.dis-nn↗

arXiv2004

Specific Heat of Quantum Elastic Systems Pinned by Disorder

We present the detailed study of the thermodynamics of vibrational modes in disordered elastic systems such as the Bragg glass phase of lattices pinned by quenched impurities. Our study and our results are valid within the (mean field) replica Gaussian variational method. We obtain an expression for the internal energy in the quantum regime as a function of the saddle point solution, which is then expanded in powers of $\hbar$ at low temperature $T$. In the calculation of the specific heat $C_v$ a non trivial cancellation of the term linear in $T$ occurs, explicitly checked to second order in $\hbar$. The final result is $C_v \propto T^3$ at low temperatures in dimension three and two. The prefactor is controlled by the pinning length. This result is discussed in connection with other analytical or numerical studies.

cond-mat.dis-nn↗

arXiv2004

Creep motion of an elastic string in a random potential

We study the creep motion of an elastic string in a two dimensional pinning landscape by Langevin dynamics simulations. We find that the Velocity-Force characteristics are well described by the creep formula predicted from phenomenological scaling arguments. We analyze the creep exponent $μ$, and the roughness exponent $ζ$. Two regimes are identified: when the temperature is larger than the strength of the disorder we find $μ\approx 1/4$ and $ζ\approx 2/3$, in agreement with the quasi-equilibrium-nucleation picture of creep motion; on the contrary, lowering enough the temperature, the values of $μ$ and $ζ$ increase showing a strong violation of the latter picture.

cond-mat.dis-nn↗

arXiv2004

X-ray spectrum of a pinned charge density wave

We calculate the X-ray diffraction spectrum produced by a pinned charge density wave (CDW). The signature of the presence of a CDW consists of two satellite peaks, asymmetric as a consequence of disorder. The shape and the intensity of these peaks are determined in the case of a collective weak pinning using the variational method. We predict divergent asymmetric peaks, revealing the presence of a Bragg glass phase. We deal also with the long range Coulomb interactions, concluding that both peak divergence and anisotropy are enhanced. Finally we discuss how to detect experimentally the Bragg glass phase in the view of the role played by the finite resolution of measurements.

cond-mat.dis-nn↗

arXiv2003

Specific heat of classical disordered elastic systems

We study the thermodynamics of disordered elastic systems, applied to vortex lattices in the Bragg glass phase. Using the replica variational method we compute the specific heat of pinned vortons in the classical limit. We find that the contribution of disorder is positive, linear at low temperature, and exhibits a maximum. It is found to be important compared to other contributions, e.g. core electrons, mean field and non linear elasticity that we evaluate. The contribution of droplets is subdominant at weak disorder in $d=3$.

cond-mat↗

arXiv2003

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.

cond-mat↗

arXiv2003

X-ray diffraction of a disordered charge density wave

We study the X-ray diffraction spectrum produced by a collectively pinned charge density wave (CDW), for which one can expect a Bragg glass phase. The spectrum consists of two asymmetric divergent peaks. We compute the shape of the peaks, and discuss the experimental consequences.

cond-mat.dis-nn↗

arXiv2003

Variable range hopping and quantum creep in one dimension

We study the quantum non linear response to an applied electric field $E$ of a one dimensional pinned charge density wave or Luttinger liquid in presence of disorder. From an explicit construction of low lying metastable states and of bounce instanton solutions between them, we demonstrate quantum creep $v = e^{- c/E^{1/2}}$ as well as a sharp crossover at $E=E^*$ towards a linear response form consistent with variable range hopping arguments, but dependent only on electronic degrees of freedom.

cond-mat.dis-nn↗

arXiv2000

Creep and depinning in disordered media

Elastic systems driven in a disordered medium exhibit a depinning transition at zero temperature and a creep regime at finite temperature and slow drive $f$. We derive functional renormalization group equations which allow to describe in details the properties of the slowly moving states in both cases. Since they hold at finite velocity $v$, they allow to remedy some shortcomings of the previous approaches to zero temperature depinning. In particular, they enable us to derive the depinning law directly from the equation of motion, with no artificial prescription or additional physical assumptions. Our approach provides a controlled framework to establish under which conditions the depinning regime is universal. It explicitly demonstrates that the random potential seen by a moving extended system evolves at large scale to a random field and yields a self-contained picture for the size of the avalanches associated with the deterministic motion. At $T>0$ we find that the effective barriers grow with lenghtscale as the energy differences between neighboring metastable states, and demonstrate the resulting activated creep law $v\sim \exp (-C f^{-μ}/T)$ where the exponent $μ$ is obtained in a $ε=4-D$ expansion ($D$ is the internal dimension of the interface). Our approach also provides quantitatively a new scenario for creep motion as it allows to identify several intermediate lengthscales. In particular, we unveil a novel ``depinning-like'' regime at scales larger than the activation scale, with avalanches spreading from the thermal nucleus scale up to the much larger correlation length $R_{V}$. We predict that $R_{V}\sim T^{-σ}f^{-λ}$ diverges at small $f$ and $T$ with exponents $σ,λ$ that we determine.

cond-mat.dis-nn↗

arXiv2000

Interchain conductivity of coupled Luttinger liquids and organic conductors

We reconsider the theory of dc and ac interchain conductivity in quasi-one dimensional systems. Our results are in good agreement with the measured c-axis optical conductivity of (TMTSF)_2{ClO}_4 and suggest that the c-axis dc-conductivity of (TMTSF)_2{PF}_6 in the 150K < T < 300Kd$ range is dominated by precursor effects of Mott localization. The crossover from a Luttinger liquid at high energy to a Fermi liquid at low energy is also addressed, within a dynamical mean-field theory. Implications for the inter-chain resistivity and Drude weight in the Fermi liquid regime are discussed.

cond-mat.str-el↗

arXiv1999

Interactions in Quasicrystals

Although the effects of interactions in solid state systems still remains a widely open subject, some limiting cases such as the three dimensional Fermi liquid or the one-dimensional Luttinger liquid are by now well understood when one is dealing with interacting electrons in {\it periodic} crystalline structures. This problem is much more fascinating when periodicity is lacking as it is the case in {\it quasicrystalline} structures. Here, we discuss the influence of the interactions in quasicrystals and show, on a controlled one-dimensional model, that they lead to anomalous transport properties, intermediate between those of an interacting electron gas in a periodic and in a disordered potential.

cond-mat.str-el↗

arXiv1999

Dynamical Transverse Meissner Effect and Transition in Moving Bose Glass

We study moving periodic structures in presence of correlated disorder using renormalisation group. We find that the effect of disorder persists at all velocities resulting at zero temperature in a Moving Bose Glass phase with transverse pinning. At non zero temperature we find two distinct moving glass phases. We predict a sharp transition, as velocity increases between the Moving Bose Glass, where the transverse Meissner effect persists in the direction transverse to motion and a Correlated Moving Glass at high velocity, where it disappears. Experimental consequences for vortex lattices and charge density wave (CDW) systems are discussed.

cond-mat↗

arXiv1999

Effects of Long Range Electronic Interactions on a One-dimensional Electron System

The effects of a long range electronic potential on a one dimensional chain of spinless fermions are investigated by numerical techniques (Exact Diagonalisation of rings with up to 30 sites complemented by finite size analysis) and analytic calculations. Due to a competition between the $2 k_F$ oscillations in the density and the (very slow) log divergence of the long wavelength part of the Coulomb potential, the metallic character of the system is enhanced at intermediate (and up to quite large) lengthscales. Despite some similarities, we found that this quasi-metallic regime is not of the Luttinger Liquid type, as evidenced by strong deviations from predictions of conformal field theory and in agreement with the picture of a (very weakly pinned) Wigner crystal. When the strength of the Coulomb interaction is substancially increased, we observe a smooth cross-over to a strongly localized charge density wave.

cond-mat.str-el↗

arXiv1998

Dislocations and Bragg glasses in two dimensions

We discuss the question of the generation of topological defects (dislocations) by quenched disorder in two dimensional periodic systems. In a previous study [Phys. Rev. B {\bf 52} 1242 (1995)] we found that, contrarily to $d=3$, unpaired dislocations appear in $d=2$ above a length scale $ξ_D$, which we estimated. We extend this description to include effects of freezing and pinning of dislocations at low temperature. The resulting $ξ_D$ at low temperature is found to be {\it larger} than our previous estimate, which is recovered above a characteristic temperature. The dependence of $ξ_D$ in the bare core energy of dislocations is a stretched exponential. We stress that for all temperatures below melting $ξ_D$ becomes arbitrarily large at weak disorder compared to the translational order length $R_a \gg a$. Thus there is a wide region of length scales, temperature and disorder where Bragg glass like behavior should be observable.

cond-mat↗

arXiv1997

Moving glass theory of driven lattices with disorder

We study periodic structures, such as vortex lattices, moving in a random potential. As predicted in [T. Giamarchi, P. Le Doussal Phys. Rev. Lett. 76 3408 (1996)] the periodicity in the direction transverse to motion leads to a new class of driven systems: the Moving Glasses. We analyse using several RG techniques the properties at T=0 and $T>0$: (i) decay of translational long range order (ii) particles flow along static channels (iii) the channel pattern is highly correlated (iv) barriers to transverse motion. We demonstrate the existence of the ``transverse critical force'' at T=0. A ``static random force'' is shown to be generated by motion. Displacements grow logarithmically in $d=3$ and algebraically in $d=2$. The persistence of quasi long range translational order in $d=3$ at weak disorder, or large velocity leads to predict a topologically ordered ``Moving Bragg Glass''. This state continues the static Bragg glass and is stable at $T>0$, with non linear transverse response and linear asymptotic behavior. In $d=2$, or in $d=3$ at intermediate disorder, another moving glass exist (the Moving Transverse Glass) with smectic quasi order in the transverse direction. A phase diagram in $T$ force and disorder for static and moving structures is proposed. For correlated disorder we predict a ``moving Bose glass'' state with anisotropic transverse Meissner effect and transverse pinning. We discuss experimental consequences such as anomalous Hall effect in Wigner crystal and transverse critical current in vortex lattice.

cond-mat↗

arXiv1997

Statics and Dynamics of Disordered Elastic Systems

We examine here various aspects of the statics and dynamics of disordered elastic systems such as manifolds and periodic systems. Although these objects look very similar and indeed share some underlying physics, periodic systems constitute a class of their own with markedly different properties. We focus on such systems, review the methods allowing to treat them, emphasize the shift of viewpoint compared to the physics of manifolds and discuss their physics in detail. As for the statics, periodicity helps the system to retain a quasi-translational order and to be stable with respect to the proliferation of free topological defects such as dislocations. A disordered periodic system thus leads to a glass phase with Bragg peaks: the Bragg glass. On the other hand, for driven lattices, transverse periodicity allows the system to retain its glassy nature, leading to a moving glass phase. The existence of these two phases has important theoretical and experimental consequences, in particular for vortex physics in superconductors, the physical system which is mainly focused here.

cond-mat.dis-nn↗

arXiv1996

Coulomb blockade in a quantum wire with long-range Coulomb interactions

We study the transport through two impurities or ``barriers'' in a one-dimensional quantum wire, taking into account the long-range $\frac1r$ Coulomb interactions. We compute the temperature-dependent conductance $G(T)$ of this system. Long-range forces lead to a dramatic increase of weak barrier potentials with decreasing temperature, even in the ``resonant'' case. The system thus always reaches a ``strong barrier'' regime in which only charge is pinned, contrary to the standard LL case. $G(T)$ vanishes faster than any power as $T$ goes to zero. In particular, resonant tunneling is suppressed at zero temperature.

cond-mat↗

arXiv1996

Reply to the Comment on `` Moving glass phase of driven lattices ''

It was shown in our Letter that the novel glassy property of the moving lattice (transverse critical force and pinned channels) originate {\it only} from the periodicity in the {\it transverse} direction, i.e the underlying smectic density modes of the structure. Thus, contrarily to the claim of the Comment, these properties should be robust to the details of the structure along the direction of motion, even in the presence of a random force (we have demonstrated the existence of a random force in both directions) or dislocations between layers.

cond-mat↗