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 _⊥ 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 _⊥ close to this crossover. At large t _⊥ 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. Received 31 July 2000     

Non-linear scission/recombination kinetics of living polymerization

Living polymers are formed by reversible association of primary units (unimers). Generally the chain statistical weight involves a factor σ < 1 suppressing short chains in comparison with free unimers. Living polymerization is a sharp thermodynamic transition for σ ≪ 1 which is typically the case. We show that this sharpness has an important effect on the kinetics of living polymerization (one-dimensional association). The kinetic model involves i) the unimer activation step (a transition to an assembly-competent state); ii) the scission/recombination processes providing growth of polymer chains and relaxation of their length distribution. Analyzing the polymerization with no chains but unimers at t = 0 , with initial concentration of unimers M ≳ M ^* (M^* is the critical polymerization concentration), we determine the time evolution of the chain length distribution and find that: 1) for M ^* ≪ M ≪ M ^*/σ the kinetics is characterized by 5 distinct time stages demarcated by 4 characteristic times t₁, t₂, t₃ and t^*; 2) there are transient regimes (t ₁ ≲ t ≲ t ₃) when the molecular-weight distribution is strongly non-exponential; 3) the chain scissions are negligible at times shorter than t₂. The chain growth is auto-accelerated for t ₁ ≲ t ≲ t ₂ : the cut-off chain length (= polymerization degree 〈n〉_w N ₁ ∝ t ² in this regime. 4) For t ₂ < t < t ₃ the length distribution is characterized by essentially 2 non-linear modes; the shorter cut-off length N₁ is decreasing with time in this regime, while the length scale N₂ of the second mode is increasing. (5) The terminal relaxation time of the polymer length distribution, t^*, shows a sharp maximum in the vicinity of M^*; the effective exponent is as high as ∼ σ^-1/3 just above M^*.     

Dynamic regimes in films with a periodic array of antidots

We have studied the dynamic response of Pb thin films with a square array of antidots by means of ac susceptibility measurements. At low enough ac drive amplitudes h, vortices moving inside the pinning potential give rise to a frequency- and h-independent response together with a scarce dissipation. For higher amplitudes, the average distance travelled by vortices surpasses the pinning range and a critical state develops. We found that the boundary h^*(H,T) between these regimes smoothly decreases as T increases whereas a step-like behavior is observed as a function of field. We demonstrate that these steps in h^*(H) arise from sharp changes in the pinning strength corresponding to different vortex configurations. For a wide set of data at several fields and temperatures in the critical state regime, we show that the scaling laws based on the simple Bean model are satisfied.Received: 13 October 2003, Published online: 19 February 2004PACS: 74.78.Na Mesoscopic and nanoscale systems - 74.25.Sv Critical currents - 74.78.Db Low-T_c films     

Investigation of the field-tuned quantum critical point in CeCoIn<Subscript>5</Subscript>

The main properties and the type of the field-tuned quantum critical point in the heavy-fermion metal CeCoIn₅ that arise upon application of magnetic fields B are considered within a scenario based on fermion condensation quantum phase transition. We analyze the behavior of the effective mass, resistivity, specific heat, charge, and heat transport as functions of applied magnetic fields B and show that, in the Landau Fermi liquid regime, these quantities demonstrate critical behavior, which is scaled by the critical behavior of the effective mass. We show that, in the high-field non-Fermi liquid regime, the effective mass exhibits very specific behavior, M*～ T^{? 2/3}, and the resistivity demonstrates T^2/3 dependence. Finally, at elevated temperatures, it changes to M*～T^?1/2, while the resistivity becomes linear in T. In zero magnetic field, the effective mass is controlled by temperature T and the resistivity is also linear in T. The obtained results are in good agreement with recent experimental facts.     

Sample-to-sample fluctuations in the conductivity of a disordered medium

We investigate the sample-to-sample fluctuations in the conductivity of a random resistor network—equivalently, in the diffusivity of a disordered medium with symmetric hopping rates. We argue that whenever the effective conductivity ^* is strictly positive, then the fluctuations are normal, i.e., proportional to (volume)^–1/2. If the local conductivities are allowed to be zero, then ^* vanishes when approaching the percolation thresholdp _c. Close top _c the fluctuations are anomalous. From the renormalization group on hierarchical lattices we find that atp _c fluctuations and mean scale in the same fashion, i.e., there is no independent scaling exponent for the fluctuations.     

On the correlation between supercooling,superheating and kinetic arrest in a magnetic glass Pr<Subscript>0.5</Subscript>Ca<Subscript>0.5</Subscript>Mn<Subscript>0.975</Subscript>Al<Subscript>0.025</Subscript>O<Subscript>3</Subscript>

We report a quantitative investigation of the magnetic field-temperature phase diagram by taking into account a simple phenomenological model arising out of the interplay of kinetic arrest and thermodynamic transitions in a magnetic glass Pr_0.5Ca_0.5Mn_0.975Al_0.025O₃, through magnetization measurements. Such studies are necessary as kinetic arrest plays an important role in the formation of “magnetic glasses”, which has been observed in systems undergoing first order magnetic phase transitions. It has been shown that disorder in a system results in the formation kinetic arrest (H _K ,T _K ) band, like supercooling (H ^*,T ^*) and superheating (H ^**,T ^**) band. Quantitative proofs are given to show that (H _K ,T _K ) band is anticorrelated with (H ^*,T ^*) and (H ^**,T ^**) bands, while the later two are correlated among themselves. Analysis of time dependence of magnetization at different temperatures is carried out to establish the fact that the kinetic arrested state is different from the supercooled state.     

Interfacial Adsorption in Two-Dimensional Potts Models

The interfacial adsorption W at the first-order transition in two-dimensional q-state Potts models is studied. In particular, findings of Monte Carlo simulations and of density-matrix renormalization group calculations at q=16 are consistent with the analytic result, obtained in the Hamiltonian limit at large values of q, that Wt ^–1/3 on approach to the bulk critical temperature T _c, t=|T _c–T|/T _c. In addition, the numerical findings allow to estimate corrections to scaling. Our study supports and quantifies a previous conclusion by Bricmont and Lebowitz based on low temperature expansions.     

Intercluster conduction in lightly doped La<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Ca<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>MnO<Subscript>3</Subscript> manganites in the paramagnetic temperature range

The magnetotransport and magnetic properties of La _{1 ? x} Ca _x MnO₃ polycrystalline samples (x = 0–0.3) annealed under vacuum and in the oxygen environment are investigated in the temperature range from 77 to 400 K. The magnetic studies of lightly doped manganites reveal persistence of short-range magnetic order up to a temperature T* ≈ 300 K, which is about 2–3 times higher than their Curie temperature T _C. The temperature dependence of the electrical resistivity measured from T* down to nearly T ≈ T _C is fitted by the relation logρ ～ T ^?1/2, which is characteristic of granular metals with electrons tunneling among nanoclusters of magnetic metals embedded in a dielectric host. The magnetoresistance of polycrystalline samples annealed in the oxygen environment has been observed to increase. The electrical, magnetic, and magnetotransport properties of the manganites can be accounted for by the formation of magnetic nanoclusters below T*, tunneling (or hopping) of carriers among the nanoclusters, variation in the magnetic cluster size, and tunneling barrier thickness with variations in temperature and magnetic field strength, as well as by the effect of annealing in different media on the cluster properties.     

Magnetic relaxation in a three-dimensional ferromagnet with weak quenched random-exchange disorder

Isothermal remanent magnetization decay,M _r(t), and ‘in-field’ growth of zero-field-cooled magnetization,M _ZFC(t), with time have been measured over four decades in time at temperatures ranging from 0.25T _c to 1.25T _c (whereT _c is the Curie temperature, determined previously for the same sample from static critical phenomena measurements) for a nearly ordered intermetallic compound Ni₃Al, which is an experimental realization of a three-dimensional (d = 3) ferromagnet with weak quenched random-exchange disorder. None of the functional forms ofM _r(t) predicted by the existing phenomenological models of relaxation dynamics in spin systems with quenched randomness, but only the expressions and closely reproduce such data in the present case. The most striking features of magnetic relaxation in the system in question are as follows: Aging effects are absent in bothM _r t andM _ZFC(t) at all temperatures in the temperature range covered in the present experiments. A cross-over in equilibrium dynamics from the one, characteristic of a pured = 3 ferromagnet with complete atomic ordering and prevalent at temperatures away from T_c, to that, typical of ad = 3 random-exchange ferromagnet, occurs asT → T_c. The relaxation times τ₁(T)(τ₁ ^′(T)) and τ₂(T)(τ₂ ^′(T)) exhibit logarithmic divergence at critical temperatures and ; and both increase with the external magnetic field strength,H, such that at any given field value, . The exponent characterizing the logarithmic divergence in τ ₁ ^′ (T) and τ ₂ ^′ T possesses a field-independent value of ≃16 for both relaxation times. Of all the available theoretical models, the droplet fluctuation model alone provides a qualitative explanation for some aspects of the present magnetic relaxation data     

Bulk singularities at critical end points: a field-theory analysis

A class of continuum models with a critical end point is considered whose Hamiltonian [φ,ψ] involves two densities: a primary order-parameter field, φ, and a secondary (noncritical) one, ψ. Field-theoretic methods (renormalization group results in conjunction with functional methods) are used to give a systematic derivation of singularities occurring at critical end points. Specifically, the thermal singularity ∼ | t|^{2 - α} of the first-order line on which the disordered or ordered phase coexists with the noncritical spectator phase, and the coexistence singularity ∼ | t|^{1 - α} or ∼ | t|^β of the secondary density <ψ> are derived. It is clarified how the renormalization group (RG) scenario found in position-space RG calculations, in which the critical end point and the critical line are mapped onto two separate fixed points _CEP ^* and _λ ^*, translates into field theory. The critical RG eigenexponents of _CEP ^* and _λ ^* are shown to match. _CEP ^* is demonstrated to have a discontinuity eigenperturbation (with eigenvalue y = d), tangent to the unstable trajectory that emanates from _CEP ^* and leads to _λ ^*. The nature and origin of this eigenperturbation as well as the role redundant operators play are elucidated. The results validate that the critical behavior at the end point is the same as on the critical line. Received 18 January 2001     

Highly mobile Einstein spaces in the large

We consider an Einstein spaceV of the Petrov type II or III admitting a group of motionsG of high order. First we calculate the composition law and topological structure ofG. ThenV (or its submanifolds of transitivity) is represented as the homogeneous spaceG/H ofG,H being a subgroup ofG, and the actionG onV and the topology ofV are determined. The topologies of the spacesV are as follows: ⁴ (spaceT*₂), ⁴ of ³ T¹ (spaceT ₂), ⁴ (spaceT*₃), ³ (submanifolds of transitivity in spaceT ₃).In two cases (spacesT ₂ andT ₃) we have obtained metrics free of singularities.     

Heat transfer in unsteady MHD oscillatory flow

Heat transfer in unsteady MHD channel flow (of an incompressible viscous and electrically conducting fluid) under oscillatory pressure gradient when the channel surfaces are conducting and moving with time-dependent velocities has been analysed. The velocity, magnetic field and temperature distributions have been obtained and their numerical results are shown graphically.Symbols u velocity - H _o applied magnetic field - H _x induced magnetic field - T temperature - T ₁ ^* ,T ₂ ^* temperatures of the upper and lower planes - density - p pressure - kinematic viscosity - magnetic diffusivity - electrical conductivity of the fluid - A ^* characteristic velocity - L characteristic length - _e magnetic permeability of the fluid - C _p specific heat - coefficient of viscosity - k thermal conductivity - ₁, ₂ permeabilities of the planes - ₁, ₂ conductivities of the planes - ₁, ₂ conductance ratios of the planes - Pr Prandtl number (=C _p /k) - E Eckert number - M Hartmann number (= _e H _o L/) - R _e Reynolds number (=LA ^*/) - R _m magnetic Reynolds number (= _e LA ^*) - S Pr.E(=S)     

Mechanisms of low-temperature high-frequency conductivity in systems with a dense array of Ge<Subscript>0.7</Subscript>Si<Subscript>0.3</Subscript> quantum dots in silicon

High-frequency (HF) conductivity in systems with a dense (with a density of n = 3 × 10¹¹ cm^?2) array of self-organized Ge_0.7Si_0.3 quantum dots in silicon with different boron concentrations n_B is determined by acoustic methods. The measurements of the absorption coefficient and the velocity of surface acoustic waves (SAWs) with frequencies of 30–300 MHz that interact with holes localized in quantum dots are carried out in magnetic fields of up to 18 T in the temperature interval from 1 to 20 K. Using one of the samples (n_B = 8.2 × 10¹¹ cm^?2), it is shown that, at temperatures T ≤ 4 K, the HF conductivity is realized by the hopping of holes between the states localized in different quantum dots and can be explained within a two-site model in the case of

Open image in new window

, where ω is the SAW frequency and τ₀ is the relaxation time of the populations of the sites (quantum dots). For T > 7 K, the HF conductivity has an activation character associated with the diffusion over the states at the mobility threshold. In the interval 4 K < T < 7 K, the HF conductivity is determined by a combination of the hopping and activation mechanisms. The contributions of these mechanisms are distinguished; it is found that the temperature dependence of the hopping HF conductivity approaches saturation at T* ≈ 4.5 K, which points to a τ₀ ≤ 1. A value of τ₀(T*) ≈ 5 × 10^?9 s is determined from the condition ωτ₀(T*) ≈ 1.

     

Nonresonant third-order susceptibility measurements in the nematic liquid crystal K18

We have observed a large nonresonant third-order nonlinear susceptibility, X ⁽³⁾ (-; , 0, 0) in the isotropic phase of a nematic liquid crystal 4-n-hexyl-4-cyanobiphenyl (K18). The highest value of X ⁽³⁾ obtained at 632.8 nm is 1.16274×10^-18 m²V^-2 corresponding to a temperature 29.3°C. The observed second-order pretransitional temperature T ^* from our measurements is 1.2°C below the first-order nematic to isotropic transition temperature. The dependence of the Kerr constant on (T-T ^*)^-1 is found to be in good agreement with the predictions of the Landau-de Gennes model.     

(T * G) t : A toy model for conformal field theory

We study a chiral operator algebra of conformal field theory and quantum deformation of the finite-dimensional Lie group to obtain the definition of (T ^* G) _t and its representation.The closeness of the Ka-Moody algebras, constituting the chiral operator algebra of a typical (and generic) conformal field theory model, namely the WZNW model, and quantum deformation of corresponding finite-dimensional Lie groupG has become more and more evident in recent years [1–5]. This in particular prompts further investigation of the differential geometry of such deformations. The notion of tangent and cotangent bundles is basic in classical differential geometry. It is only natural that the quantum deformations ofTG andT ^* G are to be introduced alongside those forG itself. Physical ideas could be useful for this goal.Indeed, theT ^* G can be interpreted as a phase space for a kind of a top, generalizing the usual top associated withG=SO(3). The classical mechanics is a natural language to describe differential geometry, whereas the usual quantization is nothing but the representation theory.In this paper we put corresponding formulas in such a fashion that their deformation becomes almost evident, given the experience in this domain. As a result we get the definition of (T ^* G) _t and its representation (t is the deformation parameter).To make the exposition most simple and formulas transparent we shall work on an example ofG=sl(2) and present results in such a way that the generalizations become evident. We shall stick to generic complex versions, real and especially compact forms requiring some additional consideration, not all of which are self-evident.This work was supported in part by a grant provided by the Academy of Finland, and the U.S. Department of Energy (DOE) under contract DE-AC02-76ER03069     

Interplay of Curie-type and Pauli-type magnetic susceptibilities in HCl-doped polyaniline pellets

The static magnetic susceptibility (χ) of own-made HCl-doped polyaniline pellets is investigated experimentally over the full range of the protonation level Y and in the temperature (T) range 10–300 K.The obtained results suggest that χ and the electrical conductivity σ – which is known from previous work – are interrelated.Namely, there is a weakly Y dependent crossover temperature T ^* where both χ and σ undergo notable changes.In χ, this refers to a simultaneous enhancement (reduction) of the Pauli-type susceptibility χ _P and reduction (enhancement) of the Curie constant C at T = T ^* when T increases (decreases).Below T < T ^*, where thermal effects are weak to moderate, a steep increase of χ _P(Y) around Y = 0.3 occurs together with a drop of C(Y).The above findings are consistent with a picture in which, at T ^*, spins that disappear from C reappear in χ _P, and vice versa.This model is used to address the longitudinal and transversal electron localisation lengths as functions of Y, the former being estimated to take values in the range 7–8 Åand the latter in the range 1–2 Å.     

Field dependent critical fluctuations aboveT g in the ESR line width of the spin glassAgMn

The ESR of the spin glassAgMn (2.7 and 9.6 at %) has been investigated below and aboveT _g(0.1T _g<T<5T _g) at various microwave frequencies. The analysis yields:1) No explicit frequency dependence but strong magnetic field effects, inherent with ESR-experiments.2) Part of the excess line width is identified as critical spin fluctuations, following a power law. However, because of the presence of the applied field, the reduced temperaturet is not a good scaling variable. We choose the non-linear susceptibility X _s divided byH ², which scales as the order parameter susceptibility. The experiment yieldsW _ex(X _s /H ²) ^p ,p=0.42. From this we deduce z3.     

High-field interlayer tunnelling transport in layered cuprates: Uncovering the pseudogap state

In high temperature (high T _c ) cuprate superconductors the gap in the electronic density of states is not fully filled at T _c ; it evolves into a partial (pseudo)gap that survives way beyond T _c , challenging the conventional views. We have investigated the pseudogap phenomenon in the field-temperature (H-T) diagram of Bi₂Sr₂CaCu₂O_{8 + y} over a wide range of hole doping ( ). Using interlayer tunneling transport in magnetic fields up to 60 T to probe the density-of states (DOS) depletion at low excitation energies we mapped the pseudogap closing field H _pg . We found that H _pg and the pseudogap onset temperature T ^* are related via a Zeeman relation , irrespective of whether the magnetic field is applied along the c-axis or parallel to CuO₂ planes. In contrast to large anisotropy of the superconducting state, the field anisotropy of H _pg is due solely to the g-factor. Our findings indicate that the pseudogap is of singlet-spin origin, consistent with models based on doped Mott insulator.Received: 2 February 2004, Published online: 10 August 2004PACS: 74.25.Dw Superconductivity phase diagrams - 74.25.Fy Transport properties (electric and thermal conductivity, thermoelectric effects, etc.) - 74.72.Hs Bi-based cuprates     

Flow equations for the spin-boson problem

Using continuous unitary transformations recently introduced by Wegner [1], we obtain flow equations for the parameters of the spin-boson Hamiltonian. Interactions not contained in the original Hamiltonian are generated by this unitary transformation. Within an approximation that neglects additional interactions quadratic in the bath operators, we can close the flow equations. Applying this formalism to the case of Ohmic dissipation at zero temperature, we calculate the renormalized tunneling frequency. We find a transition from an untrapped to trapped state at the critical coupling constant α _c =1. We also obtain the static susceptibility via the equilibrium spin correlation function. Our results are both consistent with results known from the Kondo problem and those obtained from mode-coupling theories. Using this formalism at finite temperature, we find a transition from coherent to incoherent tunneling atT ₂ ^* ≈2T ₁ ^* , whereT ₁ ^* is the crossover temperature of the dynamics known from the NIBA.     

A complete proof of the Feigenbaum conjectures

The Feigenbaum phenomenon is studied by analyzing an extended renormalization group map . This map acts on functions that are jointly analytic in a position variable (t) and in the parameter () that controls the period doubling phenomenon. A fixed point ^* for this map is found. The usual renormalization group doubling operatorN acts on this function ^* simply by multiplication of with the universal Feigenbaum ratio ^*= 4.669201..., i.e., (N ^*(,t)= ^*( ^* ,t). Therefore, the one-parameter family of functions, ^* , ^* (t)=( ^*(,t), is invariant underN. In particular, the function ₀ ^* is the Feigenbaum fixed point ofN, while ^* represents the unstable manifold ofN. It is proven that this unstable manifold crosses the manifold of functions with superstable period two transversally.