Inhomogeneous ordered states and translational nature of the gauge group in the landau continuum theory: I. General analysis

A phenomenological continuum theory of phase transitions to a global inhomogeneous state of a crystal must take into account the compensating fields that represent the fields of stresses caused by dislocations appearing at the boundaries between local homogeneous regions. These compensating fields, which are introduced in order to satisfy the condition of invariance of the Landau potential with respect to the operation of translation, enter into the theory via extended derivatives of the local order parameters with respect to macroscopic coordinates of the local homogeneous regions in the crystal. Because of this extension of derivatives, the theory of phase transitions to an inhomogeneous state must include the theory of elasticity, in which a potential of the stress field induced by the phase transition is proportional to the compensating field magnitude. The Kröner equation, which describes the state of dislocations induced by spatially inhomogeneous ordering, appears in this theory as a result of minimization of the Landau potential with respect to the compensating fields.     

Equilibrium theory of molecular fluids: Structure and freezing transitions

In this article we review equilibrium theory of molecular fluids which includes structure and freezing transitions. The application of the theory to evaluate the pair correlation functions using Integral Equation methods and Computer Simulations have been discussed. Freezing of classical complex fluids based on the density functional approach is also discussed and compare a variety of its versions. Transitions discussed are sensitive to the value of direct correlation functions of the effective liquid which is required as an input information in the theory. Accurate evaluation of pair correlation functions is emphasized. Calculation of these correlation functions which pose problems in the case of ordered phases is discussed. The pair correlation functions of the ordered phase, which are supposed to be made up of two contributions, one that preserves the symmetry of the isotropic phase and a second that breaks it, are discussed. A new free-energy functional developed for an inhomogeneous system that contains both symmetry conserved and symmetry broken parts of the direct pair correlation function is discussed. The most useful three dimensional reference interaction site model (3D-RISM) and its extension done recently by many workers is discussed. Application of this theory to a large variety of complex systems in combination with the density functional theory method implemented in the Amsterdam density functional software package is discussed. Coupling of the 3D-RISM salvation theory with molecular dynamics in the Amber molecular dynamics package is also given.     

Limiting Gibbs States and Phase Transitions of a Bipartite Mean-Field Hubbard Model

In the frame of operator-algebraic quantum statistical mechanics we calculate the grand canonical equilibrium states of a bipartite, microscopic mean-field model for bipolaronic superconductors (or anisotropic antiferromagnetic materials in the quasispin formulation). Depending on temperature and chemical potential, the sets of statistical equilibrium states exhibit four qualitatively different regions, describing the normal, superconducting (spin-flopped), charge ordered (antiferromagnetic), and coexistence phases. Besides phase transitions of the second kind, the model also shows phase transitions of the first kind between the superconducting and the charge ordered phases. A unique limiting Gibbs state is found in its central decomposition for all temperatures, even in the coexistence region, if the thermodynamic limit is performed at fixed particle density (magnetization).     

Totally symmetric order parameter in the framework of the phenomenological theory of phase transitions: Ferroelastics

A new approach is proposed for constructing the phenomenological theory of phase transitions. The approach is based on the classical Landau theory with allowance made for the order parameter that corresponds to changes in the charge distribution probability density of a crystal and does not affect the symmetry of the high-symmetry phase. It is demonstrated that this approach makes it possible to describe phase transitions in terms of a nonequilibrium polynomial Landau potential of degree four in the components of the order parameters. The capabilities of the proposed approach are illustrated with three systems that undergo ferroelastic phase transitions.     

Observation of spin susceptibility enhancement in the possible Fulde-Ferrell-Larkin-Ovchinnikov state of CeCoIn(5)

We report (115)In nuclear magnetic resonance measurements of the heavy-fermion superconductor CeCoIn(5) in the vicinity of the superconducting critical field H(c2) for a magnetic field applied perpendicular to the ? axis. A possible inhomogeneous superconducting state, the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, is stabilized in this part of the phase diagram. In an 11 T applied magnetic field, we observe clear signatures of the two phase transitions: the higher temperature one to the homogeneous superconducting state and the lower temperature phase transition to a FFLO state. We find that the spin susceptibility in the putative FFLO state is significantly enhanced as compared to the value in a homogeneous superconducting state. The implications of this finding for the nature of the low temperature phase are discussed.     

Microscopic evidence for field-induced magnetism in CeCoIn5

We present NMR data in the normal and superconducting states of CeCoIn5 for fields close to H(c2)(0)=11.8 T in the ab plane. Recent experiments identified a first-order transition from the normal to superconducting state for H>10.5 T, and a new thermodynamic phase below 290 mK within the superconducting state. We find that the Knight shifts of the In(1), In(2), and the Co are discontinuous across the first-order transition and the magnetic linewidths increase dramatically. The broadening differs for the three sites, unlike the expectation for an Abrikosov vortex lattice, and suggests the presence of static spin moments in the vortex cores. In the low-temperature and high-field phase, the broad NMR lineshapes suggest ordered local moments, rather than a long-wavelength quasiparticle spin density modulation expected for an FFLO phase.     

Theory of electrical resistance of multivalley semiconductors with screw dislocations

The diffusion theory of electrical resistance in multivalley semiconductors of Si-type with screw dislocations is developed. Intervalley electron transitions are taken into account. The effect of the inhomogeneous dislocation distribution on the electrical resistance of the crystal is considered.It is shown that randomly distributed dislocations having the mean density 10¹⁰ cm–2 contribute some percents to the electrical resistance at room temperature. Intervalley transitions make this contribution much lower (by one order or more). The inhomogeneity of dislocation distribution enhances the electrical resistance several orders as compared with randomly distributed dislocations.     

A formal theory of the conductivity and application to the giant magnetoresistance

The transport in a system with inhomogeneous elastic scattering is described in terms of a probabilityconserved Boltzmann equation. We demonstrate that the spatially varied current density depends only on the voltage drop between the ends of the sample. This fact enables us to develop a formal and general theory for the conductivity without determining the actual electric field inside the sample. The theory is first applied to multilayer systems and shown to recover the previous theory. By including the spin-dependent interface scattering and bulk scattering, we employ our theory to account for the giant magnetoresistance (MR) in magnetic granular systems with both spherical and cylindrical granules. The results obtained reproduce the experimental dependence of the MR on annealing temperature.     

Heterogeneous nucleation of martensite at dislocations and the martensitic-transformation kinetics in shape memory alloys

The martensite phase formation in elastic fields of isolated screw and edge dislocations, as well as in planar clusters of like-sign dislocations and in a two-dimensional network of opposite-sign edge dislocations, is quantitatively analyzed within the theory of smeared martensitic transitions. The heterogeneous nucleation of martensite at dislocations is shown to increase the characteristic temperature of the martensitic transition and its temperature smearing.     

Magnetic properties of cuprate superconductors based on a phase separation theory

There is a great debate concerning the hole of the inhomogeneities in high critical temperature superconductors (HTS). Several experiments indicate a possible electronic phase separation (PS). However, there is not a method to quantify how such transition occurs and how it develops. Here we show that the Cahn–Hilliard (CH) theory of phase separation provides a way to trace the phase separation process as a function of temperature. We connect these calculations with the Bogoliubov–deGennes (BdG) approach to an inhomogeneous superconductor and derive many HTS properties of the La_2−xSrCuO₄ (LSCO) system. The results yield: an onset of superconductivity that follows close the Nernst signal, the leading edge shift is close to the zero temperature average gap, and the superconducting phase is achieved by percolation. Our approach reproduces also the experimental measurements of the H_c2 field.     

The magnetostriction of Invar alloys

The principles of the theory of a phase transition into a magnetically ordered state are formulated for Invar alloys and other similar inhomogeneous ferromagnets, for which the concept of a local Curie temperature distribution corresponding to the experimentally observed broadened temperature interval of the transition into the ferromagnetic state has existed for 10 years. A method is proposed for obtaining information about the local temperature distribution from experimental data on the change in the properties of magnets in response to a change in temperature. For iron-nickel-chromium alloys it is shown how to obtain the temperature dependence of the magnetostrictional susceptibility of the paraprocess from data on the magnetic contribution to the thermal expansion coefficient. This confirms the important role of the local Curie temperature distribution, and it also indicates a need for new analysis of experimental data on temperature-broadened magnetic ordering phase transitions. Zh. éksp. Teor. Fiz. 113, 213–227 (January 1998)     

Melting pattern of diquark condensates in quark matter

Thermal color superconducting phase transitions in high density three-flavor quark matter are investigated in the Ginzburg-Landau approach. The effects of nonzero strange quark mass, electric and color charge neutrality, and direct instantons are considered. Weak coupling calculations show that an interplay between the mass and electric neutrality effects near the critical temperature gives rise to three successive second-order phase transitions as the temperature increases: a modified color-flavor locked (mCFL) phase (ud, ds, and us pairings) --> a d-quark superconducting (dSC) phase (ud and ds pairings) --> an isoscalar pairing phase (ud pairing) --> a normal phase (no pairing). The dSC phase is novel in the sense that while all eight gluons are Meissner screened as in the mCFL phase, three out of nine quark quasiparticles are always gapless.     

Screw dislocations in the field theory of elastoplasticity

A (microscopic) static elastoplastic field theory of dislocations with moment and force stresses is considered. The relationship between the moment stress and the Nye tensor is used for the dislocation Lagrangian. We discuss the stress field of an infinitely long screw dislocation in a cylinder, a dipole of screw dislocations and a coaxial screw dislocation in a finite cylinder. The stress fields have no singularities in the dislocation core and they are modified in the core due to the presence of localized moment stress. Additionally, we calculated the elastoplastic energies for the screw dislocation in a cylinder and the coaxial screw dislocation. For the coaxial screw dislocation we find a modified formula for the so‐called Eshelby twist which depends on a specific intrinsic material length.     

Ground state phase diagram of extended attractive Hubbard model

The ground state phase diagram of the weakly coupled extended Hubbard model with intraatomic attraction has been derived with the Hartree theory formulated in terms of the Bogoliubov variational approach. For a given value of electron density, the nature of the ordered ground state depends essentially on the sign and the strength of the nearest neighbor coupling. Some features are similar to those in the strong coupling limit obtained earlier.     

Influence of static and dynamic internal actions on elastic nonlinear properties of a granulated unconsolidated medium

We have studied the influence of external static (pressure) and dynamic (caused by an elastic wave with a finite amplitude) actions on the linear and nonlinear elastic properties of a granulated unconsolidated medium, which was simulated by steel spheres with diameters of 2 and 4 mm. We have analyzed the equation of state for such a medium taking into account the presence of weakly and strongly deformed contacts between individual spheres. We have obtained expressions for the elasticity coefficient and second- and third-order nonlinear elastic parameters, and we have experimentally studied the influence of external static pressure on their values. We have measured the dependence of the velocity of elastic waves on external static pressure and the probing signal amplitude. In the studied medium, a number of structural phase transitions were observed, related to rearrangement of the packing of spheres, which were caused by both static and dynamic actions. The structural phase transition was accompanied by an anomalous change in the nonlinear elastic parameters of the medium and the velocity of elastic waves. We have analyzed the results based on the Hertz theory of contact interaction.     

Vortex-glass phases in type-II superconductors

A review is given on the theory of vortex-glass phases in impure type-II superconductors in an external field. We begin with a brief discussion of the effects of thermal fluctuations on the spontaneously broken U(1) and translation symmetries, on the global phase diagram and on the critical behaviour. Introducing disorder we restrict ourselves to the experimentally most relevant case of weak uncorrelated randomness which is known to destroy the long-ranged translational order of the Abrikosov lattice in three dimensions. Elucidating possible residual glassy ordered phases, we distinguish between positional and phase-coherent vortex glasses. The study of the behaviour of isolated vortex lines and their generalization directed elastic manifolds in a random potential introduces further important concepts for the characterization of glasses. The discussion of elastic vortex glasses, i.e. topologically ordered dislocation-free positional glasses in two and three dimensions occupy the main part of our review. In particular, in three dimensions there exists an elastic vortex-glass phase which still shows quasi-long-range translational order: the 'Bragg glass'. It is shown that this phase is stable with respect to the formation of dislocations for intermediate fields. Preliminary results suggest that the Bragg-glass phase may not show phasecoherent vortex-glass order. The latter is expected to occur in systems with weak disorder only in higher dimensions (or for strong disorder, as the example of unscreened gauge glasses shows). We further demonstrate that the linear resistivity vanishes in the vortex-glass phase. The vortex-glass transition is studied in detail for a superconducting film in a parallel field. Finally, we review some recent developments concerning driven vortex-line lattices moving in a random environment.     

Correlated Huang scattering in hexagonal Jahn Teller compounds

This is a theoretical investigation on structural precursors in diffuse neutron scattering of disordered phases of cooperative Jahn-Teller compounds above their structural phase transitions. The theory is based on Huang scattering off elastic dipoles. Softening of shear modes in the smallq regime known from inelastic scattering predicts monoclinic and orthorhombic structures which are found in some of these compounds. For these smallq the Jahn-Teller effect looks dynamic and Huang scattering is not applicable. With larger wave vectors the dipoles look static and Huang theory works but one picks up neighbor correlations which have to be included. We believe to have identified the spiral correlation announcing the helical structure of CsCuCl₃ in its ordered phase. We also calculate diffuse scattering for RbCrCl₃ and the experimentally observed satellites announcing the cell doubling of the ordered phase.     

On Inhomogeneous Polarized States near the Phase Transition Point in a Thin Ferroelectric Film

It is shown in terms of the phenomenological Landau theory of phase transitions that a phase transition to an inhomogeneous polar phase preceding in temperature a phase transition to a homogeneous polar state is possible. As a result of solving a boundary eigenvalue problem for the polarization equilibrium equation and electrostatics equations, wave vector k_⊥ characterizing the inhomogeneous phase has been determined and the temperature boundaries of its existence in the dependence on the film thickness and its surface properties have been found.