Application of power expansion in the thermodynamics of compressible Markovian copolymers

The problem of constructing phase diagrams for a compressible melt of a binary Markovian copolymer is reduced to a set of nonlinear differential equations in partial derivatives with transcendental relationships. Using power expansions, the closed set of nonlinear differential equations is derived. This set allows its further analytical study. Eigenvalues of a linearized system are analyzed, and the boundaries of the thermodynamic stability of melts are defined. Nonlinear equations in normal coordinates are obtained; for symmetric melts, these equations are reduced to a single equation by adiabatic elimination of small-scale variables. Binodal curves are calculated for such solutions of this equation, which correspond to the free energy minimum of melts. Corrections reflecting the effect of melt nonsymmetry are found. The results are applied for copolymers, whose composition is similar to that of homopolymers, diblock copolymers, and random and regularly alternating copolymers. Spinodals and binodals corresponding to microphase separation are constructed.     

Strongly correlated Fermi-systems: Non-Fermi liquid behavior, quasiparticle effective mass and their interplay

Basing on the density functional theory of fermion condensation, we analyze the non-Fermi liquid behavior of strongly correlated Fermi-systems such as heavy-fermion metals. When deriving equations for the effective mass of quasiparticles, we consider solids with a lattice and homogeneous systems. We show that the low-temperature thermodynamic and transport properties are formed by quasiparticles, while the dependence of the effective mass on temperature, number density, magnetic fields, etc., gives rise to the non-Fermi liquid behavior. Our theoretical study of the heat capacity, magnetization, energy scales, the longitudinal magnetoresistance and magnetic entropy are in good agreement with the remarkable recent facts collected on the heavy-fermion metal YbRh₂Si₂.     

Energy scales and the non-Fermi liquid behavior in YbRh<Subscript>2</Subscript>Si<Subscript>2</Subscript>

Multiple energy scales are detected in measurements of the thermodynamic and transport properties in heavy fermion metals. We demonstrate that the experimental data on the energy scales can be well described by the scaling behavior of the effective mass at the fermion condensation quantum phase transition, and show that the dependence of the effective mass on temperature and applied magnetic fields gives rise to the non-Fermi liquid behavior. Our analysis is placed in the context of recent salient experimental results. Our calculations of the non-Fermi liquid behavior, of the scales and thermodynamic and transport properties are in good agreement with the heat capacity, magnetization, longitudinal magnetoresistance and magnetic entropy obtained in remarkable measurements on the heavy fermion metal YbRh₂Si₂.     

Asymmetric Tunneling Conductance and the Non-Fermi Liquid Behavior of Strongly Correlated Fermi Systems

Tunneling differential conductivity (or resistivity) is a sensitive tool to experimentally test the non-Fermi liquid behavior of strongly correlated Fermi systems. In the case of common metals the Landau–Fermi liquid theory demonstrates that the differential conductivity is a symmetric function of bias voltage V. This is because the particle–hole symmetry is conserved in the Landau–Fermi liquid state. When a strongly correlated Fermi system turns out to be near the topological fermion condensation quantum phase transition, its Landau–Fermi liquid properties disappear so that the particle–hole symmetry breaks making the differential tunneling conductivity to be asymmetric function of V. This asymmetry can be observed when a strongly correlated metal is in its normal, superconducting or pseudogap states. We show that the asymmetric part of the dynamic conductance does not depend on temperature provided that the metal is in its superconducting or pseudogap states. In normal state, the asymmetric part diminishes at rising temperatures. Under the application of magnetic field the metal transits to the Landau–Fermi liquid state and the differential tunneling conductivity becomes a symmetric function of V. These findings are in good agreement with recent experimental observations.     

Superconductivity in the presence of fermion condensation

Fermion condensation (FC) is studied within the density functional theory. FC can fulfill the role of a boundary, separating the region of strongly interacting electron liquid from the region of strongly correlated electron liquid. Consideration of the superconductivity in the presence of FC shows that, under certain circumstances, at temperatures above T _c the superconductivity vanishes and the superconducting gap smoothly transforms into a pseudogap. The pseudogap occupies only a part of the Fermi surface, and one that shrinks with increasing temperature and vanishes at T=T*, and the single-particle excitations of the gapped area of the Fermi surface have a width γ ∼(T-T _c ). Pis’ma Zh. éksp. Teor. Fiz. 68, No. 6, 491–496 (25 September 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Fermion Condensation,T-Linear Resistivity,and Planckian Limit

JETP Letters - We explain recent challenging experimental observations of universal scattering rate related to the linear-temperature resistivity exhibited by a large corps of both strongly...     

Behavior of Fermi systems approaching the fermion condensation quantum phase transition from the disordered phase

The behavior of Fermi systems that approach the fermion condensation quantum phase transition (FCQPT) from the disordered phase is considered. We show that the quasiparticle effective mass M* diverges as M* ∝ 1/¦x?x_FC¦, where x is the system density and x_FC is the critical point at which FCQPT occurs. Such behavior is of general form and takes place in both three-dimensional (3D) and two-dimensional (2D) systems. Since the effective mass M* is finite, the system exhibits the Landau Fermi liquid behavior. At ¦x? x_FC¦/x_FC?1, the behavior can be viewed as highly correlated, because the effective mass is large and strongly depends on the density. In the case of electronic systems, the Wiedemann-Franz law is valid and the Kadowaki-Woods ratio is preserved. Beyond the region ¦x–x_FC¦/x_FC?1, the effective mass is approximately constant and the system becomes a conventional Landau Fermi liquid.     

Hall coefficient in heavy fermion metals

Experimental studies of the antiferromagnetic (AF) heavy fermion metal YbRh₂Si₂ in a magnetic field B indicate the presence of a jump in the Hall coefficient at a magnetic-field tuned quantum state in the zero temperature limit. This quantum state occurs at B ≥ B_c0 and induces the jump even though the change of the magnetic field at B = B_c0 is infinitesimal. We investigated this by using the model of heavy electron liquid with the fermion condensate. Within this model, the jump takes place when the magnetic field reaches the critical value B_c0 at which the ordering temperature T_N(B = B_c0) of the AF transition vanishes. We show that at B → B_c0, this second order AF phase transition becomes the first order one, making the corresponding quantum and thermal critical fluctuations vanish at the jump. At T → 0 and B = B_c0 the Grüneisen ratio as a function of the temperature T diverges. We demonstrate that both the divergence and the jump are determined by the specific low temperature behavior of the entropy \(S(T) \propto S_0 + a\sqrt T + bT\) with S₀; a and b are temperature independent constants.     

Heating of condensation surface during magnetron sputtering

Chromium films deposited by magnetron sputtering on non-heated substrates from non-thermalized atoms crystallize in regular bcc Cr phase, with non-uniform microstructure and lattice constant along the thickness. These non-uniformities decrease with elevation of the substrate temperature and vanish at a certain value. However films deposited on non-heated substrates from thermalized atoms crystallize in a low-temperature Cr phase and have almost uniform microstructure. We have developed a model explaining this effect, which is based on the supposition of the formation of a “hot” layer on the growth surface during deposition, whose temperature depends on the flux of energy delivered to the condensation surface and can be noticeably higher than the substrate temperature. Detailed investigation of the structure of Cr films deposited at various temperatures and energy fluxes delivered to the growth surface, correlate well with the above model.     

Universal behavior of heavy-fermion metals near a quantum critical point

The behavior of the electronic system of heavy-fermion metals is considered. We show that there exist at least two main types of the behavior when the system is near quantum critical point, which can be identified as the fermion condensation quantum phase transition (FCQPT). We show that the first type is represented by the behavior of a highly correlated Fermi liquid, while the second type is depicted by the behavior of a strongly correlated Fermi liquid. If the system approaches FCQPT from the disordered phase, it can be viewed as a highly correlated Fermi liquid which at low temperatures exhibits the behavior of Landau Fermi liquid (LFL). At higher temperatures T, it demonstrates the non-Fermi liquid (NFL) behavior which can be converted into the LFL behavior by the application of magnetic fields B. If the system has undergone FCQPT, it can be considered as a strongly correlated Fermi liquid which demonstrates the NFL behavior even at low temperatures. It can be turned into LFL by applying magnetic fields B. We show that the effective mass M* diverges at the very point that the Neél temperature goes to zero. The B-T phase diagrams of both liquids are studied. We demonstrate that these B-T phase diagrams have a strong impact on the main properties of heavy-fermion metals, such as the magnetoresistance, resistivity, specific heat, magnetization, and volume thermal expansion.