Two types of the effective mass divergence and the Grüneisen ratio in heavy-fermion metals

The behavior of the specific heat c_p, effective mass M^*, and the thermal expansion coefficient of a Fermi system located near the fermion condensation quantum phase transition (FCQPT) is considered. We observe the first type behavior if the system is close to FCQPT: the specific heat , , while the thermal expansion coefficient . Thus, the Grüneisen ratio Γ(T)=/c_p does not diverges. At the transition region, where the system passes over from the non-Fermi liquid to the Landau Fermi liquid, the ratio diverges as . When the system becomes the Landau Fermi liquid, Γ(T,r)∝1/r, with r being a distance from the quantum critical point. Provided the system has undergone FCQPT, the second type takes place: the specific heat behaves as , M^*∝1/T, and =a+bT with a,b being constants. Again, the Grüneisen ratio diverges as .     

Nature of the quantum critical point as disclosed by extraordinary behavior of magnetotransport and the lorentz number in the heavy-fermion metal YbRh2Si2

Physicists are engaged in vigorous debate on the nature of the quantum critical points (QCP) governing the low-temperature properties of heavy-fermion metals. Recent experimental observations of the much-studied compound YbRh₂Si₂ in the regime of vanishing temperature incisively probe the nature of its magnetic-field-tuned QCP. The jumps revealed both in the residual resistivity ??₀ and the Hall resistivity R _H, along with violation of the Wiedemann-Franz law, provide vital clues to the origin of such non-Fermi-liquid behavior. The empirical facts point unambiguously to association of the observed QCP with a fermion-condensation phase transition. Based on this insight, the resistivities ??₀ and R _H are predicted to show jumps at the crossing of the QCP produced by application of a magnetic field, with attendant violation of the Wiedemann-Franz law. It is further demonstrated that experimentally identifiable multiple energy scales are related to the scaling behavior of the effective mass of the quasiparticles responsible for the low-temperature properties of such heavy-fermion metals.     

Fate of the Wiedemann–Franz Law near Quantum Critical Points of Electron Systems in Solids

We introduce and analyze two different scenarios for violation of the Wiedemann–Franz law in strongly correlated electron systems of solids, close to a topological quantum critical point (TQCP) where the density of states N(0) diverges. The first, applicable to the Fermi-liquid (FL) side of the TQCP, involves a transverse zero-sound collective mode that opens a new channel for the thermal conductivity, thereby enhancing the Lorenz number L(0) relative to the value L0 =π² k _B ²/3e ² dictated by conventional FL theory. The second mechanism for violation of the WF law, relevant to the non-Fermi-liquid (NFL) side of the TQCP, involves the formation of a flat band and leads instead to a reduction of the Lorenz number.     

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.     

Magnetoresistance of a highly correlated electron liquid

The behavior in a magnetic field of a highly correlated electron liquid approaching the fermion condensation quantum phase transition from the disordered phase is considered. We show that, at sufficiently high temperatures T≥T*(x), the effective mass starts to depend on T, M* ∝T^?1/2. This T^?1/2 dependence of the effective mass at elevated temperatures leads to the non-Fermi liquid behavior of the resistivity, σ(T) ∝ T and at higher temperatures σ(T) ∝ T^3/2. The application of a magnetic field B restores the common T² behavior of the resistivity. The effective mass depends on the magnetic field, M*(B) ∝ B^?2/3, being approximately independent of the temperature at T≤T*(B) ∝ B^4/3. At T≥T*(B), the T^?1/2 dependence of the effective mass is reestablished. We demonstrate that this B-T phase diagram has a strong impact on the magnetoresistance (MR) of the highly correlated electron liquid. The MR as a function of the temperature exhibits a transition from negative values of MR at T→0 to positive values at T ∝ B^4/3. Thus, at T≥T*(B), MR as a function of the temperature possesses a node at T ∝ B^4/3.     

From the Bose-Einstein to fermion condensation

The appearance of the fermion condensation, which can be compared to the Bose-Einstein condensation, in different Fermi liquids is considered; its properties are discussed; and a large amount of experimental evidence in favor of the existence of the fermion condensate (FC) is presented. We show that the appearance of FC is a signature of the fermion condensation quantum phase transition (FCQPT), which separates the regions of normal and strongly correlated liquids. Beyond the FCQPT point, the quasiparticle system is divided into two subsystems, one containing normal quasiparticles and the other, FC, localized at the Fermi level. In the superconducting state, the quasiparticle dispersion in systems with FC can be represented by two straight lines, characterized by effective masses M _FC ^* and M _L ^* and intersecting near the binding energy E₀, which is of the order of the superconducting gap. The same quasiparticle picture and the energy scale E₀ persist in the normal state. We demonstrate that fermion systems with FC have features of a “quantum protectorate” and show that strongly correlated systems with FC, which exhibit large deviations from the Landau Fermi liquid behavior, can be driven into the Landau Fermi liquid by applying a small magnetic field B at low temperatures. Thus, the essence of strongly correlated electron liquids can be controlled by weak magnetic fields. A reentrance into the strongly correlated regime is observed if the magnetic field B decreases to zero, while the effective mass M* diverges as \(M^ * \propto {1 \mathord{\left/ {\vphantom {1 {\sqrt B }}} \right. \kern-\nulldelimiterspace} {\sqrt B }}\). The regime is restored at some temperature \(T^ * \propto \sqrt B \). The behavior of Fermi systems that approach FCQPT from the disordered phase is considered. This behavior can be viewed as a highly correlated one, because the effective mass is large and strongly depends on the density. We expect that FCQPT takes place in trapped Fermi gases and in low-density neutron matter, leading to stabilization of the matter by lowering its ground-state energy. When the system recedes from FCQPT, the effective mass becomes density independent and the system is suited perfectly to be conventional Landau Fermi liquid.     

Summability of series with respect to a Haar system by the (C, 1) method

For a Haar-system series we prove that if the lower bound of the (C, 1) means of the series is larger than — ∞ on a set E of positive measure, then the series converges to a finite function almost everywhere on E; from this it follows that Haar-system series are not summable by the (C, 1) method to + ∞ on sets of positive measure.     

Synthesis,Structure, and Properties of Novel Enamine Containing Coumarin and Phosphonium Fragments

Condensation of 4-hydroxy-3-formylcoumarin with 4-aminobenzyl(triphenyl)phosphonium bromide has led to the formation of a phosphonium salt existing in DMSO solution as a mixture of two enamine forms, Z and E, according to NMR spectroscopy and quantum-chemical simulations data. Basing on the obtained salt, the ML₂ metal chelates of zinc(II), copper(II), and nickel(II) have been synthesized. Luminescence properties of the ligand and its complex with zinc have been studied.

     

Universal T/B Scaling Behavior of Heavy Fermion Compounds (Brief Review)

JETP Letters - In this brief review, we address manifestations of the T/B scaling behavior of heavy-fermion (HF) compounds, where T and B are the temperature and magnetic field, respectively. Using...     

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.