Flat Bands and Salient Experimental Features Supportingthe Fermion Condensation Theory of Strongly Correlated Fermi Systems

Physics of Atomic Nuclei - The physics of strongly correlated Fermi systems, being the mainstream topic for more than half a century, still remains elusive. Recent advancements in experimental...     

Fermi-condensate quantum phase transition in high-T c superconductors

The effect of a quantum phase transition associated with the appearance of fermionic condensation in an electron liquid on the properties of superconductors is considered. It is shown that the electron system in both superconducting and normal states exhibits characteristic features of a quantum protectorate after the point of this Fermi-condensate quantum phase transition. The single-particle spectrum of a superconductor can be represented by two straight lines corresponding to two effective masses M _FC * and M _L *. The M _FC * mass characterizes the spectrum up to the binding energy E ₀ , which is of the order of the superconducting gap in magnitude, and determines the spectrum at higher binding energies. Both effective masses are retained in the normal state; however, E ₀ ?4 T. These results are used to explain some remarkable properties of high-T _c superconductors and are in good agreement with recent experimental data.     

Fermion Condensate as a New State of Matter

We demonstrate that in very many natural systems consisting of huge numbers of identical fermions at zero temperature a phase transition can happen that leads to a quite specific state called fermion condensate. As a signal of such fermion condensation quantum phase transition serves unlimited increase of the effective mass of quasi‐particles that determine the excitation spectrum of multi‐fermion system under consideration. We discuss the conditions, under which this transition happens, and illustrate the physical properties of a system that is located near this phase transition. The effective mass diverge when the inter‐particle interaction is repulsive and medium strong as compared to particle's kinetic energy. So, low temperature and intermediate density plasma is a good candidate for such a phenomenon. Therefore, this paper can serve as a source of stimulating ideas when exploring a possible non‐Fermi liquid behavior of plasma. A common and essential feature of such systems is a possibility to introduce quasiparticles that are different, however, from those suggested by L.D. Landau almost sixty years ago, by crucial dependence of temperature, external magnetic field, pressure and so on. These systems exhibit scaling behavior of their effective mass and other characteristics that are determined by this effective mass. It is demonstrated that a huge amount of experimental data on different strongly correlated compounds suggest that they, starting from some temperature and down, are governed by the fermion condensation quantum phase transition. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Strongly correlated Fermi systems as a new state of matter

The aim of this review paper is to expose a new state of matter exhibited by strongly correlated Fermi systems represented by various heavy-fermion (HF) metals, two-dimensional liquids like ³He, compounds with quantum spin liquids, quasicrystals, and systems with one-dimensional quantum spin liquid. We name these various systems HF compounds, since they exhibit the behavior typical of HF metals. In HF compounds at zero temperature the unique phase transition, dubbed throughout as the fermion condensation quantum phase transition (FCQPT) can occur; this FCQPT creates flat bands which in turn lead to the specific state, known as the fermion condensate. Unlimited increase of the effective mass of quasiparticles signifies FCQPT; these quasiparticles determine the thermodynamic, transport and relaxation properties of HF compounds. Our discussion of numerous salient experimental data within the framework of FCQPT resolves the mystery of the new state of matter. Thus, FCQPT and the fermion condensation can be considered as the universal reason for the non-Fermi liquid behavior observed in various HF compounds. We show analytically and using arguments based completely on the experimental grounds that these systems exhibit universal scaling behavior of their thermodynamic, transport and relaxation properties. Therefore, the quantum physics of different HF compounds is universal, and emerges regardless of the microscopic structure of the compounds. This uniform behavior allows us to view it as the main characteristic of a new state of matter exhibited by HF compounds.     

Energy scales and magnetoresistance at a quantum critical point

The magnetoresistance (MR) of CeCoIn₅ is notably different from that in many conventional metals. We show that a pronounced crossover from negative to positive MR at elevated temperatures and fixed magnetic fields is determined by the scaling behavior of quasiparticle effective mass. At a quantum critical point (QCP) this dependence generates kinks (crossover points from fast to slow growth) in thermodynamic characteristics (like specific heat, magnetization, etc.) at some temperatures when a strongly correlated electron system transits from the magnetic field induced Landau-Fermi liquid (LFL) regime to the non-Fermi liquid (NFL) one taking place at rising temperatures. We show that the above kink-like peculiarity separates two distinct energy scales in QCP vicinity - low temperature LFL scale and high temperature one related to NFL regime. Our comprehensive theoretical analysis of experimental data permits to reveal for the first time new MR and kinks scaling behavior as well as to identify the physical reasons for above energy scales.     

Uniform and tangential harmonic approximation of continuous functions on arbitrary sets

Necessary and sufficient conditions which must be imposed on a set E are derived, such that functions continuous on E G can be approximated by functions harmonic in a region G (Rⁿ.Translated from Matematicheskie Zametki, Vol. 9, No. 2, pp. 131–142, February, 1971.In conclusion I wish to thank my scientific director S. N. Mergelyan and also A. A. Gonchar for their valuable advice.     

Transition from non-fermi liquid behavior to Landau–Fermi liquid behavior induced by magnetic fields

We show that a strongly correlated Fermi system with a fermion condensate which exhibits strong deviations from Landau–Fermi liquid behavior is driven into the Landau–Fermi liquid by applying a small magnetic field B at temperature T=0. This field-induced Landau–Fermi liquid behavior provides constancy of the Kadowaki–Woods ratio. A re-entrance into the strongly correlated regime is observed if the magnetic field B decreases to zero; the effective mass M* then diverges as \(M^* \propto {1 \mathord{\left/ {\vphantom {1 {\sqrt B }}} \right. \kern-\nulldelimiterspace} {\sqrt B }}\). At finite temperatures, the strongly correlated regime is restored at some temperature \(T^* \propto \sqrt B \). This behavior is of a general form and takes place in both three-dimensional and two-dimensional strongly correlated systems. We demonstrate that the observed \({1 \mathord{\left/ {\vphantom {1 {\sqrt B }}} \right. \kern-\nulldelimiterspace} {\sqrt B }}\) divergence of the effective mass and other specific features of heavy-fermion metals are accounted for by our consideration.     

Universal behavior of CePd<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Rh<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> ferromagnet at the quantum critical point

The heavy-fermion metal CePd_1−x Rh _x can be tuned from ferromagnetism at x = 0 to the nonmagnetic state at some critical concentration x _c . The non-Fermi liquid behavior (NFL) at x ≃ x _c is recognized by the power-law dependence of the specific heat C(T) given by the electronic contribution susceptibility X(T) and volume expansion coefficient α(T) at low temperatures: C/T ∝ X(T) ∝ α(T)/T∝ 1/ √T. We also demonstrate that the behavior of the normalized effective mass M _N ^* observed in CePd_1−x Rh _x at x ≃ 0.8 agrees with that of M _N ^* observed in paramagnetic CeRu₂Si₂ and conclude that these alloys exhibit the universal NFL thermodynamic behavior at their quantum critical points. We show that the NFL behavior of CePd_1−x Rh _x can be accounted for within the frameworks of the quasiparticle picture and fermion condensation quantum phase transition, while this alloy exhibits a universal thermodynamic NFL behavior that is independent of the characteristic features of the given alloy such as its lattice structure, magnetic ground state, dimension, etc. The text was submitted by the authors in English.     

Strongly correlated quantum spin liquid in herbertsmithite

Strongly correlated Fermi systems are among the most intriguing and fundamental systems in physics. We show that the herbertsmithite ZnCu₃(OH)₆Cl₂ can be regarded as a new type of strongly correlated electrical insulator that possesses properties of heavy-fermion metals with one exception: it resists the flow of electric charge. We demonstrate that herbertsmithite’s low-temperature properties are defined by a strongly correlated quantum spin liquid made with hypothetic particles such as fermionic spinons that carry spin 1/2 and no charge. Our calculations of its thermodynamic and relaxation properties are in good agreement with recent experimental facts and allow us to reveal their scaling behavior, which strongly resembles that observed in heavy-fermion metals. Analysis of the dynamic magnetic susceptibility of strongly correlated Fermi systems suggests that there exist at least two types of its scaling.