This report is devoted to the building of the theory and analyzing the phenomenon which take place in such strong correlated Fermi systems as High temperature superconductors, metals with heavy fermions and quasi two dimensional Fermi-systems. The described theory of strong correlated Fermi systems bases on conceptions of Fermi condensate quantum phase transition (FCQPT) and Fermi condensate. It develops the well known Landau paradigm based on quasi particles formalism and order parameter. The description of the FCQPT theory is followed by its verification on the different exactly solvable models, by numerical calculations and by comparing with wide collection of experimental data.
This report is devoted to the building of the theory and analyzing the phenomenon which take place in such strong correlated Fermi systems as High temperature superconductors, metals with heavy fermions and quasi two dimensional Fermi-systems. The described theory of strong correlated Fermi systems bases on conceptions of Fermi condensate quantum phase transition (FCQPT) and Fermi condensate. It develops the well known Landau paradigm based on quasi particles formalism and order parameter. The description of the FCQPT theory is followed by its verification on the different exactly solvable models, by numerical calculations and by comparing with wide collection of experimental data.
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 E 0, which is of the order of the superconducting gap. The same quasiparticle picture and the energy scale E 0 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∗∝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.
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.
Strongly correlated Fermi systems are among the most intriguing, best experimentally studied and fundamental systems in physics. There is, however, lack of theoretical understanding in this field of physics. The ideas based on the concepts like Kondo lattice and involving quantum and thermal fluctuations at a quantum critical point have been used to explain the unusual physics. Alas, being suggested to describe one property, these approaches fail to explain the others. This means a real crisis in theory suggesting that there is a hidden fundamental law of nature. It turns out that the hidden fundamental law is well forgotten old one directly related to the Landau-Migdal quasiparticles, while the basic properties and the scaling behavior of the strongly correlated systems can be described within the framework of the fermion condensation quantum phase transition (FCQPT). The phase transition comprises the extended quasiparticle paradigm that allows us to explain the non-Fermi liquid (NFL) behavior observed in these systems. In contrast to the Landau paradigm stating that the quasiparticle effective mass is a constant, the effective mass of new quasiparticles strongly depends on temperature, magnetic field, pressure, and other parameters. Our observations are in good agreement with experimental facts and show that FCQPT is responsible for the observed NFL behavior and quasiparticles survive both high temperatures and high magnetic fields.
The behavior of Fermi systems which 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 − xFC | where x is the system density and xFC is the critical point at which FCQPT occurs. Such a behavior is of general form and takes place in both three dimensional (3D) systems and two dimensional (2D) ones. Since the effective mass M ∗ is finite, the system exhibits the Landau Fermi liquid behavior. At |x −xFC|/xFC ≪ 1, the behavior can be viewed as a highly correlated one, because the effective mass is large and strongly depends on the density. In case of electronic systems the Wiedemann-Franz law is held and Kadowaki-Woods ratio is preserved. Beyond the region |x−xFC|/xFC ≪ 1, the effective mass is approximately constant and the system becomes conventional Landau Fermi liquid.
This short review paper is devoted to 90th anniversary of S.T. Belyaev birthday. Belyaev’s ideas associated with the condensate state in Bose interacting systems have stimulated intensive studies of the possible manifestation of such a condensation in Fermi systems. In many Fermi systems and compounds at zero temperature a phase transition happens that leads to a quite specific state called fermion condensation. As a signal of such a fermion condensation quantum phase transition (FCQPT) serves unlimited increase of the effective mass of quasiparticles that determines the excitation spectrum and creates flat bands. We show that the class of Fermi liquids with the fermion condensate forms a new state of matter. We discuss the phase diagrams and the physical properties of systems located near that phase transition. A common and essential feature of such systems is quasiparticles different from those suggested by L.D. Landau by crucial dependence of their effective mass on temperature, external magnetic field, pressure, etc. It is demonstrated that a huge amount of experimental data collected on different compounds suggest that they, starting from some temperature and down, form the new state of matter, and are governed by the fermion condensation. Our discussion shows that the theory of fermion condensation develops completely good description of the NFL behavior of strongly correlated Fermi systems. Moreover, the fermion condensation can be considered as the universal reason for the NFL behavior observed in various HF metals, liquids, compounds with quantum spin liquids, and quasicrystals. We show that these systems exhibit universal scaling behavior of their thermodynamic properties. Therefore, the quantum critical physics of different strongly correlated compounds is universal, and emerges regardless of the underlying microscopic details of the compounds. This uniform behavior, governed by the universal quantum critical physics, allows us to view it as the main characteristic of the new state of matter.
In this brief overview, I address some of the fundamental topics related to the physics of strongly correlated fermions, which have been also the subject of my research. After addressing the question why the field has a fundamental meaning, we next turn to the specific problems with their simple theoretical description. Those topics are: (i) the concept of spindependent masses of heavy particles and its subsequent experimental verification; (ii) the correlated metal–insulator transitions of the Mott–Hubbardtype; (iii) real space pairing and its subsequent experimental verification for high-temperature superconducting cuprates. I mention also the persistence of quantum spin and charge excitations in the superconducting phase. All those phenomena confirm the view that the strongly correlated fermionic \nsystems represent a new class of quantum liquids, with some properties quantitatively different than those of the Landau Fermi liquids. Namely, they can be classified as those that fall in between those of the anomalous Landau Fermi liquid and localized-magnetic-moment system.