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Contributions to Plasma Physics

Fermion Condensate as a New State of Matter

M. Ya. Amusia, Vasily R. Shaginyan

Published Dec 1, 2013• 9 citations
Publisher

Abstract

Abstract 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)

DOI
10.1002/ctpp.201310045

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Fermion condensate generates a new state of matter by making flat bands

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Abstract 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)
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.
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∗∝BT^ * \propto \sqrt B 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.
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.
Opportunities for topological phase transitions in strongly correlated Fermi systems near a quantum critical point are explored as an alternative to collective scenarios for experimentally observed departures from standard Fermi-liquid behavior. Attention is focused on a quantum critical point at which the effective mass is divergent due to vanishing of the quasiparticle group velocity at the Fermi surface. Working within the original Landau quasiparticle theory, it is demonstrated that the quasiparticle picture can remain meaningful beyond the quantum critical point through rearrangements of the unstable normal Fermi surface and quasiparticle spectrum. Two possibilities emerge at zero temperature, depending on whether the quasiparticle interaction is regular or singular at zero momentum transfer. In the regular case, one type of topological phase transformation leads to a state with a multiconnected Fermi surface. In the singular case, another type of topological phase transition leads to an exceptional state containing a fermion condensate – the Fermi surface swells into a volume in momentum space, within which partial occupation prevails and quasiparticle energies are pinned to the chemical potential. As the temperature increases from zero to a characteristic value Tm, a crossover can occur from the state with multiple Fermi surfaces to that containing a fermion condensate.
A model of a Fermi liquid with the fermion condensate (FC) is applied to the consideration of quasiparticle excitations in high-temperature superconductors, in their superconducting and normal states. Within our model the appearance of the fermion condensate presents a quantum phase transition that separates the regions of normal and strongly correlated electron liquids. Beyond the phase transition point the quasiparticle system is divided into two subsystems, one containing normal quasiparticles and the other---fermion condensate localized at the Fermi surface and characterized by almost dispersionless single-particle excitations. In the superconducting state the quasiparticle dispersion in systems with FC can be presented by two straight lines, characterized by effective masses MFC∗{M}_{\mathrm{FC}}^{*}MFC∗​ and ML∗,{M}_{L}^{*},ML∗​, respectively, and intersecting near the binding energy, which is of the order of the superconducting gap. This same quasiparticle picture persists in the normal state, thus manifesting itself over a wide range of temperatures as new energy scales. Arguments are presented that fermion systems with FC have features of a ``quantum protectorate'' [R. B. Laughlin and D. Pines, Proc. Natl. Acad. Sci. U.S.A. 97, 28 (2000); P. W. Anderson, cond-mat/0007185 (unpublished); cond-mat/0007287 (unpublished)].
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.