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

Abstract

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. It is demonstrated that a huge amount of experimental data collected on different compounds suggests 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.

17 Figures, 16 pages. Our review paper is dedicated to S. T. Belyaev on the occasion of his 90th birthday

References in corpus (15)

• Fractionalized excitations in the spin liquid state of a kagomé lattice antiferromagnet
• Quantum critical state in a magnetic quasicrystal
• Multiple energy scales at a quantum critical point
• The magnetic groundstate of an experimental $S=1/2$ kagomé antiferromagnet
• ^{63}Cu, ^{35}Cl, and ^{1}H NMR in the S=1/2 Kagomé Lattice ZnCu_{3}(OH)_{6}Cl_{2}
• Dynamic Scaling in the Susceptibility of the Spin-1\2 Kagome Lattice Antiferromagnet Herbertsmithite
• Scaling Behavior of Heavy Fermion Metals
• Curie law, entropy excess, and superconductivity in heavy fermion metals and other strongly interacting Fermi liquids
• Anomalous scaling behavior of the dynamical spin susceptibility of Ce${}_{0.925}$La${}_{0.075}$Ru${}_2$Si${}_2$
• Scaling in Dynamic Susceptibility of Herbertsmithite and Heavy-Fermion Metals
• Strongly correlated Fermi-systems: non-Fermi liquid behavior, quasiparticle effective mass and their interplay
• Spiky density of states in large complex Al-Mn phases
• Magnetization study of the energy scales in YbRh${}_2$Si${}_2$ under chemical pressure
• Nature of the quantum critical point as disclosed by extraordinary behavior of magnetotransport and the Lorentz number in the heavy-fermion metal YbRh2Si2
• Energy scales and the non-Fermi liquid behavior in YbRh2Si2