Topological Fermion-Condensation Quantum Phase Transition

Abstract

Here, we discuss the general properties of the topological fermion-condensation quantum phase transition (FCQPT) leading to the emergence of the fermion condensation (FC). Basing on the main results of Chap. 3, we continue to present a microscopic derivation of the main equations of FC and show that Fermi systems with FC form an entirely new class of Fermi liquids with its own topological structure, protecting the FC state. We construct the phase diagram, and explore the order parameter of these systems. We show that the fermion condensate has a strong impact on the observable physical properties of systems, where it is realized, up to relatively high temperatures of a few tens kelvin. Two different scenarios of the quantum-critical point (QCP), a zero-temperature instability of the Landau state, related to the divergence of the effective mass, are also briefly investigated. Flaws of the standard scenario of the QCP, where this divergence is attributed to the occurrence of some second-order phase transition, are demonstrated. We also consider other topological phase transitions, taking place in normal Fermi liquid. These are associated with the emergence of a multi-connected Fermi surface. Depending on the parameters and analytical properties of the Landau interaction, such instabilities lead to several possible types of restructuring of initial Fermi liquid ground state. This restructuring generates topologically distinct phases. One of them is the FC discussed above, and another one belongs to a class of topological transitions and will be called “iceberg” phase, where the sequence of rectangles (“icebergs”) \(n(p)=0\) and \(n(p)=1\) is realized at \(T=0\). At elevated temperatures the “icebergs meltdown” and the behavior of the system becomes similar to that with the fermion-condensate state.