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RESEARCH PRODUCT

The Topological Phase Transitions Related to Fermion Condensate

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In this chapter, we consider so-called topological phase transitions, taking place in normal Fermi liquid. In other words, here we are dealing with different instabilities of normal Fermi liquids relative to several kinds of perturbations of initial quasiparticle spectrum \(\varepsilon (p)\) and occupation numbers \(n(p)\) 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 Landau Fermi liquid ground state. This restructuring generates topologically distinct phases. One of them is the FC discussed above, another one belongs to a class of topological transitions (TT) 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 melt down” and the behavior of the system becomes similar to that with the fermion condensate.