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Journal of Experimental and Theoretical Physics Letters

Phase diagram of strongly correlated Fermi systems

MIKHAIL V. ZVEREV, VICTOR A. KHODEL, M. Baldo

Published Aug 1, 2000• 5 citations
Publisher

Abstract

Phase transitions caused by the redistribution of quasiparticle occupation numbers n(p) in homogeneous Fermi systems with particle repulsion are analyzed. The phase diagram of a strongly correlated Fermi system, when drawn in the coordinates “density ρ-dimensionless coupling constant η,” resembles a Washington pie for a rather broad class of interactions. Its upper part is “filled” with Fermi condensate, and the bottom part is filled with normal Fermi liquid. Both parts are separated by a narrow interlayer of Lifshitz phase with a multiply connected Fermi surface.

DOI
10.1134/1.1316814

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Phase transitions caused by the redistribution of quasiparticle occupation numbers n(p) in homogeneous Fermi systems with particle repulsion are analyzed. The phase diagram of a strongly correlated Fermi system, when drawn in the coordinates “density ρ-dimensionless coupling constant η,” resembles a Washington pie for a rather broad class of interactions. Its upper part is “filled” with Fermi condensate, and the bottom part is filled with normal Fermi liquid. Both parts are separated by a narrow interlayer of Lifshitz phase with a multiply connected Fermi surface.
A quasiparticle pattern advanced in Landau’s first article on Fermi-liquid theory is adapted to elucidate the properties of a class of strongly correlated Fermi systems characterized by a Lifshitz phase diagram featuring a quantum critical point (QCP) where the density of states diverges. The necessary condition for stability of the Landau Fermi-Liquid state is shown to break down in such systems, triggering a cascade of topological phase transitions that lead, without symmetry violation, to states with multi-connected Fermi surfaces. The end point of this evolution is found to be an exceptional state whose spectrum of single-particle excitations exhibits a completely flat portion at zero temperature. Analysis of the evolution of the temperature dependence of the single-particle spectrum yields results that provide a natural explanation of classical behavior of this class of Fermi systems in the QCP region.
A quantum phase transition in strongly correlated Fermi systems beyond the topological quantum critical point has been studied using the Fermi liquid approach. The transition takes place between topologically equivalent states with three Fermi surface sheets, but one of them is characterized by a quasiparticle halo in the quasiparticle momentum distribution n ( p ), and the other one is characterized by a hole pocket. It has been found that the transition between these states is a first-order phase transition for the interaction constant g and temperature T . The phase diagram in the vicinity of this transition has been constructed.
Modern condensed matter physics owes much of its success to Fermi liquid theory. In recent times, however, the study of strongly correlated particle systems is opening up all-new territory in many-body physics. A peculiar class of such systems, that of nodal fermions, is characterized by the quasiparticle density of states vanishing at the point-like Fermi surface and long-range inter-particle interactions surviving unscreened. In the first part, I discuss fermion pairing in one such system, 2D graphene. By solving the gap equation for the excitonic order parameter, I obtain values of critical interaction strength for a variety of power-law interactions and densities of states. Furthermore, these results are then used to compute the respective free energies and analyze possible phase transitions. In the second part, I discuss the effects of lattice disorder and impurities on the density of states in nodal fermion systems. These results and predictions will be of interest to a broad range of physical problems involving nodal fermions, and can be tested in a variety of experimental directions.
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)].
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 topological crossover, associated with the collapse of the Fermi surface in strongly correlated Fermi systems, is examined. It is demonstrated that in these systems, the temperature domain where standard Fermi liquid results hold dramatically narrows, because the Landau regime is replaced by a classical one. The impact of the collapse of the Fermi surface on pairing correlations is analyzed. In the domain of the Lifshitz phase diagram where the Fermi surface collapses, splitting of the BCS superconducting phase transition into two different ones of the same symmetry is shown to occur.