Entropy paradox in strongly correlated Fermi systems

Abstract

A system of interacting, identical fermions described by standard Landau Fermi-liquid (FL) theory can experience a rearrangement of its Fermi surface if the correlations grow sufficiently strong, as occurs at a quantum critical point where the effective mass diverges. As yet, this phenomenon defies full understanding, but salient aspects of the non-Fermi-liquid (NFL) behavior observed beyond the quantum critical point are still accessible within the general framework of the Landau quasiparticle picture. Self-consistent solutions of the coupled Landau equations for the quasiparticle momentum distribution $n(p)$ and quasiparticle energy spectrum $\epsilon (p)$ are shown to exist in two distinct classes, depending on coupling strength and on whether the quasiparticle interaction is regular or singular at zero momentum transfer. One class of solutions maintains the idempotency condition $n^2(p)=n(p)$ of standard FL theory at zero temperature $T$ while adding pockets to the Fermi surface. The other solutions are characterized by a swelling of the Fermi surface and a flattening of the spectrum $\epsilon (p)$ over a range of momenta in which the quasiparticle occupancies lie between 0 and 1 even at T=0. The latter, non-idempotent solution is revealed by analysis of a Poincaré mapping associated with the fundamental Landau equation connecting $n(p)$ and $\epsilon (p)$ and validated by solution of a variational condition that yields the symmetry-preserving ground state. Paradoxically, this extraordinary solution carries the burden of a large temperature-dependent excess entropy down to very low temperatures, threatening violation of the Nernst Theorem. It is argued that certain low-temperature phase transitions offer effective mechanisms for shedding the entropy excess. Available measurements in heavy-fermion compounds provide concrete support for such a scenario.

34 pages, 6 figures

References in corpus (9)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Quantum Criticality in Heavy Fermion Metals
• Multiple energy scales at a quantum critical point
• Scaling Behavior of Heavy Fermion Metals
• Flat band in the core of topological defects: bulk-vortex correspondence in topological superfluids with Fermi points
• Curie law, entropy excess, and superconductivity in heavy fermion metals and other strongly interacting Fermi liquids
• Violation of critical universality at the antiferromagnetic phase transition of YbRh2Si2
• Adaptation of the Landau-Migdal Quasiparticle Pattern to Strongly Correlated Fermi Systems
• Merging of single-particle levels and non-Fermi-liquid behavior of finite Fermi systems

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