V. A. Khodel

New approach in the microscopic Fermi systems theory

Abstract A new version of the microscopic theory of non-relativistic Fermi systems based on functional relations between the ground state energy of a system and its linear response function is presented. A closed functional equation linking the effective interaction between particles in uniform matter with the two-particle interaction potential in vacuum is derived. This functional equation is free from any adjustable parameters. Having it in hand one can calculate the main properties of the system: the ground state energy, the collective spectrum, etc. Methods for approximate solution of this equation, viz., the gas and the local approximations, are analyzed. The capability of the approach is demonstrated on a number of model examples by comparing the calculated ground state energies with those of the solvable Hamiltonians or obtained with the help of the Monte Carlo simulation. The extension of the formalism to non-uniform and finite systems such as multi-electron atoms allowing for a new treatment of the density functional theory is performed. An analytical expression for the effective electron-electron interaction is derived. This interaction is of finite radius and density dependent. The microscopic theory of single-particle excitation spectra of homogeneous Fermi systems is developed. The new phenomenon of fermion condensation in systems with strongly repulsive interaction is considered. This phenomenon is shown to occur when the necessary stability condition of the normal ground-state quasi-particle distribution n F ( p ) = θ ( p F − p ) is violated and this distribution is rearranged. The presence of the fermion condensate is found to result in an essential enhancement of the density of states similar to that of a Bose liquid just below the λ-point. Various properties of systems with fermion condensate are studied within simple solvable models. The possibility of superfluid correlations in such systems is also investigated. The exponential BCS-smallness of the gap Δ in the single-particle excitation spectra of such systems is found to disappear, which yields a drastic elevation of the superfluid phase transition temperature T c .

Interplay between fermion condensation and density-wave instability

It is shown that the phase transition of density-wave origin in homogeneous liquids is preceded by fermion condensation. Thus fermion condensation may be observed in low-density electron liquids, neutron stars, and liquid He3. Three-dimensional (3D) and two-dimensional (2D) liquids are considered.

Two scenarios of the quantum critical point

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 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. Salient features of a different topological scenario of the QCP, associated with the emergence of bifurcation points in the equation ∈(p) = μ that ordinarily determines the Fermi momentum, are analyzed. The topological scenario of the QCP is applied to three-dimensional (3D) Fermi liquids with an attractive current-current interaction.

Critical experiments in the search for fermion condensation

The specific features of fermion condensation — a phase transition associated with the rearrangement of the one-particle degrees of freedom in strongly correlated Fermi systems — by which this phenomenon can be detected experimentally are discussed.

Quasiparticles in the theory of fermion condensation

It is shown that Landau’s quasiparticle formalism continues to work in systems with a fermion condensate. In the case of a finite system this formalism is suitable for describing the restructuring of states at the Fermi surface. It also works in an infinite system, and the idea of quasiparticles at low temperature as well-defined excitations at the Fermi surface remains valid. The quasiparticle lifetime is directly proportional to the temperature, and the density of states is inversely proportional to the temperature.

Low-temperature phase transitions in systems with fermion condensate

Phase transitions observed in electronic systems of solids in the vicinity of the quantum critical point where the effective mass diverges are analyzed within the framework of the theory of fermion condensation. It is shown that the disordered phase contains a fermion condensate. Its entropy is finite at T → 0 and initiates a chain of transitions occurring at extremely low temperatures. The results are in agreement with experiment.

Evolution of spin susceptibility from the pauli to Curie-Weiss type in strongly correlated Fermi systems

The magnetic properties of strongly correlated Fermi systems are studied within the framework of the fermioncondensation model—phase transition associated with the rearrangement of the Landau quasiparticle distribution, resulting in the appearance of a plateau at T=0 exactly in the Fermi surface of the single-particle excitation spectrum. It is shown that the Curie-Weiss term ∼T−1 appears in the expression for the spin susceptibility χac(T) of the system after the transition point at finite temperatures. The behavior of χac(T, H) as a function of temperature and static magnetic field H in the region where the critical fermion-condensation temperature Tf is close to zero is discussed. The results are compared with the available experimental data.

Mechanisms driving alteration of the Landau state in the vicinity of a second-order phase transition

The rearrangement of the Fermi surface of a homogeneous Fermi system upon approach to a second-order phase transition is studied at zero temperature. The analysis begins with an investigation of solutions of the equation (p) = μ, a condition that ordinarily has the Fermi momentum pF as a single root. The emergence of a bifurcation point in this equation is found to trigger a qualitative alteration of the Landau state, well before the collapse of the collective degree of freedom that is responsible for the second-order transition. The competition between mechanisms that drive rearrangement of the Landau quasiparticle distribution is explored, taking into account the feedback of the rearrangement on the spectrum of critical fluctuations. It is demonstrated that the transformation of the Landau state to a new ground state may be viewed as a first-order phase transition.

Phase diagram of strongly correlated Fermi systems

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.

Damping effects and the metal-insulator transition in a two-dimensional electron gas

The damping of single-particle degrees of freedom in strongly correlated two-dimensional Fermi systems is analyzed. Suppression of the scattering amplitude due to the damping effects is shown to play a key role in preserving the validity of the Landau-Migdal quasiparticle picture in a region of a phase transition, associated with the divergence of the quasiparticle effective mass. The results of the analysis are applied to elucidate the behavior of the conductivity