Chapter 6: The Fermi Liquid

Physical Review Letters, 2009

We find that the heat capacity of a strongly correlated metal presents striking changes with respect to Landau Fermi liquid theory. In contrast with normal metals, where the electronic specific heat is linear at low temperature (with a T 3 term as a leading correction), a dynamical mean-field study of the correlated Hubbard model reveals a clear kink in the temperature dependence, marking a rapid change from a low-temperature linear behavior and a second linear regime with a reduced slope. Experiments on LiV2O4 support our findings, implying that correlated materials are more resistive to cooling at low T than expected from the intermediate temperature behavior.

2019

In this paper we are going to briefly review the Fermi liquid theory, which was firstly introduced as a generalization of Fermi gas theory and to explain the behaviour of He. Afterward, we are going through its application for a weakly-interacting metal. At the end we briefly increase the horizon by discussing breakdowns of the theory, and introducing non-Fermi liquid theories, as theories for strange metals.

Nature, 2008

For the past half century, our understanding of how the interactions between electrons affect the low-temperature properties of metals has been based on the Landau theory of a Fermi liquid 1 . In recent times, however, there have been an increasingly large number of examples in which the predictions of the Fermi-liquid theory appear to be violated 2 . Although the qualitative reasons for the breakdown are generally understood, the specific quantum states that replace the Fermi liquid remain in many cases unclear. Here we describe an example of such a breakdown where the non-Fermi-liquid properties can be interpreted. We show that the thermal and electrical resistivities in high-purity samples of the d-electron metal ZrZn 2 at low temperatures have T and T 5/3 temperature dependences, respectively: these are the signatures of the 'marginal' Fermi-liquid state 3-7 , expected to arise from effective long-range spin-spin interactions in a metal on the border of metallic ferromagnetism in three dimensions 3,5 . The marginal Fermi liquid provides a link between the conventional Fermi liquid and more exotic non-Fermi-liquid states that are of growing interest in condensed matter physics. The idea of a marginal Fermi liquid has also arisen in other contextsfor example, in the phenomenology of the normal state of the copper oxide superconductors 7 , and in studies of relativistic plasmas and of nuclear matter 3,4,6 .

As an example we consider a Na atom, which has an electron configuration of (1s) 2 (2s) 2 (2p) 6 (3s) 1. The 3s electrons in the outermost shell becomes conduction electrons and moves freely through the whole system. The simplest model for the conduction electrons is a free electron Fermi gas model. In real metals, there are interactions between electrons. The motion of electrons is also influenced by a periodic potential caused by ions located on the lattice. Nevertheless, this model is appropriate for simple metals such as alkali metals and noble metals. When the Schrödinger equation is solved for one electron in a box, a set of energy levels are obtained which are quantized. When we have a large number of electrons, we fill in the energy levels starting at the bottom. Electrons are fermions, obeying the Fermi-Dirac statistics. So we have to take into account the Pauli's exclusion principle. This law prohibits the occupation of the same state by more than two electrons. Sommerfeld's involvement with the quantum electron theory of metals began in the spring of 1927. Pauli showed Sommerfeld the proofs of his paper on paramagnetism. Sommerfeld was very impressed by it. He realized that the specific heat dilemma of the Drude-Lorentz theory could be overcome by using the Fermi-Dirac statistics (Hoddeeson et al.). 1 Here we discuss the specific heat and Pauli paramagnetism of free electron Fermi gas model. The Sommerfeld's formula are derived using Mathematica. The temperature dependence of the chemical potential will be discussed for the 3D and 1D cases. We also show how to calculate numerically the physical quantities related to the specific heat and Pauli paramagnetism by using Mathematica, based on the physic constants given by

Physical Review B, 1986

The frequency renormalization parameter of the generalized nonlinear o model introduced to describe the interacting disordered electron system is identified in terms of the specific heat. This allows us to complete the effective Landau Fermi-liquid picture for this system and to give the asymptotic behavior of the electronic specific heat in the various universality classes of the metalinsulator transition.

Atoms

This review considers the topological fermion condensation quantum phase transition (FCQPT) that leads to flat bands and allows the elucidation of the special behavior of heavy-fermion (HF) metals that is not exhibited by common metals described within the framework of the Landau Fermi liquid (LFL) theory. We bring together theoretical consideration within the framework of the fermion condensation theory based on the FCQPT with experimental data collected on HF metals. We show that very different HF metals demonstrate universal behavior induced by the FCQPT and demonstrate that Fermi systems near the FCQPT are controlled by the Fermi quasiparticles with the effective mass M* strongly depending on temperature T, magnetic field B, pressure P, etc. Within the framework of our analysis, the experimental data regarding the thermodynamic, transport and relaxation properties of HF metal are naturally described. Based on the theory, we explain a number of experimental data and show that the...

2015

Abstract-Two different ways of computing the time between collisions related to the electrical conductivity of metals are presented. The combination of them leads to the formula for the Fermi energy of metals. The Fermi energy of metals is usually determined by considering the conduction electrons as free particles living in a box, where the occupancy of the energy levels is done by taking in account the Pauli exclusion principle, reflecting the fermionic character of the charge carriers [1,2,3]. The process also

2000

General expressions for the contributions of the Van Hove singularity (VHS) in the electron density of states to the thermodynamic potential Ω are obtained in the framework of a microscopic Fermi liquid theory. The renormalization of the singularities in Ω connected with the Lifshitz electronic topological transition (ETT) is found. Screening anomalies due to virtual transitions between VHS and the Fermi level are considered. It is shown that, in contrast with the one-particle picture of ETT, the singularity in Ω turns out to be two-sided for interacting electrons.

Solid State Communications, 1978

The electrical resistance of Li, Pd, Au, and Pb is measured as a function of temperature and pressure in the region-20'C to + 30'C and 0-1.3 GPa. Self-consistent linear muffin-tin orbital band-structure calculations of these elements and of Al are performed at normal and reduced volumes. Results are obtained for the density of states N (EF), the average Fermi velocity, the optical mass, the plasma frequency co, and the volume dependence of these parameters. The pressure dependence of the electron-phonon interaction A, (p) is obtained from these measurements and the calculated co(p). For the superconducting elements there is good agreement with the measured superconducting T,(p). Results from our previous measurements and calculations on Al, V, Nb, and La and published results for co(p) are included in this comparison. A, (p) increases with pressure for bcc Li and decreases for Pd and Au. Pressure is expected to suppress spin fluctuations much faster than A, (p) in Pd. The possibility of inducing superconductivity by pressure in Pd and bcc Li is discussed. The electronic Gruneisen parameter y, is obtained from A, (p) and the volume dependence of N(EF). Comparison with other results for y, generally shows good agreement. the measurements are described and the results are presented and analyzed. The band-structure calculation is described in Sec. IV. We obtain results for the volume dependence of the plasma frequency and some other average Fermi-surface properties, i.e. , the Fermi velocity, the optical mass, and the density of states N(Ez). The results for A, (p) are presented and discussed in Sec. V. Having obtained the volume dependence of N(EF) as well as A, , it is useful to compare them with the electronic Gruneisen parameter y,. This is briefly discussed in Sec. VI. The main conclusions are summarized in Sec. VII.

Aimed at graduate students and researchers, this book covers the key aspects of the modern quantum theory of solids, including up-to-date ideas such as quantum fluctuations and strong electron correlations. It presents the main concepts of the modern quantum theory of solids, as well as a general description of the essential theoretical methods required when working with these systems.