Fermi-liquid regime of the mesoscopic Kondo problem

Physics Letters A, 2000

A scaling consideration of the Kondo lattices is performed with account of singularities in the spin excitation spectral Ž . function. It is shown that a non-Fermi-liquid NFL behaviour occurs naturally for complicated magnetic structures with several magnon branches. This may explain the fact that a NFL behaviour often takes place in the heavy-fermion systems with peculiar spin dynamics. The mechanisms proposed lead to some predictions about behaviour of specific heat, resistivity, magnetic susceptibility and anisotropy parameter, which can be verified experimentally. q 2000 Published by Elsevier Science B.V. All rights reserved. PACS: 75.30.Mb; 71.28 0375-9601r00r$ -see front matter q 2000 Published by Elsevier Science B.V. All rights reserved.

Physics of Atomic Nuclei, 2011

Strongly correlated Fermi systems are among the most intriguing, best experimentally studied and fundamental systems in physics. There is, however, lack of theoretical understanding in this field of physics. The ideas based on the concepts like Kondo lattice and involving quantum and thermal fluctuations at a quantum critical point have been used to explain the unusual physics. Alas, being suggested to describe one property, these approaches fail to explain the others. This means a real crisis in theory suggesting that there is a hidden fundamental law of nature. It turns out that the hidden fundamental law is well forgotten old one directly related to the Landau Migdal quasiparticles, while the basic properties and the scaling behavior of the strongly correlated systems can be described within the framework of the fermion condensation quantum phase transition (FCQPT). The phase transition comprises the extended quasiparticle paradigm that allows us to explain the non-Fermi liquid (NFL) behavior observed in these systems. In contrast to the Landau paradigm stating that the quasiparticle effective mass is a constant, the effective mass of new quasiparticles strongly depends on temperature, magnetic field, pressure, and other parameters. Our observations are in good agreement with experimental facts and show that FCQPT is responsible for the observed NFL behavior and quasiparticles survive both high temperatures and high magnetic fields.

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.

Physical Review B, 2013

We extend the Fermi-liquid (FL) theory to include spin-orbit (SO) splitting of the energy bands, focusing on the Rashba SO coupling as an example. We construct the phenomenological Landau interaction function for such a system using the symmetry arguments and verify this construction by an explicit perturbative calculation. The Landau function is used to obtain the effective mass, compressibility, and stability conditions of the FL. It is shown that although the charge-sector properties, such as the effective mass and compressibility, are determined solely by well-defined quasiparticles, the spin-sector properties, such as the spin susceptibility, contain a contribution from damped states in between the spin-split Fermi surfaces, and thus cannot be fully described by the FL theory, except for the case of weak SO coupling. We derive some specific properties of a chiral FL and show, in particular, that for contact interaction spin-splitting of the Fermi velocities of Rashba subbands occurs because of the Kohn anomaly, also modified by SO coupling.

Journal of the Physical Society of Japan, 1999

Entanglement of spin and orbital Kondo effect is investigated on the basis of a Kondo-type exchange model with twofold orbital degeneracy. By using Wilson's numerical renormalizationgroup method, we examine dynamical and thermal properties respecting the difference in timereversal property of multipole operators. In the presence of particle-hole symmetry, the model has a new non-Fermi-liquid fixed point with a fractional entropy. The spectral intensity of the quadrupole susceptibility diverges in the zero-frequency limit, while the dipole susceptibility shows a Fermi-liquid-like behavior. This is understood by mapping to the two-channel Kondo model, in which the dipole moment is mapped onto the operators with the scaling dimension ∆m = 1, while the quadrupole moment onto the operators with another scaling dimension ∆e = 1/2. Even for a fairly particle-hole asymmetric case with the Fermi-liquid ground state, the non-Fermi-liquid behavior has significant influences in electric and thermal properties.

Nature Communications, 2019

Kondo insulators are expected to transform into metals under a sufficiently strong magnetic field. The closure of the insulating gap stems from the coupling of a magnetic field to the electron spin, yet the required strength of the magnetic field–typically of order 100 T–means that very little is known about this insulator-metal transition. Here we show that Ce$${}_{3}$$ 3 Bi$${}_{4}$$ 4 Pd$${}_{3}$$ 3 , owing to its fortuitously small gap, provides an ideal Kondo insulator for this investigation. A metallic Fermi liquid state is established above a critical magnetic field of only $${B}_{{\rm{c}}}\approx$$ B c ≈ 11 T. A peak in the strength of electronic correlations near $${B}_{{\rm{c}}}$$ B c , which is evident in transport and susceptibility measurements, suggests that Ce$${}_{3}$$ 3 Bi$${}_{4}$$ 4 Pd$${}_{3}$$ 3 may exhibit quantum criticality analogous to that reported in Kondo insulators under pressure. Metamagnetism and the breakdown of the Kondo coupling are also discussed.

Physical Review Letters

Many correlated metallic materials are described by Landau Fermi-liquid theory at low energies, but for Hund metals the Fermi-liquid coherence scale TFL is found to be surprisingly small. In this Letter, we study the simplest impurity model relevant for Hund metals, the three-channel spinorbital Kondo model, using the numerical renormalization group (NRG) method and compute its global phase diagram. In this framework, TFL becomes arbitrarily small close to two new quantum critical points (QCPs) which we identify by tuning the spin or spin-orbital Kondo couplings into the ferromagnetic regimes. We find quantum phase transitions to a singular Fermi-liquid or a novel non-Fermi-liquid phase. The new non-Fermi-liquid phase shows frustrated behavior involving alternating overscreenings in spin and orbital sectors, with universal power laws in the spin (ω −1/5), orbital (ω 1/5) and spin-orbital (ω 1) dynamical susceptibilities. These power laws, and the NRG eigenlevel spectra, can be fully understood using conformal field theory arguments, which also clarify the nature of the non-Fermi-liquid phase.

Physica C: Superconductivity, 1991

We propose a microscopic justification for the recently proposed "marginal Fermi-liquid" (MFL) phenomenology of the high Te materials. In some models, and for sufficiently strong interactions, excitonic charge and spin modes between quasi-coherent one-particle states at the chemical potential and high-energy incoherent one-particle states which are the residual of the Hubbard bands of the insulating phase gives rise to singularities in certain low energy scattering amplitudes. The resulting new phase has the MFL polarizabilities. The one-particle spectrum near the chemical potential is predicted to be the sum of the quasi-coherent MFL spectrum and of an incoherent contribution.

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 .