Theories of non-Fermi liquid behavior in heavy fermions (original) (raw)

Origin of non-Fermi liquid behavior in heavy fermion systems: A conceptual view

We critically examine the non-Fermi liquid (NFL) behavior observed in heavy fermion systems located close to a magnetic instability and suggest a conceptual advance in physics in order to explain its origin. We argue that the treatment of electronic states responsible for magnetism near the Quantum Critical Point (QCP), should not be accomplished within the quantum mechanical formalism; instead they should be treated semi-classically. The observed NFL behavior can be explained within such a scenario. As a sequel we attempt to discuss its consequences for the explanation of high-TC superconductivity observed in Cuprates.

Weak magnetism and non-Fermi liquids near heavy-fermion critical points

Physical Review B, 2004

This paper is concerned with the weak-moment magnetism in heavy-fermion materials and its relation to the non-Fermi liquid physics observed near the transition to the Fermi liquid. We explore the hypothesis that the primary fluctuations responsible for the non-Fermi liquid physics are those associated with the destruction of the large Fermi surface of the Fermi liquid. Magnetism is suggested to be a low-energy instability of the resulting small Fermi surface state. A concrete realization of this picture is provided by a fractionalized Fermi liquid state which has a small Fermi surface of conduction electrons, but also has other exotic excitations with interactions described by a gauge theory in its deconfined phase. Of particular interest is a three-dimensional fractionalized Fermi liquid with a spinon Fermi surface and a U(1) gauge structure. A direct second-order transition from this state to the conventional Fermi liquid is possible and involves a jump in the electron Fermi surface volume. The critical point displays non-Fermi liquid behavior. A magnetic phase may develop from a spin density wave instability of the spinon Fermi surface. This exotic magnetic metal may have a weak ordered moment although the local moments do not participate in the Fermi surface. Experimental signatures of this phase and implications for heavy-fermion systems are discussed.

Fermi Liquid Near a Quantum Critical Point

Journal of Low Temperature Physics, 2007

We investigate the approach to the quantum critical point of a Pomeranchuk instability from the symmetric, disordered side of the phase diagram. In the low-temperature limit, a Fermi liquid description of the metal is possible and becomes exact for T → 0. We discuss in detail which features of the approach to quantum criticality can be captured within Fermi liquid theory and which are outside of its scope.

Strong coupling theory of heavy fermion criticality

2013

We present a theory of the scaling behavior of the thermodynamic, transport and dynamical properties of a three-dimensional metal at an antiferromagnetic critical point. We show how the critical spin fluctuations at the AFM wavevector q=Q induce energy fluctuations at small q, giving rise to a diverging quasiparticle effective mass over the whole Fermi surface. The coupling of the fermionic and bosonic degrees of freedom leads to a self-consistent relation for the effective mass, which has a strong coupling solution in addition to the well-known weak-coupling, spin-density-wave solution. We thereby use the recently-introduced concept of critical quasiparticles, employing a scale-dependent effective mass ratio m*/m and quasiparticle weight factor Z. As a consequence of the diverging effective mass the Landau Fermi liquid interaction is found to diverge in all channels except the critical one, causing important vertex corrections. The ensuing spin fluctuation spectrum obeys omega/T sc...

Heavy Fermions and Quantum Phase Transitions

Science, 2010

From Simplicity to Complexity The relatively simple properties of isolated electrons become rich and complex when the particle-particle interactions are strong enough to form a correlated system. Emergence of complex behavior from relatively simple subunits is an intensely studied topic in condensed-matter physics and applies to many systems in superconductivity and magnetism. Si and Steglich (p. 1161 ) review the physics of heavy fermion intermetallic compounds. These make ideal materials for study because they can exhibit metallic, magnetic, and superconducting behavior showing novel quantum phases and unconventional quantum criticality.

Nonperturbative behavior of the quantum phase transition to a nematic Fermi fluid

Physical Review B, 2006

We discuss shape (Pomeranchuk) instabilities of the Fermi surface of a two-dimensional Fermi system using bosonization. We consider in detail the quantum critical behavior of the transition of a two dimensional Fermi fluid to a nematic state which breaks spontaneously the rotational invariance of the Fermi liquid. We show that higher dimensional bosonization reproduces the quantum critical behavior expected from the Hertz-Millis analysis, and verify that this theory has dynamic critical exponent z = 3. Going beyond this framework, we study the behavior of the fermion degrees of freedom directly, and show that at quantum criticality as well as in the the quantum nematic phase (except along a set of measure zero of symmetry-dictated directions) the quasi-particles of the normal Fermi liquid are generally wiped out. Instead, they exhibit short ranged spatial correlations that decay faster than any power-law, with the law |x| −1 exp(−const. |x| 1/3 ) and we verify explicitely the vanishing of the fermion residue utilizing this expression. In contrast, the fermion auto-correlation function has the behavior |t| −1 exp(−const. |t| −2/3 ). In this regime we also find that, at low frequency, the single-particle fermion density-of-states behaves as N * (ω) = N * (0) + B ω 2/3 log ω + . . ., where N * (0) is larger than the free Fermi value, N (0), and B is a constant. These results confirm the non-Fermi liquid nature of both the quantum critical theory and of the nematic phase.

Critical phenomena near the antiferromagnetic quantum critical point of heavy fermions

Physical Review B, 2000

We present a study of the critical phenomena around the quantum critical point in heavy-fermion systems. In the framework of the S = 1/2 Kondo lattice model, we introduce an extended decoupling scheme of the Kondo interaction which allows one to treat the spin fluctuations and the Kondo effect on an equal footing. The calculations, developed in a self-consistent oneloop approximation, lead to the formation of a damped collective mode with a dynamic exponent z = 2 in the case of an antiferromagnetic instability. The system displays a quantum-classical crossover at finite temperature depending how the energy of the mode, on the scale of the magnetic correlation length, compares to k B T. The low temperature behavior, in the different regimes separated by the crossover temperatures, is then discussed for both 2-and 3-dimensional systems.

Breakdown of Fermi liquid in correlated electron systems

Physica A: Statistical Mechanics and its Applications, 1999

The standard description of metals is based on the Landau theory of Fermi systems (Fermi Liquid theory). This picture breaks down in one dimensional systems, which are instead described by the Luttinger Liquid theory. Actually, experimental evidence indicates that Fermi Liquid theory breaks down in a variety of physical systems, including superconducting cuprates.

How do Fermi liquids get heavy and die?

Journal of Physics: Condensed Matter, 2001

We discuss non-Fermi liquid and quantum critical behavior in heavy fermion materials, focussing on the mechanism by which the electron mass appears to diverge at the quantum critical point. We ask whether the basic mechanism for the transformation involves electron diffraction off a quantum critical spin density wave, or whether a breakdown in the composite nature of the heavy electron takes place at the quantum critical point. We show that the Hall constant changes continously in the first scenario, but may "jump" discontinuously at a quantum critical point where the composite character of the electron quasiparticles changes.