Locally critical quantum phase transitions in strongly correlated metals

Abstract

When a metal undergoes a continuous quantum phase transition, non-Fermi liquid behaviour arises near the critical point. It is standard to assume that all low-energy degrees of freedom induced by quantum criticality are spatially extended, corresponding to long-wavelength fluctuations of the order parameter.However, this picture has been contradicted by recent experiments on a prototype system: heavy fermion metals at a zero-temperature magnetic transition.In particular, neutron scattering from CeCu 6−x Au x has revealed anomalous dynamics at atomic length scales, leading to much debate as to the fate of the local moments in the quantum-critical regime. Here we report our theoretical finding of a locally critical quantum phase transition in a model of heavy fermions. The dynamics at the critical point are in agreement with experiment. We also argue that local criticality is a phenomenon of general relevance to strongly correlated metals, including doped Mott insulators.Quantum (zero-temperature) phase transitions are ubiquitous in strongly correlated metals; for a recent review, see ref.1. The extensive current interest in metals close to a secondorder quantum phase transition has stemmed largely from studies of high-temperature superconductors. In these systems, however, it has been hard to actually locate the putative quantum critical points (QCPs). The situation appears to be simpler in some related families of strongly correlated metals. In particular, there are many heavy fermion metals which can be tuned between an antiferromagnetic (AF) metal and a paramagnetic metal. In recent years QCPs have been explicitly identified in a number of stoichiometric or nearly stoi-1

Scaling of the magnetic entropy and magnetization in

“…It indicates that the characteristic energy of the heavy quasiparticles is governed only by the ratio of the thermal energy to the magnetic field increment b and vanishes upon approaching the QCP. Such a behavior is consistent with the locally-critical scenario for an AF QCP, at which the heavy quasiparticles disintegrate [2,3].…”

Band-structure and anomalous contributions to the Hall effect of YbRh2Si2

“…T N is found to be continuously suppressed with small magnetic fields to T ¼ 0 accessing the quantum critical point (QCP) [2]. The QCP in YbRh 2 Si 2 is best described by the local scenario [3]. This is mainly supported by earlier Hall effect studies [4] in which the Hall effect of YbRh 2 Si 2 was measured while tuning the material through the QCP.…”

Magnetic structure of the antiferromagnetic Kondo lattice compounds CeRhAl4Si2 and CeIrAl4Si2

“…Apart from this prototypical QCP scenario [15,16,17], so-called local quantum criticality has been proposed for the case that the Kondo temperature is suppressed to zero at the QCP, resulting in local critical fluctuations associated with the Fermi surface. In this scenario, the Fermi surface is large on one side of the QCP because it includes the delocalized f -electrons, and is small on the other because the f -elctrons are localized and do not contribute to the Fermi volume [3]. Recent calculations suggest that the type of QCP may be controlled via the dimensionality of the system [6,7].…”

“…In f -electron materials, where magnetic and electronic degrees of freedom are typically strongly coupled, the effects of dimensionality are currently under debate [3,4,5]. Notably, it has been proposed that dimension can be used to tune the type of observed quantum phase transitions, where either the electronic or magnetic degrees of freedom become quantum critical [3,6,7].…”