Quantum criticality describes the collective fluctuations of matter undergoing a second-order phase transition at zero temperature. Heavy fermion metals have in recent years emerged as prototypical systems to study quantum critical points.There have been considerable efforts, both experimental and theoretical, which use these magnetic systems to address problems that are central to the broad understanding of strongly correlated quantum matter. Here, we summarize some of the basic issues, including i) the extent to which the quantum criticality in heavy fermion metals goes beyond the standard theory of order-parameter fluctuations, ii) the nature of the Kondo effect in the quantum critical regime, iii) the non-Fermi liquid phenomena that accompany quantum criticality, and iv) the interplay between quantum criticality and unconventional superconductivity.In the classical world, matter in equilibrium freezes at absolute zero temperature. A macroscopic collection of microscopic particles adopt a stationary arrangement, forming an ordered pattern, to minimize the potential energy. Quantum mechanics, on the other hand, allows fluctuations even at zero temperature. The effective strength of such zero-point motion can be tuned through the variation of a non-thermal control parameter, such as applied pressure. When such quantum fluctuations become sufficiently strong, the system undergoes a quantum phase transition to a new ground state.As simple as this sounds, quantum phase transitions are not easy to achieve. Consider, for example, the case of ice. Anybody who has skated would appreciate the fact that the melting temperature of ice is reduced by pressure. If the melting temperature were forced to vanish at a sufficiently high pressure, a quantum phase transition would take place at this pressure. However, applying pressure larger than about 0.2 GPa to ice actually makes the melting temperature go up again.

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

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 break-down 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.

We consider the iron pnictides in terms of a proximity to a Mott insulator. The superexchange interactions contain competing nearest-neighbor and next-nearest-neighbor components. In the undoped parent compound, these frustrated interactions lead to a two-sublattice collinear antiferromagnet (each sublattice forming a Néel ordering), with a reduced magnitude for the ordered moment. Electron or hole doping, together with the frustration effect, suppresses the magnetic ordering and allows a superconducting state. The exchange interactions favor a d-wave superconducting order parameter; in the notation appropriate for the Fe square lattice, its orbital symmetry is dxy. A number of existing and future experiments are discussed in light of the theoretical considerations.

A quantum critical point (QCP) develops in a material at absolute zero when a new form of order smoothly emerges in its ground state. QCPs are of great current interest because of their singular ability to influence the finite temperature properties of materials. Recently, heavy-fermion metals have played a key role in the study of antiferromagnetic QCPs. To accommodate the heavy electrons, the Fermi surface of the heavy-fermion paramagnet is larger than that of an antiferromagnet. An important unsolved question is whether the Fermi surface transformation at the QCP develops gradually, as expected if the magnetism is of spin-density-wave (SDW) type, or suddenly, as expected if the heavy electrons are abruptly localized by magnetism. Here we report measurements of the low-temperature Hall coefficient (R(H))--a measure of the Fermi surface volume--in the heavy-fermion metal YbRh2Si2 upon field-tuning it from an antiferromagnetic to a paramagnetic state. R(H) undergoes an increasingly rapid change near the QCP as the temperature is lowered, extrapolating to a sudden jump in the zero temperature limit. We interpret these results in terms of a collapse of the large Fermi surface and of the heavy-fermion state itself precisely at the QCP.