Quantum Critical Metals: beyond the Order Parameter Fluctuations

The standard description of quantum critical points takes into account only fluctuations of the order parameter, and treats quantum fluctuations as extra dimensions of classical fluctuations. This picture can break down in a qualitative fashion in quantum critical metals: non-Fermi liquid electronic excitations are formed precisely at the quantum critical point and appear as a part of the quantumcritical spectrum. In the case of heavy fermion metals, it has been proposed that the non-Fermi liquid behavior is characterized by the destruction of the Kondo effect. The latter invalidates Hertz’s Gaussian theory of paramagnons and leads to an interacting theory that is “locally quantum critical”. We summarize the theoretical and experimental developments on the subject. We also discuss their broader implications, and make contact with recent work on quantum critical magnets. 1 The Order Parameter Fluctuation Theory of Quantum Critical Points and its Breakdown Phase transitions come in different varieties. Generically, they are characterized by the onset of an order parameter. A classical critical point, occurring at a finite temperature phase transition of second-order, is described in terms of a coarse-grained theory of spatial, but time-independent, fluctuations of the order parameter [1]. Such a description also serves as the basis to categorize the universality classes of critical points. Quantum critical points (QCPs) take place at zero temperature. They differ from their classical counterparts in that the static (classical) and dynamic (quantum) fluctuations are mixed and both have to be incorporated in the critical theory. It is, however, standard to assume that they too can be described in terms of fluctuations of the order parameter: the only distinction being that the fluctuations are not only in space but also in (imaginary) time [2,3]. It has been realized over the past few years that this picture can break down in a qualitative fashion in quantum critical metals [4,5]. Non-Fermi liquid excitations emerge precisely at the QCP, and they need to be kept as a part of the quantum-critical spectrum. This is illustrated in Fig. 1. On the one hand, quantum criticality is the mechanism for the non-Fermi liquid behavior. On the other hand, the non-Fermi liquid excitations feed back and change the universality class of the underlying QCP. The experimental motivations have largely come from heavy fermion QCPs [6,4,5]. Discussions of a similar spirit can be found in an earlier pedagogical article [7].