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FIG. 3 The critical Gr€uneisen ratio Gcr 1⁄4acr=ccr of CeNi Ge , on a log–log plot as a function V22 Quantum Critical Matter and Phase Transitions Chapter Γcr 1000 100 10 0.1 1 T(K) 5 280 303 x =1 of temperature at ambient pressure and zero field. The noncritical contributions to the specific heat cV and the thermal expansion a have been subtracted. The solid line represents G$1/T, consistent with Hertz–Millis theory. From Ku€uchler, R., Oeschler, N., Gegenwart, P., Cichorek, T., Neumaier, K., Tegus, O., Geibel, C., Mydosh, J.A., Steglich, F., Zhu, L., Si, Q., 2003. Divergence of the Gru€neisen ratio at quantum critical points in heavy fermion metals. Phys. Rev. Lett. 91 (6), 0664054. As mentioned earlier, the Gr€uneisen ratio will diverge for any QCP, even when it cannot be described by HM theory. For example, in both CeCu6xAux (see Section 2.4.2) and YbRh2Si2 (see Section 2.4.3) the Gr€uneisen ratio diverges, though with a different exponent than is expected from HM theory (K€uchler et al., 2003, 2004; Tokiwa et al., 2009). We have so far only considered static properties. Criticality can also be inferred from dynamical properties, such as the dynamical susceptibility w(k, o). For example, Sachdev (2011) introduced the scaling function k oD wðk,oÞ$Tð2Þ=zF T1=z,T,T (18) where D is the gap on either side of the transitions, so D ! 0 at the transition. It is important to note that in numerous rare earth materials unconventional SC is found (for a review, see Pfleiderer, 2009). In a superconductor, elec- trons are bound together into Cooper pairs. Understanding a superconducting phase thus boils down to finding the “glue,” and it has been suggested that quantum critical fluctuations could act as glue (Mathur et al., 1998; Metlitski et al., 2015; Miyake et al., 1986; Scalapino et al., 1986; She and Zaanen, 2009). The QPT associated with the disappearance of magnetism is then obscured by a “superconducting dome.” Whereas the idea is appealing, there are as of yet no clear experimental way to discern whether a QCP truly exists below the dome. Finally, note that in the spin-density wave picture presented in this section, the electrons play a secondary role. This means that throughout the transition, all properties of the electrons themselves such as their effective mass or their Fermi surface shape, can only change continuously (Gegenwart et al., 2008).PDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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