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Quantum Critical Matter and Phase Transitions Chapter 280 317 the f-electrons, mediated by the c-electrons (Kasuya, 1956; Ruderman and Kittel, 1954; Yosida, 1957). This RKKY interaction at energy scale ERKKY $J2N0 competes with the Kondo screening at TK $ expð1=JN0Þ, leading to a QPT as a function of the coupling J. 3.2 Kondo Breakdown A more radical idea involves a breakdown of the Kondo hybridization at the critical point. There are some strong experimental evidences that hint in such a direction, for example, the divergence of the effective mass as exemplified by the diverging specific heat coefficient C/T and the existence of T*-line in YbRh2Si2. Although the idea is certainly appealing, again it seems very difficult to extract quantitative predictions based on the scenario of the Kondo breakdown (Coleman, 1999, 2001, 2015; Coleman et al., 2001; Sengupta, 2000; Si et al., 2001, 2014). The theories of Kondo breakdown originate from dynamical mean field theory (DMFT) (Georges et al., 1996), a numerical technique where the order parameter is still local in space but can have nonlocal temporal correlations. In addition to the critical fluctuations associated with the antiferromagnetic order, in the Kondo breakdown there are also purely local critical fluctuations associated with the localization of the f-electrons. The most important prediction of the Kondo breakdown scenario is the existence of a large Fermi surface on right side of the transition, encompass- ing both f- and c-electrons, whereas on the antiferromagnetic (left) side of the transition the Fermi surface is “small” and only contains c-electrons. So far there is no direct experimental evidence, for example, ARPES (Kummer et al., 2015; Paschen et al., 2015), that supports this claim. Indirect evidence, such as the T* line based on a crossover in the Hall conductivity, can also be explained differently. Some authors have gone even further by completely discarding the antifer- romagnetic transition and focussing on an isolated Kondo breakdown. In this picture, the localized f-electrons will form a spin liquid, coexisting with a small Fermi surface metal dubbed FL* (Senthil et al., 2003, 2004). Antiferro- magnetic order would then be an instability of this FL* phase. The absence of two different transitions suggests this exotic theory is not relevant for experiments. 3.3 Two-Dimensional Physics A surprising caveat of the Kondo breakdown pictures is that requires the sys- tem to be effectively two dimensional (Si et al., 2001). In fact, many features of CeCu6xAux such as the logarithmic divergence of the specific heat coeffi- cient can be understood by d1⁄42-dimensional HM theory (Rosch et al., 1997). It is quite puzzling, however, since there is no apparent microscopic reason why these materials would be highly anisotropic.PDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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