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l l various sizes they emit different colors of light. Now the practical applica- tions are apparent, eg, solar cells, lighting, and TV (LCD) display technol- ogies. Due to nanostructuring lithography, tiny area devices may be formed of a two-dimensional electron gas (2DEG) tuned with superim- posed gates and nearby contacts that mimic the bulk Kondo effect. Here, it is required to place an odd number of electrons bearing spin on the dot. For sufficiently small dots, a single electron (spin 1⁄41/2) will generate the Kondo resonance behavior (Rau et al., 2010 and Amasha et al., 2013). In ultra-cold gases all thermal fluctuations are frozen out, only remaining are the quantum fluctuations and thus the possibility of QPT/QCP. For example, a QPT has been observed from a superfluid to a Mott insulator (Greiner et al., 2002). While limited in experimental observational techni- ques, the detectable spatial resolution from a “spread out” coherent gas to localized gas of atoms at each lattice site characterizes the transition. The tuning parameter is the depth of the lattice potential. A review of such many-body cold-gas physics is given by Bloch et al. (2008). Two-dimensional superconducting Josephson-junction arrays form a model system with which to study quantum dynamics and QPT. Basically there are two competing energy scales: the Josephson energy associated with the coupling of Cooper pairs between the superconducting islands; and the charging energy necessary to add an extra electron to a neutral island. By tuning these combinations one can generate a superconductor to insulator QPT, along with associated vortex dynamics (Fazio and Van Der Zant, 2001). A magnetic field or disorder can also be used to tune the Josephson array to a QCP. Presently graphene is being overlaid over superconducting discs and gate tuned to reach the QCP (Han et al., 2014). SUMMARY AND CONCLUSIONS 6 Quantum Critical Matter and Phase Transitions Chapter 280 329 In this chapter, we have introduced quantum criticality and its manifestations of phase transitions in rare earth compounds. These T 1⁄4 0 K phase transitions are created by quantum fluctuations that can be tuned by pressure, doping or disorder, frustration, and magnetic field. The effects of the change of phase reveal themselves at finite temperatures in the basic experimental properties of specific heat, resistivity and magnetic susceptibility. We have summarized the theoretical background and synopsized the latest controversial develop- ments. Rather than focusing on the many materials that are claimed to exhibit QPTs at a QCP, we discuss a few well-studied examples with critique of the experimental shortcomings. Some illustrations of quantum criticality beyond the rare earths are offered in the final section. Generically speaking there are certain limitations with all the possible tuning methods. However, the disorder or doping randomness as a tuningPDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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