New Research


New Quantum Critical Phenomena

Development of a Theory of Critical Valence Fluctuations

Professor Kazumasa Miyake, Associate Professor Shinji Watanabe,

Quantum critical phenomena are characterized by anomalous temperature dependence of a series of physical quantities, such as susceptibility, resistivity, specific heat and so on, and arise near the critical point (where the long range order, such as magnetism, disappears) at zero temperature by tuning an external parameter such as the pressure.

The anomalous behaviors near the magnetic critical points are clarified by the SCR theory initiated by Moriya and his coworkers in mid \'70s. Temperature dependences of physical quantities are summarized in the upper panel (shown in black letters). However, from the end of the 20th century, some peculiar compounds were discovered not to follow the SCR theory. A typical example is YbRh_2Si_2 reported in 2000, the last year of the 20th century. The temperature dependence in the lower panel (shown in red letters) is quite different from that of 3d AF in the upper panel, i.e., has different critical exponents. Such anomalous temperature dependences were observed also in YbAuIn_5 and YbCu_(5-x)Al_x. Although a variety of theories were proposed so far, there has been no theory which explains all of those anomalous behaviors consistently. In 2008, it was reported that YbAlB_4 exhibits essentially the same critical exponent and even show the superconductivity, attracting a great attention.

Recently, our group succeeded in explaining those anomalous temperature dependences in a unified way on the basis of critical valence fluctuation scenario
(Phys. Rev. Lett. 105, 186403 (2010)). We have also developed a theory for understanding whole physical properties (such as enhancement of the superconducting transition temperature and the T-linear resistivity) observed in Ce-based heavy fermion systems, CeCu_2Si_2, CeCu_2Ge_2, CeIrIn_5, and CeRhIn_5, on the basis of critical valence fluctuation scenario (J. Phys. Soc. Jpn. 69 (2000) 3955; Phys. Rev. B 69 (2004) 024508; Phys. Rev. Lett. 100, 236401 (2008); J. Phys. Soc. Jpn. 79 (2010) 033707).

Quite recently, other compounds (such as YbIr_2Zn_20) which seem to be classified in this series were discovered, suggesting a promising development of research.

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