“…When the critical temperature is suppressed by tuning material parameters and enters the Fermi-degeneracy regime, diverging valence fluctuations are considered to be coupled with the Fermi-surface instability. This multiple instability seems to be a key mechanism which dominates the low-temperature properties of the materials including the valence-fluctuating ions such as Ce and Yb [7,8,9,10].Actually, a remarkable increase of the superconducting transition temperature far from antiferromagnetic QCP in CeCu 2 X 2 (X=Ge, Si) [11,12,13] and CeIrIn 5 [14] as well as linear-temperature dependence of resistivity observed in variety of Ce and Yb compounds [12,13,14,15,16,17] seems to a sign of underlying influence of the proximity of the QCP of the valence transition (VQCP) [17].So far, to reduce the critical temperature of the valence transition toward absolute zero, intensive efforts have been made by chemical substitutions and applying pressure [18]. Usually, magnetic field also offers one of the efficient control parameters.…”