To clarify the origin, we construct the mode coupling theory of critical Yb-valence fluctuations taking account of local correlation effects of f electrons [6]. We find that the extremely dispersionless critical mode emerges near q =0 in the momentum space. This almost local valence-fluctuation mode causes extremely small characteristic temperature of critical valence fluctuation, T₀. Hence, even at low-enough temperature than the effective Fermi temperature (i.e., so-called Kondo temperature) of the system, scaled temperature by T₀ can be large, which causes the unconventional criticality in physical quantities. A new type of quantum criticality is shown to emerge as divergence of uniform magnetic susceptibility χ∼ T  ^-ζ (0.5 ∼ ζ ∼ 0.7), NMR/NQR relaxation rate 1/(T₁T ) ∼ T  ^-ζ and specific heat C/T ∼ -logT, giving rise to a huge enhancement of the Wilson ratio, and emergence of T -linear resistivity. At the quantum critical point (QCP) of the valence transition, not only the valence susceptibility diverges, but also the magnetic susceptibility diverges [7]. Hence, uniform spin fluctuation diverges at the QCP, giving rise to enhancement of the Wilson ratio. This gives a natural explanation for the unconventional criticality commonly observed in YbRh₂Si₂ and β-YbAlB₄ in a unified way.

Recently, NMR measurement has revealed that two heavy-electron states coexist at low temperatures in YbRh₂Si₂ [8]. This suggests that phase separation of higher and lower valences of Yb occurs in YbRh₂Si₂, which is expected to appear due to proximity to the first-order Yb-valence transition.