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is quite consistent with the dHvA measurement that the dHvA frequencies, including the β$_{2}$ blanch, keep almost constant for 0 ≤ P < P$_{c}$ , and they suddenly jump at P = P$_{c}$ and remain constant for P > P$_{c}$ . 

We find that the measured enhancement of the ef- fective mass of electrons from m ∗ ∼ 6 m$_{0}$ at P = 0 to m ∗ ∼ 60 m$_{0}$ at P → P$_{c}$$_{−}$ 9 is also reproduced; The ε$_{f}$ dependence of the density of states (DOS) at the chemical potential µ , D ( µ ), is shown in Fig. 3(b), where D ( ω ) ≡ ∑ k $_{σ}$δ ( ω − E$_{k}$$_{σ}$ ) / (2 N ) with E$_{k}$$_{σ}$ being the en- ergy band of Eq. (1). The DOS is enhanced about 10 times when ε$_{f}$ approaches ε c $_{f}$, as shown in the inset of Fig. 3(b). However, the renormalization factor √$_{Z}$$_{σ}$$_{, due}$ to the many-body effect, does not show divergent growth even as ε$_{f}$ approaches ε c $_{f}$. This implies that the diver- gent growth of the DOS is mainly due to the band ef- fect. Then, D ( µ ) is proportional to m ∗ and √$_{A}$$_{, explain-}$ ing the measured √$_{A/m}$ ∗ =const. scaling. 11, 28 We note that D ( µ ) at ε$_{f}$ = − 0 . 4 is about 10 times larger than the density of states of conduction electrons at ¯ n$_{c}$ = 0 . 8, D$_{c}$ ( µ ) = 0 . 092, which is also consistent with enhanced γ of CeRhIn$_{5}$ 5 from that of LaRhIn$_{5}$ 13, 14 at P = 0. When ε$_{f}$ increases, m$_{s}$ decreases, as shown in Fig. 1(c). Since the increase in ε$_{f}$ tends to increase the renormalization factor √$_{Z}$$_{σ}$$_{, the energy gap between the original lower-}$ hybridized band and the folded band in the AF phase is increased. This effect pushes up the latter band in the 1st Brillouin zone, making the flat part of the band, mainly contributed from f electrons, whose bottom is lo- cated at k = (0 , 0) start to emerge at the Fermi level (see Fig. 2(b)). c 

In the paramagnetic phase for ε$_{f}$ > ε $_{f}$, D ( µ )’s have larger values than those in the AF phase, as shown in Fig. 3(b). The increase in the DOS toward ε c f in the para- magnetic phase is naturally understood since as ε$_{f}$ de- creases, ¯ n$_{f}$ increases to approach 1, i.e., the Kondo state, giving rise to the reduction of T$_{K}$ , i.e., enhancement of D ( µ ). In CeRhIn$_{5}$, the dHvA signal of the β$_{2}$ blanch has not been detected for P > P$_{c}$ , probably because its effec- tive mass is too large, close to 100 m$_{0}$ . 9 This is also consis- tent with our result. For ε$_{f}$ > ε c $_{f}$, D ( µ ) decreases as h in- 

creases. This is also consistent with the field-dependence of m ∗ of the β$_{2}$ blanch in CeCoIn$_{5}$, 29 which is expected to correspond to the paramagnetic state of CeRhIn$_{5}$ for P > P$_{c}$ . 23, 30 c 

The increase in D ( µ ) toward ε $_{f}$, shown in Fig. 3(b), suggests that total DOS at the 3D Fermi surface of CeRhIn$_{5}$ gives rise to the measured peak structure of the A coefficient at P = P$_{c}$ . 11 Our results clearly show that the “small” Fermi surface can be observed by dHvA mea- surement even without switching off the c-f hybridiza- tion, which reminds us of the elucidation of metamag- netism in CeRu$_{2}$Si$_{2}$. 31–33 

Recently, a possibility that the AF and paramagnetic transition is continuous under pressure has been reported by the In-NQR measurement at H = 0. 34 To clarify the detailed nature of the phase competition at the mag- netic field smaller than the upper critical field, ∼ 10 T, existence of the superconductivity should be taken into account, which is out of scope of the present study. 

In summary, we have shown that the drastic change of Fermi surface with huge mass enhancement as well as the transport anomalies in CeRhIn$_{5}$ under pressure are naturally explained from the viewpoint of the interplay of the AF order and Ce-valence fluctuations. 

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