Pseudogap phase in the U(1) gauge theory with incoherent spinon pairs

The pseudogap effect of underdoped high-$T_c$ superconductors is studied in the U(1) gauge theory of the t-J model including the spinon pairing fluctuation. The gauge fluctuation breaks the long range correlation between the spinon pairs. The pairing fluctuation, however, suppresses significantly the low-lying gauge fluctuations and leads to a stable but phase incoherent spin gap phase which is responsible for the pseudogap effects. This quantum disordered spin gap phase emerges below a characteristic temperature $T^{\ast }$ which is determined by the effective potential for the spinon pairing gap amplitude. The resistivity is suppressed by the phase fluctuation below $% T^{*}$, consistent with experiments.