Tunneling Spectroscopy of the Underdoped High-$T_c$ Superconductors

Considering a possibility that the pseudogap state in the underdoped high-$T_c$ superconductors is not due to a superconducting correlation, we study the tunneling spectroscopy below $T_c$ based on the phenomenological models of the pseudogap state. Specifically we consider two cases: (1) the pseudogap is a simple suppression of the density of states with an unknown origin; (2) the pseudogap state is due to an antiferromagnetic correlation. For both cases we calculate $dI\mathrm{/}dV$ using the BTK theory. The results are discussed in comparison with experiments.