  In the ring-shaped tunnel-junction array with four islands, the secondary
Coulomb blockade gap in a low bias-voltage range is observed in the I-V
characteristics. We attribute its appearance to the unique topology of the
array which induces up to two electrons to get trapped inside. We have analyzed
the formation and destruction of the gap in terms of detailed single-electron
tunneling processes. The negative differential resistance behavior when the
thermal and quantum fluctuations are present is also studied.
