  Recently, much attention has been paid to search for Majorana fermions in
solid-state systems. Among various proposals there is one based on
radio-frequency superconducting quantum interference devices (rf-SQUIDs), in
which the appearance of 4$\pi$-period energy-phase relations is regarded as
smoking-gun evidence of Majorana fermion states. Here we report the observation
of truncated 4$\pi$-period (i.e., 2$\pi$-period but fully skewed) oscillatory
patterns of contact resistance on rf-SQUIDs constructed on the surface of
three-dimensional topological insulator Bi$_2$Te$_3$. The results reveal the
existence of 1/2 fractional modes of Cooper pairs and the occurrence of parity
switchings, both of which are necessary signatures accompanied with the
formation of Majorana fermion states.
