  We investigate the effect of helical Majorana fermions at the surface of
superconducting topological insulators (STI) on the Josephson current by
referring to possible pairing states of Cu-doped Bi2Se3. The surface state in
the present STI has a spin helicity because the directions of spin and momentum
are locked to each other. The Josephson current-phase relation in an STI/s-wave
superconductor junction shows robust sin(2{\phi}) owing to mirror symmetry,
where \phi denotes the macroscopic phase difference between the two
superconductors. In contrast, the maximum Josephson current in an STI/STI
junction exhibits a nonmonotonic temperature dependence depending on the
relative spin helicity of the two surface states. Detecting these features
qualifies as distinct experimental evidence for the identification of the
helical Majorana fermion in STIs.
