  Since the experimental formation of a vortex with a fractional quantized
magnetic flux in a thin superconducting $s$-wave bi-layer was recently
reported, we calculate the local density of states (LDOS) around two half
quantum vortices in a $s$-wave superconductor on the basis of the
quasiclassical Eilenberger theory to investigate the effect of the phase
discontinuity. We show that the LDOS pattern around fractional vortices is
qualitatively different from that around conventional vortex. We find that the
novel bow-tie-shaped bound states appear in the high energy region, which can
be an evidence for the fractional vortices through scanning tunneling
microscopy/spectroscopy. We also show that the system with $n$ fractional
vortices with the vorticity $1/n$ has a similarity to the Josephson junctions.
