  We study a bilayer two-dimension-electron-gas (2DEG) adjacent to a type-II
superconductor thin film with a pinned vortex lattice. We find that with
increasing interlayer tunneling, the system of half filling presents three
phases: gapped phase-I (topological insulator), gapless critical phase-II
(metal), and gapped phase-III (band insulator). The Hall conductance for
phase-I/III is 2/0 $e^{2}/h$, and has non-quantized values in phase-II. The
excitation (response to topological defect, a local vortex defect) in these
three phases shows different behaviors due to the topological property of the
system, including fractional charge $e/2$ for each layer in phase-I. While in
the case of quarter filling, the system undergoes a quantum phase transition
from metallic phase to topological insulator phase (with excitation of
fractional charge $e/4$).
