  We present a novel quasiparticle state driven by a supercurrent in GaAs (100)
quantum wells in proximity to an $s$-wave superconductor, which can be tuned by
the superconducting velocity. Rich features such as the suppressed Cooper
pairings, large quasiparticle density and non-monotonically tunable momentum
current can be realized by varying the superconducting velocity. In the
degenerate regime, the quasiparticle Fermi surface is composed by two arcs,
referred to as Fermi arcs, which are contributed by the electron- and hole-like
branches. The D'yakonov-Perel' spin relaxation is explored, and intriguing
physics is revealed when the Fermi arc emerges. Specifically, when the order
parameter tends to zero, it is found that the branch-mixing scattering is
forbidden in the quasi-electron band. When the condensation process associated
with the annihilation of the quasi-electron and quasi-hole is {\em slow}, this
indicates that the electron- and hole-like Fermi arcs in the quasi-electron
band are independent. The open structure of the Fermi arc leads to the nonzero
angular-average of the effective magnetic field due to the spin-orbit coupling,
which acts as an effective Zeeman field. This Zeeman field leads to the spin
oscillations even in the strong scattering regime. Moreover, in the strong
scattering regime, we show that the open structure of the Fermi arc also leads
to the insensitiveness of the spin relaxation to the momentum scattering, in
contrast to the conventional motional narrowing situation. Nevertheless, with a
{\em finite} order parameter, the branch-mixing scattering can be triggered,
opening the inter-branch spin relaxation channel, which is dominant in the
strong scattering regime. In contrast to the situation with an extremely small
order parameter,....(omitted due to the limit of space)
