We investigate the quasiparticle spin relaxation with superconducting velocity tunable state in GaAs (100) quantum wells in proximity to an s-wave superconductor. We first present the influence of the supercurrent on the quasiparticle state in GaAs (100) quantum wells, which can be tuned by the superconducting velocity. Rich features such as the suppressed Cooper pairings, large quasiparticle density and nonmonotonically 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 holelike branches. The Dyakonov-Perel spin relaxation is then 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 quasielectron band. When the condensation process associated with the annihilation of the quasielectron and quasihole is slow, this indicates that the electron- and holelike Fermi arcs in the quasielectron 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 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 finite order parameter, the branch-mixing scattering can be triggered, opening the interbranch spin relaxation channel, which is dominant in the strong-scattering regime. In contrast to the situation with an extremely small order parameter, due to the interbranch channel, the spin oscillations vanish and the spin relaxation exhibits a motional narrowing feature in the strong-scattering regime.
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