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Exciting phenomena may emerge in non-centrosymmetric two-dimensional (2D)electronic systems when spin-orbit coupling (SOC) interplays dynamically withCoulomb interactions, band topology, and external modulating forces, etc. Here,we report illuminating synergetic effects between SOC and Stark incentrosymmetric few-layer black arsenic (BAs), manifested as giant Rashbavalley splitting and exotic quantum Hall states (QHS) reversibly controlled byelectrostatic gating. The unusual finding is rooted in the puckering squarelattice of BAs, in which heavy $4p$ orbitals form highly asymmetric $\Gamma$valley with the $p_{z}$ symmetry and $D$ valleys of the $p_{x}$ origin, locatedat the Brillouin zone (BZ) center and near the time reversal invariant momentaof $X$, respectively. When the structure inversion symmetry is broken byperpendicular electric field, giant Rashba SOC is activated for the $p_{x}$bands to produce strong spin-polarized $D^{+}$ and $D^{-}$ valleys related bytime-reversal symmetry, coexisting with weak $\Gamma$ Rashba bands constrainedby the $p_{z}$ symmetry. Intriguingly, strong Stark effect shows the same$p_{x}$-orbital selectiveness for $D$, collectively shifting the valence bandmaximum of $D^{\pm}$ valleys to exceed the $\Gamma$ pockets. Such anorchestrating effect between SOC and Stark allows us to realize gate-tunablespin valley manipulations for 2D hole gas, as revealed by unconventionalmagnetic field triggered even-to-odd transitions in QHS. For electron doping,the quantization of the $\Gamma$ Rashba bands is characterized by peculiardensity-dependent transitions in band topology from two parabolic valleys to aunique inner-outer helical structure when charge carrier concentrationsincrease.

Manipulating Giant Rashba Valley Splitting and Quantum Hall States in Few-Layer Black Arsenic by Electrostatic Gating