Rashba valleys and quantum Hall states in few-layer black arsenic.

Exciting phenomena may emerge in non-centrosymmetric two-dimensional electronic systems when spin-orbit coupling (SOC)1 interplays dynamically with Coulomb interactions2,3, band topology4,5 and external modulating forces6-8. Here we report synergetic effects between SOC and the Stark effect in centrosymmetric few-layer black arsenic, which manifest as particle-hole asymmetric Rashba valley formation and exotic quantum Hall states that are reversibly controlled by electrostatic gating. The unusual findings are rooted in the puckering square lattice of black arsenic, in which heavy 4p orbitals form a Brillouin zone-centred Γ valley with pz symmetry, coexisting with doubly degenerate D valleys of px origin near the time-reversal-invariant momenta of the X points. When a perpendicular electric field breaks the structure inversion symmetry, strong Rashba SOC is activated for the px bands, which produces spin-valley-flavoured D± valleys paired by time-reversal symmetry, whereas Rashba splitting of the Γ valley is constrained by the pz symmetry. Intriguingly, the giant Stark effect shows the same px-orbital selectiveness, collectively shifting the valence band maximum of the D± Rashba valleys to exceed the Γ Rashba top. Such an orchestrating effect allows us to realize gate-tunable Rashba valley manipulations for two-dimensional hole gases, hallmarked by unconventional even-to-odd transitions in quantum Hall states due to the formation of a flavour-dependent Landau level spectrum. For two-dimensional electron gases, the quantization of the Γ Rashba valley is characterized by peculiar density-dependent transitions in the band topology from trivial parabolic pockets to helical Dirac fermions.