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We report on $\vec{k}\cdot\vec{p}$ calculations of Rashba spin-orbit couplingcontrolled by external gates in InAs/InAsP core-shell nanowires. We show thatcharge spilling in the barrier material allows for a stronger symmetry breakingthan in homoegenous nano-materials, inducing a specific interface-relatedcontribution to spin-orbit coupling. Our results qualitatively agree withrecent experiments [S. Futhemeier \textit{et al.}, Nat. Commun. \textbf{7},12413 (2016)] and suggest additional wavefunction engineering strategies toenhance and control spin-orbit coupling.

Enhanced Rashba spin-orbit coupling in core-shell nanowires by the interfacial effect