  Van Hove singularities (VHSs) in proximity to the Fermi level promote
electronic interactions and generate diverse competing instabilities. It is
also known that a nontrivial Berry phase derived from spin-orbit coupling (SOC)
can introduce an intriguing decoration into the interactions and thus alter
correlated phenomena. However, it is unclear how and what type of new physics
can emerge in a system featured by the interplay between VHSs and the Berry
phase. Here, based on a general Rashba model on the square lattice, we
comprehensively explore such an interplay and its significant influence on the
competing electronic instabilities by performing a parquet renormalization
group analysis. Despite the existence of a variety of comparable fluctuations
in the particle-particle and particle-hole channels associated with
higher-order VHSs, we find that the chiral $p \pm ip$ pairings emerge as two
stable fixed trajectories within the generic interaction parameter space,
namely the system becomes a robust topological superconductor. The chiral
pairings stem from the hopping interaction induced by the nontrivial Berry
phase. The possible experimental realization and implications are discussed.
Our work sheds new light on the correlated states in quantum materials with
strong SOC and offers fresh insights into the exploration of topological
superconductivity.
