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We study the superconducting transition in a two-dimensional electron gaswith strong Rashba spin-orbit coupling. We assume low electron density, suchthat only the majority spin band participates in the transition. We show thatthe superconducting transition follows either the Bose-Einstein condensation(BEC), or the Bardeen-Cooper-Schrieffer (BCS) scenarios, depending on theposition of the chemical potential with respect to the bottom of the majorityband, and the strength of the Coulomb repulsion between electrons. Hence, theBEC-BCS crossover in this system can be driven either by the change in thechemical potential, or the distance to a gate.

Superfluid-insulator transition and the BEC-BCS crossover in the Rashba moat band