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In a recent experiment by Wu et al.,a Raman-assisted two-dimensional spin-orbit coupling has been realized for a Bose-Einstein condensate in an optical lattice potential.In light of this exciting progress,we study in detail key properties of the system.As the Raman lasers inevitably couple atoms to high-lying bands,the behaviors of the system in both the single-and many-particle sectors are significantly affected.In particular,the high-band effects enhance the plane-wave phase and lead to the emergence of rotongaps at low Zeeman fields.