  Non-Hermitian skin effect(NHSE) describes a unique non-Hermitian phenomenon
that all eigen-modes are localized near the boundary, and has profound impact
on a wide range of bulk properties. In particular, topological systems with
NHSE have stimulated extensive research interests recently, given the fresh
theoretical and experimental challenges therein. Here we propose a readily
implementable scheme for achieving NHSE with band topology in ultracold gases.
Specifically, the scheme realizes the one-dimensional optical Raman lattice
with two types of spin-orbit coupling (SOC) and an additional laser-induced
dissipation. By tuning the dissipation and the SOC strengths, NHSE and band
topology can be individually controlled such that they can coexist in a
considerable parameter regime. To identify the topological phase in the
presence of NHSE, we have restored the bulk-boundary correspondence by invoking
the non-Bloch band theory, and discussed the dynamic signals for detection. Our
work serves as a guideline for engineering topological lattices with NHSE in
the highly tunable environment of cold atoms, paving the way for future studies
of exotic non-Hermitian physics in a genuine quantum many-body setting.
