  Nonlocal interaction between ultracold atoms trapped in optical lattices can
give rise to interesting quantum many-body phenomena. However, its realization
usually demands unconventional techniques, for example the artificial gauge
fields or higher-orbit Feshbach resonances, and is not highly controllable.
Here, we propose a valid and feasible scheme for realizing a tunable
finite-range interaction for spinless fermions immersed into the bath of
bosons. The strength of the effective interaction for the fermionic subsystem
is artificially tunable by manipulating bosons, ranging from the repulsive to
attractive regime. And the interaction distance is locked to the hopping of
bosons, making the finite-range interaction perfectly clean for the fermionic
subsystem. Specifically we find that, by introducing an additional staggered
hopping of bosons, the proposal is readily applied to search the Majorana
corner modes in such a spinless system, without implementation of complex
artificial gauge fields, which is totally distinct from existing results
reported in spinful systems. Therefore this scheme provides a potential
platform for exploring the unconventional topological superfluids and other
nontrivial phases induced by long-range interactions in ultracold atoms.
