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We investigate the topological phase transition with large Chern number in acoupled layer system. The topological transitions between different topologicalsuperfluids can be realized by controlling the binding energy, interlaytunneling and layer asymmetry {\it etc}. These topological phase transitionscan be characterized by energy gap closing and reopening at the critical pointsat zero momentum, where the Pfaffian and Chern number undergo a discontinuouschange. The bulk-edge correspondence ensures that the number of edge modesexactly equals the Chern number. However all these edge modes localized at thesame edge have the same chirality and propagate along the same direction. Thesetopological phases can be detected by spin texture at or near zero momentum,which changes discontinuously across the phase transition point due to bandinversion. This model can be easily generalized to multilayer system in whichthe Chern number equals any positive integer --- similar to that in integerquantum Hall effect --- can be realized. This work paves a new way in therealization of topological superfluids with large Chern number.

Large Chern Number Topological Superfluids in Coupled Layer System