Topological phase separation in trapped ultracold fermionic gases

We consider harmonically trapped two-dimensional fermionic systems with an effective spin-orbit coupling and intrinsic s-wave superfluidity under the local density approximation. We find that, when the Zeeman field is above a critical value, there is a ubiquitous phenomenon, topological phase separation, in the weakly trapped systems. The topological phase separation is formed between the superfluid phases with different topological numbers in real space. When the Zeeman field is below the critical value, the superfluid phase is topologically trivial and the spatial topological phase separation vanishes.