Nucleation of domain walls by Z₂ symmetry breaking transition in pₓ+ipy superconductors

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We show that time reversal symmetry breaking pₓ+ipy wave superconductors undergo several phase transitions subjected to external magnetic field or supercurrent. In such system the discrete Z₂ symmetry can recover before the complete destruction of the order parameter. The topological defects associated with Z₂ symmetry - domain walls can be created in a controllable way by magnetic field or current sweep according to the Kibble-Zurek scenario. Such domain wall generation can take place in exotic superconductors like Sr₂RuO₄ and some heavy fermion compounds.