Dissipation driven dynamical topological phase transitions in two-dimensional superconductors

We induce and study a topological dynamical phase transition between two planar superconducting phases. Using the Lindblad equation to account for the interactions of Bogoliubov quasiparticles among themselves and with the fluctuations of the superconducting order parameter, we derive the relaxation dynamics of the order parameter. To characterize the phase transition, we compute the fidelity and the spin-Hall conductance of the open system. Our approach provides crucial informations for experimental implementations, such as the dependence of the critical time on the system-bath coupling.