Non-adiabatic dynamics in d+id-wave fermionic superfluids

We consider a problem of non-adiabatic dynamics of a 2D fermionic system with $d+id$-wave symmetry of paring amplitude. Under the mean-field approximation, we determine the asymptotic behavior of the pairing amplitude following a sudden change of coupling strength. We also study an extended $d+id$ pairing system for which the long-time asymptotic states of the pairing amplitude in the collisionless regime can be determined exactly. By using numerical methods, we have identified three non-equilibrium steady states described by different long-time asymptotes of the pairing amplitude for both the non-integrable and the integrable versions of $d+id$-wave models. We found that despite of its lack of integrability, long-time dynamics resulting from pairing quenches in the non-integrable $d+id$ model are essentially similar to the ones found for its exactly-integrable extended $d+id$ model. We also obtain the long-time phase diagram of the extended $d+id$ model through the Lax construction that exploits underlying integrability showing that the dynamic phases obtained by numerics are consistent with the dynamics of the exactly integrable approach. Both models describe a topological fermionic system with a topologically non-trivial BCS phase appearing at weak coupling strength. We show that the presence of oscillating order parameter region in the chiral $d+id$ pairing dynamics differs from the d-wave ($d_{x^2-y^2}$), which may be used to probe pairing symmetries of chiral superconductors.