Non-adiabatic Dynamics in d + id-Wave Fermionic Superfluids

Abstract

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 exactlyintegrable 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.

Collective modes in pumped unconventional superconductors with competing ground states

“…We concentrate on the region of the phase diagram where s-wave and d-wave symmetries are neighbors, but avoid the regime of coexistence of both order parameters, i.e. a possible s + id state, as this state (and the similar case of d + id state) and its non-equilibrium dynamics were discussed previously, 28,32,33 . Instead, we focus on pairing fluctuations of the sub-dominant symmetry close to the transition points.…”