Dynamical generation of superconducting order of different symmetries in hexagonal lattices

Abstract

The growth of superconducting order after an interaction quench in a hexagonal lattice is studied. The cases of both time-reversal (TR) preserving graphene, as well as the TR broken Haldane model, are explored. Spin singlet superconducting order is studied where the s,d+id, and d−id wave orders are the irreducible representations of the hexagonal lattice. For small quenches, the d-wave order parameter grows the fastest, a result also expected when the system is in thermal equilibrium. For the TR symmetry preserving case, the growth rate of the two d-wave orders is identical, while the TR-broken case prefers one of the chiral d-wave orders over the other, leading to a TR broken topological superconductor. As the interaction quench becomes larger, a smooth crossover is found where eventually the growth rate of the s wave becomes the largest. Thus for large interaction quenches, the s wave is preferred over the d wave for both TR preserving and TR broken systems. This result is explained in terms of the high energy quasiparticles responsible for the dynamics as the interaction quench amplitude grows. The results are relevant for time-resolved measurements that can probe the symmetry of the superconducting fluctuations in a transient regime.

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