Universal dynamical scaling of long-range topological superconductors

We study the out-of-equilibrium dynamics of p-wave superconducting quantum wires with long-range interactions when the chemical potential is linearly ramped across the topological phase transition. We show that the heat produced after the quench scales with the quench rate δ according to the scaling law δθ where the exponent θ depends on the power-law exponent of the long-range interactions. The presence of the long-range pairing term increases the exponent θ and thus improves the adiabatic preparation of topological states. Moreover, we identify the parameter regimes where the heat scaling can be cast in terms of the universal equilibrium critical exponents and can thus be understood within the Kibble-Zurek framework. When the electron hopping decays more slowly in space than pairing, it dominates the equilibrium scaling. Surprisingly, in this regime the dynamical critical behavior arises only from pairing and thus exhibits a dynamical universality unrelated to equilibrium scaling. The discrepancy from the expected Kibble-Zurek scenario can be traced back to the presence of multiple universal terms in the equilibrium scaling functions of long-range interacting systems close to a second order critical point.