Fate of high winding number topological phases in the disordered extended Su-Schrieffer-Heeger model

We use the Lindblad equation approach to investigate topological phases hosting more than one localized state at each side of a disordered Su-Schrieffer-Heeger chain with properly tuned long-range hoppings. Inducing a nonequilibrium steady state across the chain, we probe the robustness of each phase and the fate of the edge modes looking at the distribution of electrons along the chain and the corresponding standard deviation in the presence of different kinds of disorder either preserving the symmetries of the Hamiltonian or not.