Topological phases, topological flat bands, and topological excitations in a one-dimensional dimerized lattice with spin-orbit coupling

Abstract

The Su-Schrieffer-Heeger (SSH) model describes a one-dimensional Z2 topological insulator, which has two topological distinct phases corresponding to two different dimerizations. When a modulated spin-orbit coupling is introduced into the SSH model, we find that the structure of the Bloch bands can be greatly changed, and most interestingly, a new topological phase with single zero-energy bound state which exhibits non-Abelian statistics at each end emerges, which suggests that a new topological invariant is needed to fully classify all phases. In a comparatively large range of parameters, we find that the modulated spin-orbit coupling induces a completely flat band with non-trivial topology. For the case with non-uniform dimerizaton, we find that the modulated spin-orbit coupling changes the symmetric structure of topological excitations known as solitons and antisolitons and when the modulated spin-orbit coupling is strong enough to induce a topological phase transition, the whole system is topologically non-trivial with the disappearance of solitons and antisolitons, consequently, the system is a real topological insulator with well-protected end states.