Topological properties of subsystem-symmetry-protected edge states in an extended quasi-one-dimensional dimerized lattice

Abstract

We investigate theoretically the topological properties of dimerized quasi-one-dimensional (1D) lattice comprising of multi legs (L) as well as multi sublattices (R). The system has main and subsidiary exchange symmetries. In the basis of latter one, the system can be divided into L 1D subsystems each of which corresponds to a generalized SSHR model having R sublattices and onsite potentials. Chiral symmetry is absent in all subsystems except when the axis of main exchange symmetry coincides on the central chain. We find that the system may host zero-and finite-energy topological edge states. The existence of zero-energy edge state requires a certain relation between the number of legs and sublattices. As such, different topological phases, protected by subsystem symmetry, including zero-energy edge states in the main gap, no zero-energy edge states, and zeroenergy edge states in the bulk states are characterized. Despite the classification symmetry of the system belongs to BDI but each subsystem falls in either AI or BDI symmetry class.