Topological Solitons in Square-root Graphene Nanoribbons Controlled by Electric Fields

Graphene nanoribbons (GNRs) are unique quasi-one-dimensional (1D) materials that have garnered a lot of research interest in the field of topological insulators. While the topological phases exhibited by GNRs are primarily governed by their chemical structures, the ability to externally control these phases is crucial for their potential utilization in quantum electronics and spintronics. Here we propose a class of GNRs featured by mirror symmetry and four zigzag segments in a unit cell that has unique topological properties induced and controlled by an externally applied electric field. Their band structures manifest two finite gaps which support topological solitons, as described by an effective square-root model. To demonstrate the experimental feasibility, we design and synthesize a representative partially zigzag chevron-type GNR (pzc-GNR) with the desired zigzag segments using a bottom-up approach. First-principles calculations on pzc-GNR reveal band inversions at the two finite gaps by switching the direction of the electric field, which is in accordance with predictions from the square-root Hamiltonian. We show different topological phases can be achieved by controlling the direction of the field and the chemical potential of the system in square-root GNRs. Consequently, upon adding a step-function electric field, solitons states can be generated at the domain wall. We discuss the properties of two types of soliton states, depending on whether the terminating commensurate unit cell is mirror symmetric.