Generation and edge-state transitions of pseudohelical edge state based on side potentials in graphene

Pseudohelical edge state (PHES) was proposed based on a staggered spin–orbit coupling (SOC) uniformly applied on graphene. In this work, we investigate the formation of the PHES and its edge-state transitions by the side potentials composed of a uniform SOC, an antiferromagnetic exchange field and a staggered electric field that are applied on the boundaries in zigzag graphene nanoribbon. The results reveal that the PHESs can also be achieved by the side potential of the antisymmetric uniform spin–orbit coupling, which is attributed to the fact that the opposite (same) sign of energies at the valleys and indicates the presence (absence) of the edge state. Based on this modulated mechanism, the PHES can be further transformed into two different types of the PHESs, spin-polarized antichiral edge states (AESs) and one-sided spin-polarized AESs, by modulating the applied direction and location of the side potentials. More strikingly, by utilizing these edge-state transitions, we propose a spin dual-channel or single-channel field-effect transistor that can be operated by a staggered electric field. Moreover, we confirm that the proposed transistor is robust against disorders, with the assistance of calculating the transmission.