Orbital Magnetoelectric effect in px-py Zigzag nanoribbon.

Motivated by the recent synthetization of the monolayer of bismuthene on SiC substrate, which can be effectively described by a simple two orbitals model with strong atomic spin-orbit coupling, we study the spin and orbital angular momentum response in px-py zigzag nanoribbon to an applied longitudinal electric field. The electric field induces a finite nonequilibrium spin and orbital angular momentum along the lines of the ribbon. When only SOC is present, the sum of induced spin and orbital angular momentum over lines of the ribbon adds up to zero. When a sublattice potential induced by the substrate is included in the Hamiltonian, due to the break of spatial-inversion symmetry, the total spin on the ZZ ribbon still vanishing, but the total orbital angular momentum acquires a finite value pointing to the existence of a magnetoelectric effect in the orbital degree of freedom. Our result suggests that nanoribbons made of multi-orbital materials, such as bismuthene, can be used to found cleary signatures of non-trivial orbital-phenomena and serve as a versatile platform to the emergent field
of spin-orbitronics.