Orbital currents in lattice multiorbital systems: Continuity equation, torques, and RKKY interaction

Utilizing the electron orbital degree of freedom in heterostructures is attracting increasing attention due to the possibility of achieving much larger conversion rates between charge and orbital angular momentum flow compared to the intrinsic electron spin. Here, we consider orbital angular momentum currents in a tight-binding multiorbital lattice model and derive their continuity equation. From it, we observe that the current is not conserved and apply similar considerations to the recently discovered altermagnets. We find nonzero orbital torque terms, elucidate their physical mechanism, and show numerically that they contribute to dampening the orbital angular momentum current flowing in multiorbital heterostructures. Moreover, we compute the orbital RKKY interaction and find it exhibits similar characteristics as the orbital angular momentum current mediating it, thus serving as a direct experimental probe of such currents.