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Superconducting magnetoelectric effect, which is the current-inducedmagnetization in a superconductor, mainly focused on the spin magnetization inprevious studies, but ignore the effect of the orbital magnetic moments carriedby the paired Bloch electrons. In this work, we show that orbital magneticmoments in superconductors can induce large orbital magnetization in thepresence of a current. We constructed a unified description for thecurrent-induced spin and orbital magnetization across the superconductivitynormal metal phase transition. We find that in a superconductor with uniformpairing, the current-induced magnetization at a given current density is thesame as that in its normal metal state, while with the nonuniformsuperconducting pairing, the current-induced magnetization exhibits an abruptchange in magnitude near the superconductivity normal metal phase transition.Importantly, our theory predicts the orbital magnetoelectric effect insuperconducting twisted bilayer graphene which has paired Bloch electrons withlarge orbital magnetic moments and negligible spin-orbit coupling. We proposethat the measurement of the current-induced orbital magnetoelectric effect canbe used to detect the possible nonuniform pairings in twisted bilayer grapheneand other newly discovered superconductors with non-trivial Berry curvatures.

Superconducting Orbital Magnetoelectric Effect and its Evolution across the Superconductivity Normal Metal Phase Transition