We theoretically show that in a crystal with a helical lattice structure, orbital and spin magnetizations along a helical axis are induced by an electric current along the helical axis. We propose a simple tight-binding model for calculations, and the results can be generalized to any helical crystals. The induced magnetizations are opposite for right-handed and left-handed helices. The current-induced spin magnetization along the helical axis comes from a radial spin texture on the Fermi surface. This is in sharp contrast to Rashba systems where the induced spin magnetization is perpendicular to the applied current.

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We theoretically study current-induced orbital magnetization in a chiral crystal. This phenomenon is an orbital version of the Edelstein effect. We propose an analogy between the current-induced orbital magnetization and an Ampère field in a solenoid in classical electrodynamics. To quantify this effect, we define a dimensionless parameter from the response coefficients relating a current density with an orbital magnetization. This dimensionless parameter can be regarded as a number of turns within a unit cell when the crystal is regarded as a solenoid, and it represents how "chiral" the crystal is. By focusing on the dimensionless parameter, one can design a band structure that realizes the induction of large orbital magnetization. In particular, a Weyl semimetal with all of the Weyl nodes close to the Fermi energy can have a large value for this dimensionless parameter, which can exceed that of a classical solenoid.

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