In a magnetic field, bilayer graphene hosts an octet of pseudo-zero-mode (PZM) electron levels nearly degenerate in orbitals $n=(0,1)$, valleys, and spins. They split in valleys by electrostatic gating. In gated bilayer graphene, in which the interlayer bias is set up to flip sign across a line, one has a line junction that traps a portion of PZM electrons inside the insulating bulk band gap, giving rise to electron states localized along the junction, known as kink states. A close look is made into the spectra and electromagnetic response of such kink states. There are two species of valley current associated with them, a drift current driven by the bias gradient and a circulating current coming from cyclotron motion. It turns out that they both flow in essentially the same direction, with the circulating current exhibiting a magnetic character distinct from those of other higher levels. In equilibrium, they spatially circulate within the kink states, creating a quasi-one-dimensional channel of orbital magnetization. The electric control of the orbital magnetization and valley currents via a network of gated junctions will find useful applications in valley electronics.

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• Edge states
• Landau levels
• Valley degrees of freedom
• Graphene
• Junctions
• Effective field theory
• Gauge theory techniques