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We consider a waveguide formed in a clean graphene monolayer by a spatiallyinhomogeneous magnetic field. The single-particle dispersion relation for thiswaveguide exhibits a zero-energy Landau-like flat band, while finite-energybands have dispersion and correspond, in particular, to snake orbits. Forzero-mode states, all matrix elements of the current operator vanish, and afinite conductance can only be caused by virtual transitions to finite-energybands. We show that Coulomb interactions generate such processes. In starkcontrast to finite-energy bands, the conductance is not quantized and shows acharacteristic dependence on the zero-mode filling. Transport experimentsthereby offer a novel and highly sensitive probe of electron-electroninteractions in clean graphene samples. We argue that this interaction-drivenzero-mode conductor may also appear in other physical settings and is notcaptured by the conventional Tomonaga-Luttinger liquid description.

Interaction-induced conductance from zero modes in a clean magnetic graphene waveguide