Nonreciprocal transport — current flowing more easily in one direction than the other — is supposed to require broken time-reversal symmetry. A magnetic field, a magnetic material, or some form of internal magnetization. This is not merely conventional wisdom but a consequence of Onsager reciprocal relations: in linear response, the conductivity tensor is symmetric under time reversal. To break reciprocity, you must break the symmetry.

This paper shows that disorder provides a loophole. Skew-scattering and side-jump processes — asymmetric impurity scattering mechanisms well-known in the anomalous Hall effect — can generate a nonlinear longitudinal current that breaks reciprocity without breaking time-reversal symmetry. The effect is second-order in the electric field, evading the linear-response constraint.

A systematic symmetry analysis identifies 42 crystallographic point groups that permit this extrinsic mechanism. The requirement is not magnetism but a crystal structure that allows odd-order scattering asymmetry. As a concrete demonstration, Bernal-stacked bilayer graphene exhibits a large and gate-tunable nonreciprocal response near its Lifshitz transition — a purely nonmagnetic system with no applied field.

The impurities that degrade conductivity in the usual picture are the same impurities that create directional asymmetry here. The disorder is not noise obscuring the signal. It is the mechanism producing the signal.