The Disordered Diode

Nonreciprocal charge transport — current flowing more easily in one direction than the other — is supposed to require broken time-reversal symmetry. Magnets do it. External magnetic fields do it. The connection seems fundamental: Onsager reciprocity relates transport coefficients to time-reversal, and breaking one breaks the other.

This paper identifies 42 crystal point groups where nonreciprocal longitudinal transport occurs without any time-reversal breaking at all.

The mechanism is disorder-induced asymmetric scattering. In crystals with sufficiently low symmetry, impurity scattering processes (skew-scattering and side-jump) generate a nonlinear longitudinal current that depends on the direction of the applied field. The key is that the nonreciprocity lives in the nonlinear response — the linear conductivity still obeys Onsager reciprocity. But at second order in the electric field, the crystal’s point group symmetry permits terms that distinguish forward from backward current.

Bilayer graphene in Bernal stacking demonstrates the effect concretely: a substantial, gate-tunable nonreciprocal response that peaks near the Lifshitz transition where the Fermi surface topology changes. No magnets, no magnetic field. Just the crystal symmetry and the disorder it contains.

The conventional wisdom was almost right: linear nonreciprocity requires time-reversal breaking. Nonlinear nonreciprocity does not. The diode effect was hiding in the second-order response of 42 crystal classes that were never checked because the linear theory said they couldn’t do it.