Nonreciprocal charge transport — current flowing more easily in one direction than the other — requires broken time-reversal symmetry. This means magnets, magnetic fields, or magnetic order. The rectification effect in a p-n junction diode, for instance, relies on the built-in electric field across the junction, and magnetoresistive effects require applied fields. The connection between directionality and broken symmetry is textbook physics.

Except in 42 crystal point groups, where disorder alone is sufficient.

The finding: longitudinal nonreciprocal transport can arise in nonmagnetic conductors through plain disorder-induced asymmetric scattering. No magnetic field, no magnetic ordering, no broken time-reversal symmetry in the conventional sense. The crystal symmetry permits a directional bias, and disorder — random impurities, defects, surface roughness — provides the scattering asymmetry that realizes it.

The mechanism is subtle. Time-reversal symmetry is not broken globally. The crystal structure, combined with the scattering geometry, creates situations where forward-propagating and backward-propagating electrons encounter different effective scattering cross-sections. The asymmetry is not in the Hamiltonian but in the scattering matrix, where the combination of crystal symmetry and disorder breaks the reciprocity that clean systems preserve.

This inverts the usual role of disorder in transport theory. Disorder is standardly treated as noise — something that reduces conductivity uniformly in both directions, smearing out clean features and degrading performance. Here, disorder is a symmetry-breaking resource. The random scatterers, in the context of the right crystal symmetry, produce a directional bias that perfectly ordered crystals cannot achieve.

The practical implication: nonreciprocal devices (rectifiers, diodes, isolators) may be achievable in nonmagnetic materials by engineering disorder rather than applying fields. The 42 point groups that permit this effect include common crystal classes, meaning the phenomenon is not exotic but widespread — just overlooked because the standard theoretical framework assumes disorder is symmetric.