Nonreciprocal critical currents without applying an external magnetic field have been observed recently in several superconductors, in various forms of graphene, a kagome compound and in an underdoped cuprate. A necessary requirement for this is that the usual supercurrent be accompanied by an antisymmetric chiral supercurrent, i.e., with the symmetry of a Hall current; equivalently that the superfluid density tensor have an antisymmetric chiral component. It also requires inversion breaking. The conditions for this phenomena are derived to find that their normal states must break time reversal and chirality and that the superconducting states must in addition be nonunitary. Each of the superconductors where spontaneous nonreciprocal critical currents are observed have shown some evidence for such broken symmetries in the normal state. The superconducting state of such materials have topological edge currents, but their projected electromagnetic part is in general not an integer. The edge states are protected in the superconductor due to a gap. The normal state should show a Kerr effect and, under ideal conditions, an anomalous Hall effect.

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• Hall effect
• Superconductivity
• Topological superconductors
• 2-dimensional systems
• Cuprates
• Graphene
• Kagome metal
• Bogoliubov-de Gennes equations