This paper explains how a magnetic field can make certain two-dimensional superconductors conduct electricity better in one direction than the other. The effect appears in “Ising” superconductors, a class of atomically thin materials where a strong spin-orbit interaction pins electron spins out of the plane. The authors show that an in-plane magnetic field deforms that pinned spin pattern and converts ordinary singlet Cooper pairs into equal-spin triplet pairs. When the mirror symmetry of the monolayer is broken by a substrate or gate, those field-induced triplets produce an intrinsic superconducting diode effect.

The authors build a symmetry-aware two-component Ginzburg–Landau (GL) theory that couples the usual singlet order to a triplet order parameter. They derive every coefficient of that GL functional from a microscopic model of an Ising superconductor, including a small Rashba (asymmetric) spin-orbit term to represent the effect of a supporting substrate or electric gate. A key technical point is that the odd-in-momentum terms of the GL expansion, called Lifshitz invariants, appear once the triplet component is present and the basal mirror symmetry is broken. Those Lifshitz terms make the superconducting state prefer a finite Cooper-pair momentum and, when treated to the proper order, produce unequal critical currents in opposite directions — the diode response.

Why this matters: the mechanism gives a route to a sizable intrinsic diode effect that is controlled by the ratio of the Zeeman energy (the energy scale set by the applied magnetic field) to the Ising spin-orbit energy. That ratio does not involve the large Fermi-energy scale and so can be much larger than the small parameter that limits parity-mixing mechanisms based on band splitting. Practically, this means materials such as monolayer NbSe2, TaS2, or gated MoS2 could show a prominent intrinsic diode response when their basal mirror symmetry is lifted. The theory also predicts that an attractive triplet interaction changes the diode behavior: at low fields it can reduce efficiency by destructive interference, while at higher fields it can extend the diode regime well beyond the singlet-only critical field and boost the maximal efficiency along a triplet-enhanced phase boundary.