Layer-Parity Control of the Superconducting Diode Effect in Monolayer NbSe$_2$

Abstract

The superconducting diode effect is often associated with finite-momentum pairing, although model studies indicate that rectification reflects the asymmetry of the free energy about its minimum rather than the equilibrium pair momentum itself. Using a Wannier-based, self-consistent finite-$\mathbf Q$ Bogoliubov-de Gennes approach with a Fermi-surface-adaptive quadrature that converges the critical currents, we show that the layer parity and orientation of magnetic proximity select the diode response of monolayer NbSe$_2$. For in-plane exchange, the equilibrium pair momentum $\mathbf Q_{\rm eq}$ and the diode efficiency are both linear in the layer-odd exchange contrast: parallel proximity on the two Se sublayers is reciprocal, and antiparallel proximity doubles the response. An out-of-plane component separates the two observables. It leaves $\mathbf Q_{\rm eq}$ nearly unchanged but, through pair breaking, suppresses the efficiency by more than an order of magnitude and, at low temperature, reverses it. Purely out-of-plane exchange, for which $C_3$ symmetry forbids a helical term, keeps $\mathbf Q_{\rm eq}=0$ yet produces a trigonal diode effect, controlled by the layer-even exchange and larger than the in-plane one above $0.65$~meV at $0.58$~K. Magnetic layer parity thus selects between a helical and a trigonal diode channel. This trigonal channel provides a candidate intrinsic contribution to the field-free rectification reported in NbSe$_2$/CrBr$_3$. The model predicts that two-sided out-of-plane proximity cancels it when antiparallel and, at the same exchange per layer, enhances it about fourfold when parallel, in the computed range.