$p$-wave magnet driven field-free Josephson diode effect

Recently, the superconducting diode effect (SDE), characterized by unequal critical currents in opposite directions, has been observed experimentally and predicted theoretically in models of bulk superconductors and Josephson junctions (JJs). In this work, we construct a Josephson junction using a recently discovered unconventional coplanar magnet, the $p$-wave magnet (PM), with proximity-induced superconductivity, and demonstrate the emergence of a Josephson diode effect (JDE). The barrier region is formed by another unconventional collinear magnet, namely an altermagnet (AM). We illustrate that apart from time-reversal and inversion symmetries, the mirror operation $M_{yz}$ emerges as the key symmetry constraint. Also, unlike earlier models that realize the JDE using unconventional magnets, this setup does not require Rashba spin-orbit coupling (SOC) or different superconductors across the junction. Moreover, we demonstrate that the realization of the JDE in this framework requires only minimal conditions while maintaining high performance. The effect remains robust across a broad parameter regime, and thus making the system particularly promising for applications in quantum circuits and computing technologies.

💡 Research Summary

The paper presents a theoretical proposal for a field‑free Josephson diode effect (JDE) based on a planar Josephson junction (JJ) that incorporates two recently discovered unconventional magnetic phases: a p‑wave magnet (PM) and an altermagnet (AM). The left and right superconducting leads are formed by proximity‑inducing superconductivity in a p‑wave magnet (referred to as PMSC), while the barrier region consists of an altermagnet. The authors emphasize that, unlike earlier proposals, the device does not require Rashba spin‑orbit coupling (SOC), external magnetic fields, or different superconductors on the two sides. The essential symmetry breaking involves time‑reversal (T), inversion (I), and, crucially, the mirror operation M_yz. When M_yz is broken by the combined effect of the p‑wave spin‑splitting in the PM and the exchange‑field‑induced hopping in the AM, the current–phase relation (CPR) becomes highly non‑sinusoidal, leading to distinct positive and negative critical currents (I_c⁺ ≠ I_c⁻) and thus a diode effect.

The model is built on a tight‑binding square lattice. The Bogoliubov‑de Gennes Hamiltonian for the PMSC region includes spin‑dependent hopping t_PMj that generates p‑wave symmetric spin splitting, a conventional hopping t_PM, chemical potential μ, and an isotropic s‑wave pairing Δ₀ with a controllable phase ϕ. The AM Hamiltonian contains a standard kinetic term (t_AM), an exchange field term t_AMj that depends on the crystallographic “lobes” angle α, a gate‑controlled onsite potential U, and optionally a Rashba SOC term λ. The full junction Hamiltonian is H_JJ = H_PMSC + H_AM + H_CL + H_CR, where H_CL and H_CR describe the coupling between the leads and the barrier.

The Josephson current is obtained from the time derivative of the particle number operator in the left lead, which reduces to a trace over the product of the coupling Hamiltonian and the lesser Green’s function. The lesser Green’s function is computed via the standard relation G⁽<⁾ = –f(E)