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

Abstract

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.

Figures (6)

• Figure 1: (a) Schematic representation of a JJ consisting of the PMSC leads separated by an AM barrier. The red and green lattice sites in the PMSC denote the 'A' and 'B' sublattices, respectively, while the black lattice sites belong to the AM region. Tunneling between PMSC and AM is assumed to be nearest neighbor only and hence, hopping is in AM lattice sites and their adjacent PMSC sublattice sites. (b) and (c) show the schematic Fermi surfaces of the PMSC and AM, respectively, where the red and blue contours correspond to spin-up and spin-down bands.
• Figure 2: (a) CPR plots for different crystallographic angles of AM, $\alpha=0$ (blue), $0.1\pi$ (orange), and $0.3\pi$ (green), demonstrating nonreciprocal critical currents ($|I_C^{+}|\neq|I_C^{-}|$) . (b) CPR plots for different gate potentials in the AM region at $\alpha=0$: $U=0$ (blue), $U=0.2$(orange) and $U=-0.2$(green). Other system parameters are $t_j^{PM}=0.35$, $t_j^{AM}=0.2$, $t_0=1$, $\mu=-2$, and the length of the left and right SCs are taken as $N_x^{L(R)}=80$. The junction width is fixed at $N_{y}=6$ and the AM barrier length is $L_{x}^{AM}=5a$
• Figure 3: (a-d) Variation of $\eta$ with (a) AM exchange field strength, $t_j^{AM}$, (b) PM exchange field strength, $t_{j}^{PM}$, (c) crystallographic lobe angle of AM, $\alpha$ and (d) Rashba Strength, $\lambda$. We consider $N_{x}^{L/S}=80$, $N_{x}^{AM}=5$ and $N_{y}=6$. In (a), (b), and (d), $\alpha=0$ and $\lambda=0$ for (a-c). $t_{j}^{PM}=0.2$ is set for (a), $t_{j}^{AM}=0.4$ for (b), $t_{j}^{PM}=0.35$ and $t_{j}^{AM}=0.2$ for (c) and $t_{j}^{PM}=0.1$ and $t_{j}^{AM}=0.4$ for (d)
• Figure 4: (a-c) are contour plots of $\eta$(as colorbar) with $t_j^{AM}$ and $t_{j}^{PM}$ for both SC of ABAB.. configuration. (d-f) are corresponding contour plots for ABAB.. and BABA.. configuration of SC leads. Other parameters are $\alpha=0$ for (a,d), $\alpha=0.05\pi$ for (b,e), $\alpha=0.1\pi$ for (c,f), $N_{x}^{L/R}=80$, $N_{x}^{AM}=5$, $N_{y}=6$ and $\lambda=0$.
• Figure 5: Schematic of a Josephson junction comprising $90^{0}$ rotated PMSC leads separated by an AM barrier. At the left interface, both A and B sublattices of the PMSC are coupled to a nearest single AM lattice site.[Fukaya2025]