Altermagnetism-induced non-collinear superconducting diode effect and unidirectional superconducting transport

Abstract

Current studies of non-reciprocal superconducting (SC) transport have centered on the forward-backward asymmetry of the critical current measured along a single axis. In most realizations, this diode effect is achieved via introducing ferromagnetism or applying an external magnetic field, which drives system into an effective Fulde-Ferrell (FF) state but often at the cost of severely suppressing the SC gap and thus compromising device robustness. Here we propose and theoretically demonstrate that coupling a conventional $s$-wave SC thin film to a $d$-wave altermagnet offers a more resilient alternative. The momentum-dependent spin splitting inherent to altermagnets induces a non-collinear SC-diode effect in the BCS state, with the critical-current anisotropy exhibiting a fourfold ($C_4$) symmetry. Upon entering the FF state at large splitting, this anisotropy gradually evolves into a unidirectional ($C_1$) pattern. Crucially, the FF pairing momentum locks to the discrete crystal axes, eliminating the rotational Goldstone mode and preserving a sizable SC gap without any abrupt or significant suppression. These combined features make the altermagnetic proximity an appealing platform to engineer symmetry-protected, energy-efficient and programmable SC diodes for next-generation electronic devices.

Figures (4)

• Figure 1: Schematic of spin-up and spin-down Fermi surfaces under ferromagnetic (left) and $d$-wave altermagnetic (right) spin splitting.
• Figure 2: Simulated order-parameter (OP) results for the optimal CM momentum $q_0$ and the corresponding practical SC gap $\Delta = \Delta_{\bf q=q_0}$ as functions of the spin-splitting strength for (a) ferromagnetic and (b)$d$-wave altermagnetic proximity. Insets: the $\Delta_{\bf q}$ landscape plotted in $q_x$–$q_y$ plane, which reflects the inverse of the free-energy profile. The plotted $q$ range extends up to $0.8q_0$ in each direction. $T=0.1~$K. Normalized parameters used here are: the zero-splitting gap $\Delta_0=2~$meV, coherence length $\xi_0 = v_F/\Delta_0$, and splitting unit $\gamma_0 = \Delta_0/k_F^2$.
• Figure 3: De-pairing critical current $J_{c}(\delta\phi)$ as a function of the current direction at various spin splittings. (a) and (b): results for ferromagnetic proximity at different strengths $\gamma_{s}/\gamma_0$ in BCS and FF regimes, respectively; (c) and (d): results for $d$-wave altermagnetic proximity at different strengths $\gamma_{d}/\gamma_0$ in BCS and FF regimes, respectively. The characteristic current scale $J_0=en_s/(m\xi_0)$ and then $J_c/J_0=p_{s,c}\xi_0$. The angle $\delta\phi=\phi_{\bf p_s}-\pi/4$ and we set $\phi_{\bf q_0}=\pi/4$ throughout.
• Figure 4: Temperature–splitting phase diagram of the (a) SC gap and (b) the optimal CM momentum. (c) Overall phase diagram, where the BCS, normal, and FF phases are indicated in blue, red, and green, respectively.