Field-free Superconducting Diode Effect and Topological Fulde-Ferrell Superconductivity in Altermagnetic Shiba Chains

TL;DR

The study addresses the challenge of realizing topological superconductivity and a strong superconducting diode effect without external magnetic fields. It proposes a field-free platform based on a 1D Shiba chain on an s-wave superconductor proximized by a d-wave altermagnet, analyzed with a self-consistent Bogoliubov–de Gennes framework that yields a tunable Fulde–Ferrell state and Majorana zero modes, controllable via the injected current that sets the pairing momentum q. A key finding is a robust topological FF phase hosting Majorana modes, with a finite minigap δ_m and bulk polarization P_x = 0.5, whose topological region shifts with q, enabling current-driven switching. The same FF phase supports strong nonreciprocal transport, achieving diode efficiencies η up to ≈0.45 for helical textures and ≈0.35 for conical textures in a junction-free, field-free architecture, thanks to distinct symmetry-breaking mechanisms of altermagnetism. Overall, the work provides a scalable platform that combines topological Majorana physics with intrinsic superconducting diode functionality, with experimental feasibility in altermagnet–superconductor heterostructures and potential extensions to higher dimensions.

Abstract

The superconducting diode effect (SDE), characterized by a directional asymmetry in the critical supercurrents, typically requires external magnetic fields to break time-reversal symmetry -- posing challenges for scalability and device integration. Here, we demonstrate a field-free realization of the SDE in a helical Shiba chain proximitized by a $d$-wave altermagnet. Using a self-consistent Bogoliubov-de Gennes approach, we uncover a topological Fulde-Ferrell (FF) superconducting state that hosts tunable Majorana zero modes at the chain ends. The Cooper pair momentum is directly controlled by an externally injected supercurrent providing an experimentally accessible tuning parameter for driving and manipulating the topological FF phase. This state is stabilized by the interplay between the exchange coupling of magnetic adatoms and the induced altermagnetic spin splitting. Crucially, the same topological FF phase supports strong nonreciprocal supercurrents, achieving diode efficiencies exceeding $45\%$ without applied magnetic fields. The $d$-wave altermagnet plays a dual role: it intrinsically breaks time-reversal symmetry, enabling topological superconductivity, and introduces inversion symmetry breaking via momentum-dependent spin-splitting, driving the field-free SDE in a junction-free architecture. Our results establish the Shiba chain-altermagnet heterostructure as a promising platform for realizing topological superconducting devices with efficient, intrinsic superconducting diode functionality -- offering a scalable pathway towards dissipationless quantum technologies.

Figures (12)

• Figure 1: Schematic of an altermagnet-proximitized Shiba chain: A 1D chain of magnetic adatoms with noncollinear classical spins is placed on the surface of a 3D $s$-wave superconductor and proximally coupled to a $d_{x^2-y^2}$-wave altermagnet.
• Figure 2: FF ground state for a helical Shiba chain: (a) Self-consistent superconducting gap $\Delta(q)$ plotted as a function of the Cooper pair momentum $q$ for exchange coupling $J/\Delta_0 = 0.65$. (b) Optimal Cooper pair momentum $q_0$ corresponding to the FF ground state as a function of the proximity-induced altermagnetic field strength $J_A$. The model parameters used are: ($t/\Delta_0$, $g$, $U/\Delta_0$, $\mu/\Delta_0$, $(\beta \Delta_0)^{-1}$) = ($0.5$, $\pi/2$, $1.38$, $1.0$, $0.01$).
• Figure 3: Topological phase transition and the emergence of MZMs: (a) Bogoliubov quasiparicle energy spectrum under open boundary conditions as a function of Cooper pair momentum $q$, incorporating the self-consistently calculated pairing gap $\Delta(q)$ for exchange coupling $J/\Delta_0 = 0.65$ and altermagnetic exchange strength $J_A/\Delta_0 = 0.3$. (b) Spectrum plotted as a function of $J$ for fixed $q = -0.8$ and $J_A/\Delta_0 = 0.3$. The system exhibits three distinct phases: I) a trivial superconducting phase, II) a topological superconducting phase hosting MZMs, protected by a finite minigap $\delta_m$, and III) a normal phase where the superconducting order vanishes. Calculations are performed for a chain of 400 sites with model parameters: ($t/\Delta_0$, $g$, $U/\Delta_0$, $\mu/\Delta_0$, $(\beta~\Delta_0)^{-1}$) = ($0.5$, $\pi/2$, $1.38$, $1.0$, $0.01$).
• Figure 4: Topological signatures and local density of states (LDOS) of the MZMs: (a) Site– and energy–resolved LDOS profile clearly demonstrates strong localization of MZMs at the ends of the chain for fixed $q = -0.8$ and $J_A/\Delta_0 = 0.3$. The LDOS also shows the Shiba bands inside the superconducting gap separated by a minigap $(\delta_m)$. (b) Topological phase diagram showing the minigap $\delta_m$ as functions of $J_A$ and $q$. The white contour delineates the phase boundary separating the topological regime $(P_x=0.5)$ from trivial regime $(P_x=0)$, indicating that a finite minigap protects the MZMs. Other Model parameters are: ($t/\Delta_0$, $g$, $U/\Delta_0$, $\mu/\Delta_0$, $(\beta \Delta_0)^{-1}$, $J/\Delta_0$) = ($0.5$, $\pi/2$, $1.38$, $1.0$, $0.01$, $0.65$).
• Figure 5: Field-free SDE with a helical spin texture: (a) Supercurrent density $I(q)$ as a function of Cooper pair momentum $q$ for $J/\Delta_0 = 0.5$. Nonreciprocal behavior ($I(q) \ne -I(-q)$) arises only when both the magnetic exchange $J$ and the altermagnetic coupling $J_A$ are finite, leading to an asymmetry in critical currents $|I_c^+| \ne |I_c^-|$ and a nonzero diode efficiency $\eta \ne 0$. Here, $I_0 \equiv |I_c^+(J_A = 0)| = |I_c^-(J_A = 0)|$. (b) and (c): Diode efficiency $\eta$ as a function of $J$ (at fixed $J_A$) and $J_A$ (at fixed $J$), respectively. Model parameters: ($t/\Delta_0$, $g$, $\mu/\Delta_0$, $(\beta~\Delta_0)^{-1}$, $U/\Delta_0$) = ($1.0$, $2\pi/3$, $1.0$, $0.1$, $1.574$).