Spin transport in a normal meta-altermagnetic superconducting nanowire junction

Abstract: Spin triplet superconductors are considered a promising platform for dissipationless spin transport, where spin currents are carried by spin triplet Cooper pairs. In this paper, we propose that the spin triplet superconductivity and spin supercurrent can be engineered in an altermagnetic superconducting nanowire, where a one-dimensional nanowire is placed on the surface of an s-wave superconductor and in proximity to the altermagnet. Using the nonequilibrium Green's function method, we demonstrate a nonzero equal spin Andreev reflection coefficient at the normal metal-altermagnetic superconducting nanowire interface, thereby verifying the injection of spin triplet Cooper pairs. Furthermore, we systematically investigate the spin transport properties in this hybrid system under a spin bias. Our results demonstrate that these properties can be effectively tuned by the chemical potential and spin bias orientation. Our proposal provides a pathway toward realizing dissipationless spin transport.

• The paper demonstrates that equal-spin Andreev reflection processes enable tunable spin-triplet supercurrents controlled by bias orientation and altermagnetic alignment.
• Numerical analysis shows that adjusting the chemical potential and altermagnet strength maximizes spin injection efficiency and achieves quantized conductance of e/2π in the topological phase.
• The study reveals that SOC introduces additional triplet pairing channels, enabling Majorana zero modes and expanding the potential for superconducting spintronic devices.

Spin Transport in Normal Metal–Altermagnetic Superconducting Nanowire Junctions

Overview

The paper investigates spin transport phenomena in a junction formed between a normal metal and a one-dimensional (1D) nanowire that exhibits proximity-induced superconductivity and altermagnetism. By employing the nonequilibrium Green's function formalism and pairing correlation analysis, the authors rigorously characterize the injection of spin-triplet Cooper pairs and the resulting spin supercurrents. The work explores both the presence and absence of spin–orbit coupling (SOC), provides detailed numerical analysis, and discusses the sensitivity of spin transport to tunable physical parameters such as chemical potential and spin bias orientation.

Theoretical Framework and Model

A 1D nanowire is positioned atop an s-wave superconductor and adjacent to an altermagnet. The system is described by a tight-binding lattice Hamiltonian, which in the low-energy regime reduces to a Bogoliubov–de Gennes (BdG) model incorporating proximitized s-wave pairing, momentum-dependent altermagnetic splitting, and SOC. The normal metal lead is connected to the nanowire, facilitating injection of spin-polarized electrons.

The primary mechanisms for spin transport are (i) equal-spin Andreev reflection, which signifies the formation of spin-triplet Cooper pairs, (ii) spin-flip reflection, and (iii) quasiparticle tunneling. Due to the dissipationless nature of the superconducting state, only triplet pairing substantially contributes to long-range spin supercurrents.

Spin Transport Without SOC

In the absence of SOC, the triplet pairing correlations are aligned with the altermagnet's Néel vector (z-axis). Spin-triplet pairing exhibits the $|S=1, S_z=0\rangle$ symmetry, indicating pairing between electrons of opposite spin along z. No spin supercurrent is generated for bias along z, but rotating the spin quantization axis enables equal-spin triplet pairing when the bias is perpendicular to z, yielding nonzero equal-spin Andreev reflection.

Substantial numerical evidence shows that the equal-spin Andreev reflection coefficient can be maximized by adjusting the chemical potential and aligning the incident spin orientation perpendicular to the Néel vector. The spin conductance and spin injection efficiency are both highly tunable, but with efficiency nearly independent of the spin bias angle due to similar angular dependence in the dissipation channels.

Spin Transport With SOC

SOC introduces both $d_x$ and $d_y$ components to the triplet pairing (in addition to $d_z$), causing triplet pairing correlations to exist for arbitrary spin orientations. This enables injection of z-aligned spin supercurrents, even without rotating the bias. Key numerical results demonstrate that, upon entering the topological superconducting phase (identified by $(4tJ)^2 > \Delta^2 + (4t-p)^2$), the Andreev reflection peaks become pinned at zero energy with magnitude approaching unity, indicative of resonant Andreev reflection via Majorana zero modes.

Spin conductance reaches a quantized value of $e/2\pi$ in the topological phase, robust against bias direction, and the spin injection efficiency is maximized when the bias aligns with the Néel vector. Strong dependence of the spin injection efficiency is observed on the bias orientation owing to the SOC-induced anisotropy in the reflection coefficients. The ability to achieve quantized spin conductance through tuning chemical potential or altermagnet strength has direct implications for device design.

Comparison to Ferromagnetic Structures and Anisotropy

The comparison between altermagnetic and ferromagnetic systems reveals that the momentum-dependent altermagnetic splitting is fundamentally less detrimental to superconductivity than ferromagnetic splitting, due to its zero net magnetization and spatial anisotropy. This anisotropy imparts an additional control knob: the induced triplet pairing magnitude in the nanowire varies with its orientation relative to the altermagnet's band structure, including possible complete suppression for specific directions.

Numerical Results and Strong Claims

• The equal-spin Andreev reflection coefficient displays strong dependence on both chemical potential and altermagnet strength, with peak splitting increasing upon raising these parameters.
• SOC protection yields a robust superconducting gap, enabling topological phase transitions and quantized spin conductance ($e/2\pi$).
• Majorana-induced Andreev reflection dominates in the topological phase, with the spin supercurrent exhibiting nearly perfect injection efficiency under optimal bias orientation.
• Contradicting prior constraints, SOC allows injection of spin supercurrent along the Néel vector, expanding practical device architectures.

Practical and Theoretical Implications

These findings underpin several key implications:

• The engineering of dissipationless spin transport in superconducting nanowires proximitized by altermagnets provides a pathway toward integrated superconducting spintronic devices.
• Direct tunability of spin transport characteristics via chemical potential, altermagnet strength, and spin bias orientation offers flexibility for device optimization.
• The quantized spin conductance and its robustness in the topological phase facilitate reliable spintronic operation, while Majorana zero modes promise applications in quantum information.

Future theoretical extensions may focus on higher-dimensional altermagnetic structures, interplay of disorder, dynamical effects, and integration into on-chip architectures. Practically, advances in fabrication and control of altermagnetic superconducting nanowires will accelerate the development of superconducting spintronic platforms and topological quantum computing.

Conclusion

The paper provides a comprehensive analysis of spin transport in normal metal–altermagnetic superconducting nanowire junctions, establishing the existence and tunability of spin-triplet supercurrents via equal-spin Andreev processes. The results deepen understanding of spin superconductivity in proximitized systems and highlight the critical role of altermagnetic anisotropy and SOC in dictating spin injection and conductance properties. These findings open new avenues for design and realization of spintronic and topological devices (2606.20279).