Field-free diode effects in one-dimensional superconductor: a complex interplay between Fulde-Ferrell pairing and altermagnetism

TL;DR

This work demonstrates field-free nonreciprocal superconducting transport in 1D by combining Fulde–Ferrell pairing with altermagnetism and spin–orbit coupling. By constructing two BdG models (Ising and Rashba SOC) and exploring three Josephson-junction setups, it shows that magnetochiral anisotropy arising from AM and FF pairing yields sizable SDE and JDE without external magnetic fields, with the crystallographic angle α providing a robust tuning knob for the diode efficiency. The study identifies parallel-spin AM components and complementary momentum functions as central to enabling SDE in 1D, and reveals ABS-dominated contributions to JDE that persist even when p-wave pairing is absent. Overall, AM-superconductor hybrids emerge as a promising, tunable platform for magnet-free diodes, with implications for quantum rectification and potential topological extensions.

Abstract

We investigate the emergence of nonreciprocal dissipationless supercurrents in one-dimension manifested through the superconducting diode effect (SDE) and the Josephson diode effect (JDE) in the absence of any external magnetic field, where inversion symmetry (IS) and time-reversal symmetry (TRS) can be intrinsically broken by spin-orbit coupling (SOC), and altermagnetism (AM), respectively. We investigate Ising and Rashba SOC separately in two models where two-component AM, assembled with crystallographic angle, can lead to qualitatively similar indirect band-gap closing and non-reciprocal supercurrent in a Fulde-Ferrell (FF) superconductor. Interestingly, in the absence of the above SOCs, SDE persists and the sign of efficiency can be altered by tuning the angle only. Parallel spin components with complementary momentum functions, ensuring the breaking of IS and TRS, can induce SDE in the presence of FF pairing. Continuing the analysis in the context of JDE, we explore the interplay between SOCs and AM with the p-wave and Fulde-Ferrell superconductivity in three different setups. The bulk bands contributes to the non-reciprocity in the case of p-wave superconductivity while JDE is dominated by Andreev bound states for FF superconductivity. Importantly, JDE continues to exist due to finite momentum Cooper pair even without AM and SOC unlike the p-wave superconductivity. The sign of JD efficiency can be tuned with angle for p-wave superconductivity while absence of such sign reversal is a hallmark signature of FF superconductivity. Similar to SDE, parallel spin components in conjunction with p-wave superconductivity can lead to JDE that can also be mediated by only FF pairing in the absence of SOC and AM.

Figures (16)

• Figure 1: We show $E_{\rm I}(k)$, derived from Eq. (\ref{['eq:2']}) and (\ref{['eq:4']}) for Model I low-energy Hamiltonian, for $(J_A,J)=(0,0), (0.2,0), (0.2,1.18),$ and $(0.2,-0.35)$ in (a), (b), (c), and (d), respectively. The plot (b) depicts the inner and outer circle crossings for $E_{\rm I}(K) = 7$. For this Ising Case: $k_o^-=-3.796$, $k_i^-=-2.572$, $k_i^+=+2.199$, $k_o^+=+5.103$. Parameters: $t=1$, $\mu=4$, $\Delta=3$, $\lambda=2$, $\alpha=0$.
• Figure 2: We show $E_{\rm II}(k)$, derived from Eq. (\ref{['eq:2']}) and (\ref{['eq:4']}) for Model II low-energy Hamiltonian, for $(J_A,J)=(0,0), (0.6,0), (0.6,1.18),$ and $(0.6,-0.75)$ in (a), (b), (c), and (d), respectively. The plot (b) depicts the inner and outer circle crossings for $E_{\rm II}(K) = 7$. For this Rashba Case: $k_o^-=-4.757$, $k_i^-=-2.247$, $k_i^+=+2.159$, $k_o^+=+5.347$. Parameters: $t=1$, $\mu=4$, $\Delta=3$, $\lambda=2$, $\alpha=0.125\pi$.
• Figure 3: We show $E_{\rm I}(k)$, derived from Eq. (\ref{['eq:2']}) and (\ref{['eq:3']}) for Model I lattice Hamiltonian, for $(J_A,J)=(0,0), (0.4,0), (0.4,0.35),$ and $(0.4,-1.18)$ in (a), (b), (c), and (d), respectively. Parameters: $t=1$, $\mu=0.6$, $\Delta=0.6$, $\lambda=1$, $\alpha=0$.
• Figure 4: We show $E_{\rm II}(k)$, derived from Eq. (\ref{['eq:2']}) and (\ref{['eq:3']}) for Model II lattice Hamiltonian, for $(J_A,J)=(0,0), (1.3,0), (1.3,0.55),$ and $(1.3,-1.95)$ in (a), (b), (c), and (d), respectively. Parameters: $t=1$, $\mu=0.2$, $\Delta=1$, $\lambda=1$, $\alpha=0.125\pi$.
• Figure 5: In (a), we show the variation of supercurrent $j_{\rm I}(q)$, derived from Eqs. (\ref{['eq:5']}), (\ref{['eq:6']}) for Model I low-energy Hamiltonian, with the finite momentum of the Cooper pair. In (b), we illustrate the heat-map of $\gamma_{\rm I}$ derived from Eq. (\ref{['eq:7']}) as a function of angle $\alpha$, and amplitude $J_A$ of altermagnet term. In (c,d), we display the variation of SD efficiency with $\mu$ and Ising SOC $\lambda$, respectively. We consider $\mu=-1.52$ for (a),(b) and (d). We choose $\lambda=1.97$ for (a),(b) and (c). We choose $\alpha=0.017\pi$ for (a),(c) and (d). Parameters: $t=1$, $\Delta=2.02$, $\beta=10000$.