Diode effect in a skyrmion-coupled high-temperature Josephson junction

TL;DR

We address nonreciprocal superconducting transport in a planar Josephson junction formed by two $d$-wave superconducting leads with a skyrmion crystal underneath. The authors employ a tight-binding Bogoliubov–de Gennes framework to model a 2DEG with Rashba spin-orbit coupling and a spatially varying Zeeman field, deriving the current-phase relation $I_s(\varphi)=(2e/\hbar)\, d\mathcal{F}/d\varphi$ from the thermodynamic free energy $\mathcal{F}(\varphi)$ and mapping it to the resistively and capacitively shunted junction (RCSJ) model to obtain $I$–$V$ characteristics. They demonstrate strong nonreciprocity, with $|I_c^{+}| \neq |I_c^{-}|$ and diode efficiency up to approximately $\eta \approx 0.5$, tunable via Zeeman coupling $E_z$, chemical potential $\mu$, superconducting gap $\Delta$, and skyrmion radius $R_{Sk}$, facilitated by the emergent real-space gauge field of the skyrmion texture in conjunction with $d$-wave pairing. The work proposes a practical, gate-tunable, field-free superconducting diode platform compatible with planar fabrication and potential operation at higher temperatures using high-$T_c$ superconductors, opening avenues for reconfigurable superconducting circuits based on magnetic textures.

Abstract

We show that a planar Josephson junction having $d$-wave superconducting regions, with a skyrmion crystal placed underneath, produces a robust gate-tunable superconducting diode effect. The spatially-varying exchange field of the skyrmion crystal breaks both inversion and time-reversal symmetries, leading to an asymmetric current-phase relation with an anomalous phase shift. Our theoretical calculations, obtained using resistively and capacitively shunted junction model combined with Bogoliubov-de Gennes method, reveal that the diode efficiency is largely tunable by controlling external gate voltage and skyrmion radius. Incorporation of a $d$-wave superconductor such as high-$T_c$ Cuprate enables the diode to function at higher operating temperatures. Our results establish a unique and practically-realizable mechanism for devising tunable field-free superconducting diodes based on magnetic texture-superconductor hybrid platforms.

Figures (4)

• Figure 1: (a) Schematic of the planar Josephson junction with two $d$-wave superconducting regions separated by a non-superconducting channel. (b) Spin configuration of a skyrmion crystal, which is placed underneath the planar Josephson junction. The arrows represent the $x$ and $y$ components of the spin vector ${\bf S}_i$, while the colorbar represents the $z$ component. (c) Representative current-voltage characteristic of the superconducting diode, showing asymmetry in the critical currents in forward and reverse directions.
• Figure 2: (a) Calculated current--phase relations for different Zeeman couplings $E_z$ at fixed $\mu = 8.96~\text{meV}$. Increasing $E_z$ leads to stronger asymmetry and higher diode efficiency $\eta$. (b) Gate-tunable current–phase relations for varying chemical potential $\mu$ at fixed $E_z = 3.58~\text{meV}$.
• Figure 3: Simulated current-voltage characteristics using the RCSJ model. (a) Variation with Zeeman coupling at fixed $\mu = 8.96~\text{meV}$. (b) Variation with chemical potential at fixed $E_z = 3.58~\text{meV}$. Asymmetric switching currents confirm diode operation. Inset in (a) shows a representative diagram for RCSJ model.
• Figure 4: (a–d) Color maps of the diode efficiency $\eta$ as functions of Zeeman coupling $E_z$ and superconducting gap $\Delta$ at a fixed temperature $T = 0.1$ K. (a) For $\mu = 8.96~\text{meV}$ and $R_{\text{Sk}} = 100~\text{nm}$, $\eta$ exhibits an enhancement around $E_z \approx 3.58~\text{meV}$ and $\Delta \approx 4.0~\text{meV}$, reaching values up to $0.5$. The red rectangle highlights the region of maximal efficiency, which is magnified in panel (c) to show the high-$\eta$ domain. (b) For a lower chemical potential $\mu = 6.72~\text{meV}$ (at the same of $R_{\text{Sk}}$), the pattern of $\eta$ becomes more intricate, and the overall magnitude decreases, indicating a weaker diode response at lower carrier density. (d) For a smaller skyrmion radius $R_{\text{Sk}} = 50~\text{nm}$, the value of $\eta$ is reduced.