Perfect supercurrent diode efficiency in chiral nanotube-based weak links

TL;DR

This paper addresses the challenge of achieving perfect dc Josephson diode behavior by modeling a chiral nanotube-based weak link with a Ginzburg-Landau formalism. It reveals a purely orbital anomalous phase $\phi_0$ emerging under an axial magnetic field, while the supercurrent diode effect is dominated by a non-reciprocal persistent current protected by fluxoid quantization, allowing the diode efficiency $\eta$ to approach unity when extrinsic flux terms dominate intrinsic stiffness. The work provides both numerical and analytical insights (short-junction limit) that demonstrate near-perfect to perfect diode efficiency without relying on higher-order pair tunneling, and it discusses practical routes to realize such devices in carbon nanotube–based systems. These results offer a new mechanism for engineering high-efficiency superconducting diodes and establish clear parameters for experimental realization, including the roles of anisotropic superfluid stiffness and flux quantization.

Abstract

The supercurrent diode effect (SDE) describes superconducting systems where the magnitude of the superconducting-to-normal state switching current differs for positive and negative current bias. Despite the ubiquity of such diode effects in Josephson devices, the fundamental conditions to observe a diode effect in a Josephson junction and achieve perfect diode efficiency remain unclear. In this work, we analyze the supercurrent diode properties of a chiral nanotube-based Josephson junction within a Ginzburg-Landau theory. We find a diode effect and anomalous phase develop across the junction when a magnetic field is applied parallel to the tube despite the absence of spin-orbit interactions in the system. Unexpectedly, the SDE in the junction is independent of the anomalous phase. Alternatively, we determine a non-reciprocal persistent current that is protected by fluxoid quantization can activate SDE, even in the absence of higher-order pair tunneling processes. We show this new type of SDE can lead to, in principle, a perfect diode efficiency, highlighting how persistent currents can be used to engineer high efficiency supercurrent diodes.

Figures (4)

• Figure 1: Chiral nanotube-based supercurrent diode: (a) Schematic of voltage-current curve of a supercurrent diode having a negative diode polarity. (b) Cartoon of the ChNt-JJs and the helical persistent current inducing the Josephson diode effect. (c) Schematic of $\mathcal{C}_2$-symmetric Fermi surface. (d) Illustration of chiral nanotube on a square lattice.
• Figure 2: Approaching perfect supercurrent diode efficiency: (a) $\eta$ versus $\hat{\Phi}$ for various ratios of $L/R$, $m_1/m_0 = 100$, and $\theta = 0.1\pi$. (b) $\eta$ versus $\theta$ for $\hat{\Phi} = 0.1,~0.2,~0.3,~0.4$, $m_1/m_0 = 100$, and $L/R=10^{-3}$. (c) $\eta$ versus $m_1$ for various ratios of $L/R$ and with $\hat{\Phi} = 0.1$ and $\theta = 0.1\pi$. (d) CPR of the junction for various ratios of $L/R$ with $\hat{\Phi} = 0.1$, $m_1/m_0 = 100$, and $\theta = 0.1\pi$ using the normalization $I_c = \frac{4e\hbar \rho_1 \psi_{\infty}^2 A_{\perp}}{L}$. We numerically solved Eq. (\ref{['eq:Jnt_2']}-\ref{['eq:GLnt_2']}) as described in the main text with $\frac{\hbar^2}{m_0 \zeta_0 L^2} = 2 \times 10^{-3}$, $\frac{\hbar^2 m_0}{m_1^2 \zeta_0 L^2} = \frac{\hbar^2 m_0}{m_1^2 \zeta_0 L^2} = 2 \times 10^{-4}$, and $\frac{\alpha m_0 L^2}{\hbar^2} = 10^{-4}$.
• Figure 3: Non-reciprocal persistent supercurrent: Phase-integrated CPR over a $2\pi$ cycle versus (a) $\hat{\Phi}$ for various ratios of $L/R$, and (b) $\theta$ for $\hat{\Phi} = 0.1,~0.2,~0.3,~0.4$ using the normalization $I_c = \frac{4e\hbar \rho_1 \psi_{\infty}^2 A_{\perp}}{L}$. Here we used numerically solved Eq. (\ref{['eq:Jnt_2']}-\ref{['eq:GLnt_2']}) as described in the main text with $m_1/m_0 = 100$, $\frac{\hbar^2}{m_0 \zeta_0 L^2} = 2 \times 10^{-3}$, $\frac{\hbar^2 m_0}{m_1^2 \zeta_0 L^2} = \frac{\hbar^2 m_0}{m_1^2 \zeta_0 L^2} = 2 \times 10^{-4}$, and $\frac{\alpha m_0 L^2}{\hbar^2} = 10^{-4}$.
• Figure 4: Optimizing diode efficiency: (a) $\vert \eta \vert$ versus $\theta$ in polar coordinates for $\hat{\Phi}=0.5$ and $L/R = 10$. (b) $\eta$ versus $I_0 / I_c$. $\eta$ versus $\theta$ for $\hat{\Phi}=0,~0.1,...,~0.5$ with (c) $L/R = 10$ and (d) $L/R = 1$. Here we used $m_1/m_0 = 5$, $\kappa_1 m_1 / R^2 = 50$, and $\lambda m_1 / R^2 = 10$ in Eq. (\ref{['eq:diode_eff']}).