Phase-sensitive non-reciprocal transport in high-temperature superconductor

Abstract

We propose the superconducting diode effect (SDE) in a planar s-wave/d-wave/s-wave Josephson junction as a direct phase-sensitive probe of the d-wave pairing function in high-Tc superconductors. Asymmetric interface coupling breaks inversion symmetry and induces a spontaneous Pi/2 phase difference, thereby breaking time-reversal symmetry without a magnetic field. In this TRS-broken state, the SDE emerges when single-Cooper-pair tunneling is enabled at the s-d interfaces, with its polarity and efficiency controllable by rotating the d-wave crystallographic orientation or perturbing its intrinsic C4 symmetry. Our results reveal a robust link between nonreciprocal Josephson transport and pairing symmetry, establishing the SDE as a powerful diagnostic tool for high-Tc superconductors and a tunable element for superconducting electronics.

Figures (4)

• Figure 1: (a) Schematic diagram of planar s-d-s Josephson junction with asymmetric s-d interface couplings $t_{c1}<t_{c2}$, $\theta$ the lobe angle of $d$-wave pairing function, $L_d$ the $d$-wave length. (b) Schematic diagram of s-d Josephson junction, with the potential $E\propto\cos2\phi$ at $\theta=\pi/4,\Delta_{ds=0}$. (c) Diode efficiency as a function of $\theta$ with different $\Delta_{ds}$, with $\theta_c$ the critical point for reversing the polarity of $\eta$.
• Figure 2: The 2D Josephson potential of s-d-s junction (normalized to 0.25) with the condition $\theta=\pi/4,t_{c2}=t_{c1}$ (a), $\theta=\pi/4,t_{c2}=4t_{c1}$ (b), $\theta=0.26\pi,t_{c2}=4t_{c1}$ (c), lower panels are the line-cut plot of the 2D potential, inset in (c) shows the current phase relation, (a)(b)(c) are calculated with $t_{c1}=0.25t, L_d=26a$, the dashed lines in lower panel (b) are calculated with $L_d=30a$. (d) With $\phi_2=\pi/2$, 1D Josephson potential $V_1(\phi_1)$ of s-d-s junction as a function of $\theta$, with $t_{c2}=4t_{c1}$. The solid lines are contour lines, the purple line is $V_1(\phi_1)=0$ (d) Diode efficiency as a function of $\theta$ and $d$-wave superconductor length $L_d$ with $\phi_2=\pi/2,3\pi/2$.
• Figure 3: (a) The Josephson potential of the s-d junction with $\theta/\pi=0.23,0.25,0.27$. (b) The leading Fourier coefficients $E_J^{(i)}(i=1,2,3,4)$ of the Josephson potential change with $\theta/\pi$, the red dashed line is proportional to $\cos2\theta$, the inset shows an enlargement near $\theta/\pi=0.25$. (a) and (b) are calculated at $t_c=0.62$. (c) The ratio of the coefficient $E_J^{(1)}/E_J^{(2)}$ changes with $t_c$ with $\theta/\pi$ ranging from 0.25 to 0.3 (lines with $E_J^{(1)}/E_J^{(2)}>0$) and 0.25 to 0.2 (lines with $E_J^{(1)}/E_J^{(2)}<0$), the inset shows the coefficients change with $t_c$ at $\theta/\pi=0.25,0.26$. (d) The minimal point $\phi_{\rm{min}}/\pi$ changes with $\theta$ and interlayer couplings $t_c$.
• Figure 4: For the s-d junction (a) $\theta=\pi/4$, the minimal point $\phi_{min}$ changes with $\Delta_{ds}/\Delta_d$; (b) The ratio of coefficient $|E_{J}^{(1)}/E_{J}^{(2)}|$ changes with $\theta$ with $\Delta_{ds}/\Delta_d=\pm10\%,\pm15\%$, the dots correspond to the dots in (c) and (d), dashed lines correspond negative values. For the s-d-s junction, the diode efficiency changes with $\theta$ and $L_d$ with $\Delta_{ds}/\Delta_d=-15\%$ (c), $15\%$ (d), the calculation is the same as that in Fig. \ref{['sds-jde']}(e).