Field-Resilient Supercurrent Diode in a Multiferroic Josephson Junction

Abstract

The research on supercurrent diodes has surged rapidly due to their potential applications in electronic circuits at cryogenic temperatures. To unlock this functionality, it is essential to find supercurrent diodes that can work consistently at zero magnetic field and under ubiquitous stray fields generated in electronic circuits. However, a supercurrent diode with robust field tolerance is currently lacking. Here, we demonstrate a field-resilient supercurrent diode by incorporating a multiferroic material into a Josephson junction. We first observed a pronounced supercurrent diode effect at zero magnetic field. More importantly, the supercurrent rectification persists over a wide and bipolar magnetic field range beyond industrial standards for field tolerance. By theoretically modeling a multiferroic Josephson junction, we unveil that the interplay between spin-orbit coupling and multiferroicity underlies the unusual field resilience of the observed diode effect. This work introduces multiferroic Josephson junctions as a new field-resilient superconducting device for cryogenic electronics.

Figures (14)

• Figure 1: 2D Multiferroic NiI$_2$ and zero-field supercurrent diode effect in the NiI$_2$ vdW JJ.a, Crystal structure and multiferroic order of NiI$_2$, which consists of a spiral magnetic order (described by the wave vector $\vec{\mathbf{q}}$kuindersma_magnetic_1981) and an in-plane ferroelectric order ($\vec{\mathbf{P}}$kurumaji_magnetoelectric_2013). The yellow arrow on the Ni atoms represents the spin direction and the shaded area represents the spin spiral plane. b, Device geometry of the NiI$_2$ JJ. c, $V-I$ characteristic of the NiI$_2$ JJ. 0-p, p-0, 0-n, and n-0 refer to curves with current sweeping from 0 $\mu$A to $+1000$$\mu$A, $+1000$$\mu$A to 0 $\mu$A, 0 $\mu$A to $-1000$$\mu$A, and $-1000$$\mu$A to 0 $\mu$A. The critical current $I_{c+}$ (600 $\mu$A) and $I_{c-}$ (718 $\mu$A) are defined by the first critical jump in $V$ in the 0-p and 0-n (switching) curves, respectively. d, Demonstration of supercurrent rectification with $I_\text{bias}=\pm 650$$\mu$A. e, Comparison of zero-field supercurrent diode rectification efficiency ($\eta=\frac{I_{c+}-\lvert I_{c-}\rvert}{I_{c+}+\lvert I_{c-}\rvert}$) between the Gr JJ and the NiI$_2$ JJ under different current-sweeping and field-training protocols. The magnetic field was set to oscillate to zero from 3 T before performing the 0p0n0 and 0n0p0 measurements. The measurements for 0p0n0 and 0n0p0 tests are repeated five times to acquire error bars, which are smaller than the marker size for both cases. The 0p0n0 and 0n0p0 refer to opposite current-sweeping protocols, where a positive bias current is applied first in the 0p0n0 measurement and a negative bias current is applied first in the 0n0p0 measurement, respectively. The training fields $\pm H_\parallel = \pm 1$ T were used for both devices. The field training was performed at $T=10$ K.
• Figure 2: In-plane field dependence of the supercurrent diode effect in the NiI$_2$ JJ.a, Top panel: $V-I$ characteristic of the NiI$_2$ JJ with 0 mT $<H_\parallel<$ 24 mT, with a 2 mT field increment. Bottom panel: $V-I$ characteristic of the NiI$_2$ JJ with -24 mT $<H_\parallel<$ 0 mT. All plotted curves are switching curves (0-p and 0-n sweeps). b, Top panel: critical current $I_{c+}$ and $\lvert I_{c-}\rvert$ as a function of $H_\parallel$. The pink and cyan background represents the negative and positive field range, respectively. The yellow block marks the bipolar working field range of the supercurrent diode between $\pm10$ mT with a figure of merit $F_\text{R} = \Delta I_\text{R} \times \Delta H_\text{bpR} \sim 10^3\ \text{mT}\cdot \mu \text{A}$. Bottom panel: $\eta$ as a function of $H_\parallel$ of Gr JJ and NiI$_2$ JJ.
• Figure 3: Non-monotonic temperature dependence of supercurrent diode effect in the NiI$_2$ JJ.a, $V-I$ characteristic (switching curves) measured at different temperatures. b, $V-\lvert I \rvert$ characteristic recorded at $T\leq 5$ K. The solid and dashed lines represent 0-p sweep and 0-n sweeps, respectively. The critical transitions are pointed out by short black line segments with varied widths. c, $I_{c+}$ and $\lvert I_{c-}\rvert$ as a function of temperature. d, $\eta$ normalized by the maximum $\lvert \eta_{\text{max}} \rvert$ as a function of temperature for both NiI$_2$ JJ at zero field and Gr JJ at nonzero field. $\eta_{\text{max}}$ is -10 % and -20 % for NiI$_2$ and Gr JJ, respectively.
• Figure 4: Multiferroic JJ simulation.a, Schematic of the cross junction device where the supercurrent density $\bf J_s$ tends to reside near the surfaces of the superconducting electrodes. b, Schematic of the planar junction corresponding to the SC/helimagnet/SC cross-section marked by the red rectangle in panel $\bf a$. c, The simulated junction CPR with (solid) and without (dashed) RSOC for $\bf q \parallel \bf x$ and $\bf q \parallel \bf y$. Unless otherwise stated, parameters used in simulations are: $\Delta = 0.4 t$, $\mu = 1.57 t$, $\alpha_R = 0.004ta$, $J_{exc} = 0.3t$, $U_{barrier}= 4t$, $\vert \mathbf{q} \vert = 0.01 \frac{\pi}{a}$, $L_{x,s} = 300a$, $L_{x,n} = 3a$, $L_y = 10a$, and $\xi_{exc} = 5a$ where $t = \frac{\hbar^2}{2m^* a^2}$ and $a$ is the tight binding lattice constant. d, Diode rectification efficiency $\eta$ versus Zeeman splitting along $\bf x$ with RSOC for $\bf q \parallel \bf x$ and $\bf q \parallel \bf y$. e, Critical current difference $\Delta I_c = I_{c +} - \vert I_{c -} \vert$ versus temperature with RSOC. f, The simulated Andreev bound state spectrum for $\bf q \parallel \bf y$ and $B = 0$.
• Figure 5: Schematics and optical images of the reported superconducting devices.a-c, Side views of NiI$_2$ JJ, Gr JJ, and NbSe$_2$/NbSe$_2$ devices. d-f, Optical images of NiI$_2$ JJ, Gr JJ, and NbSe$_2$/NbSe$_2$ devices. The junction area of NiI$_2$ JJ with a lateral dimension of 2-3 $\mu$m is pointed out by the white arrow. The thickness of the following flakes was measured by AFM: NiI$_2$ in panel d: 2.8(2) nm (4ML); few-layer graphene in panel e: 4.0(2) nm. The thickness of the following flakes is estimated from the thickness of the flakes with similar color contrast measured by AFM: top NbSe$_2$ in panel d: $\sim$20 nm; bottom NbSe$_2$ in panel d: 30-40 nm; top NbSe$_2$ flake in panel e: $\sim$20 nm; bottom flake in panel e: 60-70 nm; both NbSe$_2$ flakes in panel f: $\sim$30 nm. Multiple colors can sometimes be seen in a single flake, and the thickness above provided the best estimation of the thickness near the junction area.