Supercurrent diode effect and magnetochiral anisotropy in few-layer NbSe2

Abstract

Nonreciprocal transport refers to charge transfer processes that are sensitive to the bias polarity. Until recently, nonreciprocal transport was studied only in dissipative systems, where the nonreciprocal quantity is the resistance. Recent experiments have, however, demonstrated nonreciprocal supercurrent leading to the observation of a supercurrent diode effect in Rashba superconductors. Here we report on a supercurrent diode effect in NbSe₂ constrictions obtained by patterning NbSe₂ flakes with both even and odd layer number. The observed rectification is a consequence of the valley-Zeeman spin-orbit interaction. We demonstrate a rectification efficiency as large as 60%, considerably larger than the efficiency of devices based on Rashba superconductors. In agreement with recent theory for superconducting transition metal dichalcogenides, we show that the effect is driven by the out-of-plane component of the magnetic field. Remarkably, we find that the effect becomes field-asymmetric in the presence of an additional in-plane field component transverse to the current direction. Supercurrent diodes offer a further degree of freedom in designing superconducting quantum electronics with the high degree of integrability offered by van der Waals materials.

Fig. 1. Supercurrent diode effect in a van der Waals superconductor.

a Scheme of the typical device. The central constriction is 250 nm wide and 250 nm long. The x-direction is chosen to be that of the supercurrent, i.e., the constriction axis. The z-direction is perpendicular to the crystal plane. The device is fabricated starting from a stack of hBN (≈10 nm, tens of layers), NbSe₂ (2, 3 or 5 layers) and again hBN (tens of layers). b Optical micrograph of sample B. The dashed white contour highlights the NbSe₂ crystal. Electrodes are fabricated by edge contact techniques^,,, while the constrictions are made by reactive ion etching. The yellow arrow indicates the supercurrent pathway. The scale bar corresponds to 5 μm. c Current–voltage characteristics (IVs) for opposite bias polarities (i.e., opposite current directions) measured on sample G in a 3-terminal configuration for zero out-of-plane field B_z. The sweep direction is always from zero to finite bias. A contact resistance R_c = 1 kΩ has been subtracted. d Similar measurements, but for B_z = 32.5 mT. Notice the difference between the two critical currents. e Same as in panel (d), but with opposite field orientation. Notice that the role of the two bias polarities now is swapped. f Absolute critical current for positive (black) and negative (red) bias as a function of B_z. Each value is the average of 10 consecutive measurements. The critical current is maximal for a nonzero B_z, namely for $\mid B_z\mid =B_{\max ,I_c}\approx 10$ mT (black and red arrow). The red and black solid line are guides to the eye, mutually symmetric upon reflection around B_z = 0. g Supercurrent rectification efficiency $Q\equiv 2\left(I_c^{+}-\mid I_c^{-}\mid \right)/\left(I_c^{+}+\mid I_c^{-}\mid \right)$, plotted versus B_z. Q is maximal for $B_z=B_{\max ,Q}\approx 35$ mT (arrow). Measurements in (c–g) were performed at 1.3 K. As discussed in the Supplementary Information, an offset of −2.5 mT and 0.17 μA has been removed from B_z and I_c, respectively.

Fig. 2. Supercurrent diode effect versus in- and out-of-plane field.

a The color plot shows $Q\equiv 2\left(I_c^{+}-\mid I_c^{-}\mid \right)/\left(I_c^{+}+\mid I_c^{-}\mid \right)$ as a function of out-of-plane (B_z) and in-plane (B_ip) field, measured in sample F for θ = 90^∘ (i.e., for B_ip⊥I). B_z here includes both the field produced by the orthogonal coils and the finite z-component of B_ip arising due to misalignment. Red and blue arrows indicate the areas where the diode effect is enhanced. b Similar measurements, but for θ = 0^∘. c As in (b), but for θ = −90^∘. Notice that this graph can be mapped onto that in (a), provided that B_ip → −B_ip. The color contrast is the same in (a), (b) and (c). d Absolute value of $I_c^{+}$ (black) and $I_c^{-}$ (red) plotted versus B_z, for B_ip = 0 and for the sample orientation θ = −90^∘. e As in (d), but for B_ip = 2 T. Note that data in (d, e) were measured in a different session (with higher resolution in B_z) compared to data in c. f Supercurrent rectification efficiency Q as a function of B_z at θ = −90^∘ for B_ip = −2 T (green), 0 T (gray), and 2 T (magenta). Here, we used the same data as in panel c, for B_ip values indicated in the legend. For B_ip = 0 we have substituted three outliers (for B_z = −48, −64 and −80 mT) with the corresponding values for the adjacent in-plane field B_ip = −0.25 T. For B_ip = −2 T we have substituted one outlier (for B_z = −43 mT) with the corresponding value for the adjacent in-plane field B_ip = −1.75 T, see Supplementary Information. Outliers are also visible in panels (a–c). All measurements reported in this figure were performed at 500 mK.

Fig. 3. Temperature dependence of the supercurrent diode effect.

The graph shows the temperature dependence of S ≡ Q/B_z for sample D, F, and G. S is evaluated from linear fits of Q(B_z) near B_z = 0, i.e. in the linear regime of the supercurrent rectification efficiency, where Q ∝ B_z. The error bars correspond to the standard error of the fits. The S values are normalized to the lowest temperature value S_LT (e.g. 17.2 T⁻¹ for sample G), while the temperatures are normalized to the critical temperature T_c of the corresponding sample. Orange, blue and purple symbols refer to sample D, F and G, where the critical temperature of the constriction region is 4.3 K, 2.25 K and 4.0 K, respectively.