Abstract
Non-reciprocal electronic transport in a spatially homogeneous system arises from the simultaneous breaking of inversion and time-reversal symmetries. Superconducting and Josephson diodes, a key ingredient for future non-dissipative quantum devices, have recently been realized. Only a few examples of a vertical superconducting diode effect have been reported and its mechanism, especially whether intrinsic or extrinsic, remains elusive. Here we demonstrate a substantial supercurrent non-reciprocity in a van der Waals vertical Josephson junction formed with a Td-WTe2 barrier and NbSe2 electrodes that clearly reflects the intrinsic crystal structure of Td-WTe2. The Josephson diode efficiency increases with the Td-WTe2 thickness up to critical thickness, and all junctions, irrespective of the barrier thickness, reveal magneto-chiral characteristics with respect to a mirror plane of Td-WTe2. Our results, together with the twist-angle-tuned magneto-chirality of a Td-WTe2 double-barrier junction, show that two-dimensional materials promise vertical Josephson diodes with high efficiency and tunability.
Similar content being viewed by others
Introduction
The non-reciprocal behavior in dissipative current flows, known as the diode effect, has played a central role in modern electronic devices and circuits1,2. In conventional schemes, non-reciprocity along the current direction arises from spatial inhomogeneity1,2. Recently, it has been shown that when inversion and time-reversal symmetries are both broken, and in combination with a spin-orbit interaction (SOI), even spatially homogeneous systems can provide for diode functionality3,4,5. By implementing this magneto-chirality with superconductors (SCs) and matching the superconducting gap with the SOI energy6,7, one can achieve a directional, non-dissipative, supercurrent flow, which is a prerequisite for the realization of future superconducting quantum devices.
To date, several methods at the materials and device levels have been developed to intrinsically and/or extrinsically break the inversion symmetry. For example, via artificially patterned conformal arrays of nanoscale holes in a MoGe film8, via ionic-liquid gating of two-dimensional (2D) MoS2 flakes, and via the formation of non-centrosymmetric V/Nb/Ta superlattices or using a few layers of 2H-NbSe2 have enabled the observation of non-reciprocal critical currents near their corresponding superconducting transition temperatures Tc9,10,11. Notably, non-reciprocity in Josephson supercurrents have also been realized in lateral Josephson junctions (JJs) with structures: Al/InAs 2D electron gas (2DEG)/Al7, Nb/proximity-magnetized Pt/Nb12, Nb/NiTe2 type-II Dirac semimetal/Nb13, three-terminal Al/InAs 2DEG/Al JJs14. To break the inversion symmetry, the first two utilize a Rashba(-type) superlattice and barrier, respectively, the third one exploits topological surface states in a NiTe2 barrier, whereas the last one employs the geometric breaking of the device’s inversion symmetry by the presence of third terminal. On the other hand, there have been only a few relevant studies on vertical JJs. A field-free Josephson diode effect has been recently observed in vertical NbSe2/Nb3Br8/NbSe2 junctions15, but the non-reciprocal supercurrents appear in the direction along which the inversion symmetry is broken and the diode polarity is, moreover, independent of an applied magnetic field, making investigations of other devices highly desirable to unravel the role of van der Waals barriers. Moreover, whether or not there can be an intrinsic Josephson diode effect in such vertical junctions is the outstanding quest in this increasing research field of supercurrent non-reciprocity.
Very recent studies16,17 on the Al/InAs 2DEG/Al lateral junctions have investigated a possible correlation between the bulk inversion symmetry breaking (i.e. Dresselhaus-type) and the supercurrent non-reciprocity. In the case of interface inversion symmetry breaking (i.e. Rashba-type), the associated spin-orbit (SO) field in k-space is fundamentally isotropic16. When the Josephson barrier possesses the Dresselhaus-type symmetry breaking in addition to the Rashba-type symmetry breaking, the overall SO field becomes anisotropic, making the magneto-chiral anisotropy of supercurrent non-reciprocity dependent of the Josephson barrier’s crystal structure16. However, the strength of Dresselhaus-type SO field in such lateral devices turns out to be quite small (<10% at most) as compared with that of Rashba SO field. For this reason, to the best of our knowledge, the lateral device geometry is less suited for the investigation of supercurrent non-reciprocity derived solely from the bulk inversion symmetry breaking of the Josephson barrier.
Here, we utilize Td-WTe2 single-crystal exfoliated flakes as an inherently inversion symmetry breaking barrier in van der Waals (vdW) JJs and through extensive measurements of the Td-WTe2 flake thickness, magnetic field strength/angle and temperature dependences, we demonstrate that the supercurrent non-reciprocity along the vertical direction is intimately connected and is highly dependent on the crystal structure of the Td-WTe2 barrier, thereby allowing a clear distinction between intrinsic and extrinsic mechanisms7,12,13 and providing the experimental realization of the intrinsic JDE that results purely from the bulk inversion symmetry breaking of the Td-WTe2 barrier. Our study establishes that the co-existence of the magneto-linearity, the magneto-chirality and the thickness and temperature-scaleable diode efficiency constitute the intrinsic supercurrent non-reciprocity, coupled to the crystal structure of a vdW barrier.
Results
As illustrated in Fig. 1a, we fabricate vdW vertical JJs, in which a Td-WTe2 flake (2−60 nm thick) is sandwiched between two superconducting 2H-NbSe2 flakes, in an inert atmosphere glovebox using dry transfer techniques (see Methods for details). Here, we employed the NbSe2 flakes thicker than 10 nm (16−17 \(\times\) the monolayer thickness) to preclude the unintended contribution of Ising Cooper paring18 to the non-reciprocal transport properties of WTe2 JJs. Note that Td-WTe2 itself exhibits highly interesting physical properties including a type-II Weyl semi-metallic behavior19, higher-order topological hinge states20 and quantum spin-Hall edge states21. In the present study, we focus on how the crystal inversion symmetry of Td-WTe2 is reflected in a vertical Josephson diode effect. Due to the lack of a screw rotational symmetry in Td-WTe2 from the Te atoms, the orthorhombic phase Td-WTe2 is non-centrosymmetric20,22,23. The mirror-symmetry plane of Td-WTe2 along the b-axis (green plane in Fig. 1b) creates a polar axis, that is, an internal crystal electric field \({\varepsilon }_{{cr}}\)22 and together with the heavy W atoms provide a strong SOI. This, in conjunction with an external in-plane (IP) magnetic field \({\mu }_{0}{H}_{\parallel }\), that breaks the time reversal symmetry, allows for an anomalous phase \({\varphi }_{0}\) to be created in the current-phase relationship (CPR) of the vertical JJ24,25,26. As previously discussed theoretically24,25,26, the presence of a finite \({\varphi }_{0}\) is essential to generate a rectified Josephson supercurrent, namely, unequal positive and negative Josephson switching supercurrents \({I}_{c}^{+} \, \ne \, {I}_{c}^{-}\)7,12.
Below, we will separate a crystal-asymmetry-driven intrinsic diode effect from other extrinsic possibilities in the following manner. When the dc bias current I is applied along the vertical direction (// c-axis) and the IP magnetic field is applied in the a-b plane of the WTe2 (blue plane in Fig. 1b), the Josephson diode efficiency \(\eta=\frac{{I}_{c}^{+}-|{I}_{c}^{-}|}{{I}_{c}^{+}+|{I}_{c}^{-}|}\) is given by \({\eta \propto \varphi }_{0}\propto {\mu }_{0}{H}_{\parallel }\cdot \sin ({\theta }_{{MC}})\). Here \({\theta }_{{MC}}\) is the relative angle between the polar axis (// b-axis) of WTe2 and the applied \({\mu }_{0}{H}_{\parallel }\)7,24,25,26. The magneto-linearity (\(\propto {\mu }_{0}{H}_{\parallel }\)) and the magneto-chirality [\(\propto \sin ({\theta }_{{MC}})\)] of \(\eta\) are key measures of the intrinsic Josephson diode effect.
Figure 1c displays representative current-voltage (I–V) curves for a NbSe2/Td-WTe2/NbSe2 vdW JJ formed with a 23-nm-thick Td-WTe2 barrier. I–V curves are shown when \({\mu }_{0}{H}_{\parallel }\) = 0 (black), +6 (orange) and −6 (green) mT are applied at a fixed \({\theta }_{{MC}}\) ≈ 86.6o (\(\theta\) = 45o). These measurements are performed at 20 mK, far below the junction’s Tc \(\approx\) 5 K. \(\theta\) is the angle of \({\mu }_{0}{H}_{\parallel }\) relative to an edge of the Si wafer on which the exfoliated layers were placed: the wafer had been cut into a rectangular shape to define a clear reference direction. Note that \({\theta }_{{MC}}\) in Fig. 1c is determined from comparison of the \({\mu }_{0}{H}_{\parallel }\) angular dependence of \(\eta\) of JJ with polarization-resolved Raman spectra (see Supplementary Information S3 for details). It is clear that a critical current asymmetry (\(\triangle {I}_{c}={I}_{c}^{+}-\left|{I}_{c}^{-}\right|\ne 0\)) is only developed when \({\mu }_{0}{H}_{\parallel }\) is non-zero and that the polarity of \(\triangle {I}_{c}\) is inverted when the direction of \({\mu }_{0}{H}_{\parallel }\) is reversed. These features correspond to a Josephson diode effect. Note that since our Td-WTe2 barrier JJs show a weak hysteresis in the I–V curves, indicating overdamped characteristics and the ignorable re-trapping, these can thus be the best example of experimental investigating the intrinsic Cooper-pair tunneling non-reciprocity by circumventing the unintentional contribution of quasiparticle tunneling25 to the non-reciprocity.
The magneto-linearity of \(\eta (\propto {\mu }_{0}{H}_{\parallel })\) is first checked by measuring how \({I}_{c}^{+}\) and \(\left|{I}_{c}^{-}\right|\) vary with the strength of \({\mu }_{0}{H}_{\parallel }\) for a fixed \({\theta }_{{MC}}\ne\) 0o (\(\theta\) = 0o). From a comparison of\(\,\left|{I}_{c}({\mu }_{0}{H}_{\parallel })\right|\) and \(\eta ({\mu }_{0}{H}_{\parallel })\) for several values of the thickness of WTe2 (2, 7, and 60 nm) (Fig. 2a−f), three notable features are revealed. First, for all the JJs, \(\eta\) increases linearly with increasing \({\mu }_{0}{H}_{\parallel }\) up to a certain critical field, above which \(\eta\) starts to decay (Fig. 2d−f). Second, when this field coincides with the first-order minimum field of the Fraunhofer interference pattern, \(\eta\) decays in a complex way with an accompanying sign change (Fig. 2b, c, e, and f). Third, the slope of the low-field \(\eta ({\mu }_{0}{H}_{\parallel })\) data (Fig. 2d−f) depends critically on the orientation of the polar axis of the WTe2 with respect to the applied \({\mu }_{0}{H}_{\parallel }\). While the first and second features are qualitatively similar to previous studies on Al/2DEG/Al7 and Nb/NiTe2/Nb13 lateral JJs, the third, signifying the magneto-chirality of \(\eta [\propto \sin ({\theta }_{{MC}})]\), is a new finding from the NbSe2/WTe2/NbSe2 vertical JJs. Note that no signature of fast oscillations, often attributed to topological edge states of WTe227, are detected in measurements of the magnetic-field interference patterns for our vertical JJs (Fig. 2a−c). This is in agreement with theoretical considerations that topological edge states, that reside on the a-b planes of WTe228, may contribute to lateral transport29,30 but not to vertical transport. This indicates the crystallographic origin of the WTe2 barrier for the magneto-chirality that we report here.
To confirm this distinctive magneto-chirality, the \({\mu }_{0}{H}_{\parallel }\) angular dependence of \(\eta\) is measured for each JJ. Note that this measurement is conducted in the low-field regime where the magneto-linearity of \(\eta (\propto {\mu }_{0}{H}_{\parallel })\) holds (see Fig. 2d−f). As summarized in Fig. 3a−c, the measured \(\eta (\theta )\) data are all well fitted by a sine function, suggesting a magneto-chiral origin of the Josephson diode effect in the vdW WTe2 JJs. Furthermore, there exists a visible shift between the sine fits to the \(\eta (\theta )\) data for different WTe2 JJs. This indicates that the crystal structure of the WTe2 barrier indeed governs the Josephson supercurrent non-reciprocity in our system. The magneto-chirality described above predicts \(\eta\) to be maximized (minimized) when the applied \({\mu }_{0}{H}_{\parallel }\) is aligned along the a-axis (b-axis). Note that in Fig. 3a−c, there exist non-zero constant offsets that are irrelevant to the intrinsic supercurrent rectification of magneto-chiral origin12. It is highly likely that such constant offsets arise from the asymmetric interface of the junctions as discussed previously15. Furthermore, a small out-of-plane component of the applied magnetic field due to a misalignment can, in principle, generate the field-angle-independent offset (Supplementary Information S9). To identify the a- and b-axis of each WTe2 barrier in the fabricated junctions, angle-resolved polarized Raman spectroscopy was carried out: this technique can readily characterize the crystal orientation of low-dimensional materials20,22. Figure 3d−f, show the polarization angle dependent relative intensities of two distinct Raman peaks at ~160 cm-1 and ~210 cm-1. The extracted a- and b-axis of the WTe2 from the Raman data (Fig. 3d−f, see Supplementary Information S3 for the detailed analysis) agree with those from the \(\eta (\theta )\) data (Fig. 3a−c). These results strongly support an intrinsic-crystal-structure-reflected vertical Josephson diode effect. For completeness, we also fabricated and measured control vdW JJs, where the non-centrosymmetric WTe2 barrier is replaced with a MoTe2 barrier that is locally centrosymmetric and may have a mixed Td/1 T′ structure (see Supplementary Information S4)31. In addition, the effect of direct tunneling between the top and bottom superconducting NbSe2 electrodes in JJs without any vdW-WTe2 (Supplementary Information S6) were fabricated. None of the magneto-linearity and the magneto-chirality effects are found in these experiments (see Supplementary Information S4), thereby pinpointing the critical role of the Josephson barrier’s crystal structure for the supercurrent non-reciprocity in our WTe2 JJs. Based on these results, we can rule out other extrinsic possibilities for the supercurrent non-reciprocity in our WTe2 JJs, e.g., pinning of Abrikosov vortices or a kinetic inductance contribution which have little to do with the crystal structure of the Josephson barrier (see Supplementary Information S8 for more discussions). In addition, one may expect the vdW gap formed at either side of the WTe2 Josephson barrier to function as a tunnel barrier at the interface between NbSe2 and WTe2 flakes. As shown by the exponential decay of the characteristic voltage of WTe2 JJs as a function of the thickness of the WTe2 barrier (Supplementary Information S5), this is the case and so, our WTe2 JJs need to be regarded as superconductor-insulator (vdW gap)-normal metal-insulator-superconductor (SINIS) junctions. This is in contrast with a previous study on lateral Nb/WTe2/Nb JJs32 that in the case of ballistic junctions with transparent/direct contacts, the barrier-thickness-dependent characteristic voltage is expected to reveal the 1/L dependence in the long junction limit. Here L is the lateral spacing of the neighboring Nb electrodes. Nevertheless, given the presence (absence) of crystal-structure-coupled magneto-chirality in WTe2 (MoTe2) JJs, it is unlikely that the crystal-structure-less vdW gaps play a significant role in producing such a characteristic magneto-chirality.
The proportionality of \({\varphi }_{0}\) to the barrier length is another characteristic feature of the intrinsic Josephson diode effect24,25,26, so one can anticipate that the thicker the WTe2 barrier, the greater the diode efficiency. To test this, we next investigate how the field-strength-normalized diode efficiency \({\eta }^{*}=\frac{\eta }{{\mu }_{0}{H}_{\parallel }}\), measured at θMC = 90°, scales with the WTe2 thickness (Fig. 4a). Note that since \(\eta\) \(\propto\) \({\mu }_{0}{H}_{\parallel }\) in the low-field regime, \({\eta }^{*}\) (\(=\frac{\eta }{{\mu }_{0}{H}_{\parallel }}\)) allows for a more quantitative comparison. As the WTe2 thickness is increased from 2 to 23 nm, we find that \({\eta }^{*}\) increases linearly. This linear scaling behavior is, in fact, predicted theoretically for a ballistic JJ24. When the thickness of the WTe2 is increased to 60 nm, which is larger than the coherence length (~30 nm, Supplementary Information S5) and the c-axis mean free path (~40 nm)33, \({\eta }^{*}\) deviates from the linear thickness dependence. Given the distinctively different barrier-thickness dependence of \({\varphi }_{0}\) on whether the junction is in the ballistic or diffusive regime, such a deviation is likely related to a ballistic-to-diffusive (long-junction) transition24,25,26. As the c-axis mean free path is close to the c-axis coherence length of our WTe2 JJs, one should also consider a short-to-long junction transition32 within the ballistic limit (Supplementary Information S5). To clarify whether the non-monotonic thickness-dependent \({\eta }^{*}\) results from the ballistic-to-diffusive transition24,25,26 or the short-to-long ballistic transition32, further study is necessary in the future.
The temperature T dependent evolution of η*, gives additional information about the intrinsic Josephson diode properties. Figure 4b shows the T/Tc-dependent η*for several WTe2 JJs. It is especially noteworthy that the \({\eta }^{*}(T/{T}_{c})\) data can be well described by a \(\scriptstyle \sqrt{1-\frac{T}{{T}_{c}}}\) function for\(\,\frac{T}{{T}_{c}}\gtrsim \frac{1}{3}\), as predicted in several earlier theoretical studies24,25,26,34,35,36. For\(\,\frac{T}{{T}_{c}} < \frac{1}{3}\), \({\eta }^{*}\) tends to saturate, which is qualitatively similar to recent related experiments7,11. A very recent theory predicts a rather complicated T-dependence of the superconducting diode effect in diffusive Rashba-type SCs35 as the low-T limit diode efficiency is affected sensitively by structural disorder and impurity scattering. On the other hand, for Al/2DEG/Al ballistic JJs7, the field-strength-dependent supercurrent non-reciprocity is explained by considering contributions from first and second order harmonics in the JJ CPR. If we apply this analysis to our \({\eta }^{*}(T/{T}_{c})\) data, both harmonics seem to become constant at \(\frac{T}{{T}_{c}} < \frac{1}{3}\), as is consistent with the calculation in Ref. 7
To further show the importance of our vertical JJ platform, that goes beyond recent studies7,8,9,10,11,12, we have fabricated vertical JJs with a twisted WTe2 double-barrier (Methods). In these twisted double-barrier junctions, the vector addition of the internal crystal fields of the top and bottom WTe2 layers, respectively, with a twist angle between two layers leads to a new artificial polar axis of the entire Josephson barrier. Note that the twist angle \({\theta }_{{twist}}\) between two distinct WTe2 layers uniquely forms an artificial polar axis of the entire Josephson barrier in a controllable manner (Fig. 5). In this sense, one can expect that the \({\theta }_{{MC}}\) is determined with respect to this new artificial polar axis. As shown in Fig. 6c, the diode efficiency of a twisted WTe2 double-barrier JJ shows a visible sinusoidal behavior and the diode efficiency of the JJ goes to zero when the magnetic field is applied to the parallel direction of the vector addition of the internal crystal field of top and bottom WTe2 layers. This indicates that the magneto-chirality of twisted-double barrier JJ can be determined by the artificial polar axis of the barrier, demonstrating a tunable magneto-chirality via twist-angle engineering and opens an avenue for the development of twistable36 active Josephson diodes.
We have carefully fabricated vdW vertical JJs with an inherently inversion symmetry breaking Td-WTe2 barrier. This has allowed us to unambiguously demonstrate the intrinsic origin of the Josephson non-reciprocity that we observe in these vertical JJs. We clearly demonstrate that the crystal structure of the Td-WTe2 Josephson barrier governs the overall properties of the Josephson diode effect, which has not been previously been shown. We have also shown that whether or not the magneto-linearity, the magneto-chirality and the thickness and temperature-scaleable diode efficiency coexist is a key criterion in distinguishing intrinsic and extrinsic mechanisms. We believe that our results have definitely shown the critical role of the barrier in the realization of rectified Josephson supercurrents in vdW heterostructures15 and provides the first demonstration of twist engineering of the magneto-chirality. Our approach can be extended to other low-dimensional, low-symmetric and twisted vdW systems37,38,39 for accelerating the development of two-dimensional superconducting devices and circuits.
Methods
Device fabrication
The NbSe2/WTe2/NbSe2 van der Waals (vdW) heterostructures (Fig. S1a−d) were formed using standard dry transfer techniques. All the needed processes, including mechanical exfoliation, pick-up and dry transfer of the vdW flakes, were performed inside a nitrogen gas filled glovebox to prevent the flakes from oxidizing in ambient air. First, NbSe2 (\(\ge\) 10 nm thick) and WTe2 (2−60 nm thick) flakes were exfoliated on to a 300-nm-thick SiO2/p + + Si substrate. Each of the flakes needed to form the heterostructure was chosen by optical microscopy examination. The chosen flakes were picked up sequentially using a polycarbonate (PC) film coated dome-shaped polydimethylsiloxane (PDMS) stamp. The flakes were aligned one on top of each other and them the entire stack was released and then placed on top of a set of pre-patterned gold electrodes on a second 300-nm-thick SiO2/p + + Si substrate. The release process was performed at 200 C°, after which the entire stack in the Si substrate was immersed in a chloroform solution to remove any PC residue. Using this fabrication process flow, we also prepared three distinct types of JJs: (1) a control vdW JJ, in which the non-centrosymmetric WTe2 barrier20,22,23 is replaced by a MoTe2 barrier31 that may have a mixed Td/1 T′ structure and is to a certain extent locally centrosymmetric at low temperatures (Supplementary Information S4), (2) a reference vdW JJ with no WTe2 barrier (Supplementary Information S6), and (3) a twisted WTe2 double-barrier JJ (Figs. 5–6), where one WTe2 is twisted in-plane relative to the other WTe2. For the formation of the twisted WTe2 double-barriers, we first identified the crystal orientation of two chosen WTe2 flakes through their elongated shapes20 (which tends to be along the a-axis), and then carefully twisted and stacked one on top of the other to realize \({\theta }_{{twist}}\) ≈ 90°. After completing the transport measurements, we finally confirmed the respective crystal orientations of the top and bottom WTe2 flakes by a means of angle-resolved polarized Raman spectroscopy.
Electrical measurements
The current-voltage (I–V) curves of the fabricated NbSe2/WTe2/NbSe2 vdW vertical Josephson junctions (JJs) were measured in a BlueFors dilution refrigerator or a Quantum Design Physical Property Measurement System with base temperatures of ~20 mK and ~1.8 K, respectively. The four-point I–V measurements were carried out using a Keithley 6221 current source and a Keithley 2182 A nanovoltmeter. We determined the critical current Ic values at the point where V(I) ≈ 1 μV. An external in-plane magnetic field (\({\mu }_{0}{H}_{\parallel }\)), that was needed to break the time-reversal symmetry, was applied within the a-b plane of the WTe2 single crystalline barrier. Note that \(\theta\) is the angle of \({\mu }_{0}{H}_{\parallel }\) relative to one edge of the Si wafer on which the exfoliated layer stack was placed: the wafer had been purposely cut into a rectangular shape to define a clear reference direction. The typical Josephson penetration depth40 of our junctions (of at least a few μm) is much larger than the WTe2 thickness, so we can exclude orbital magnetic field effects (or Meissner demagnetizing supercurrents) as a possible extrinsic source for of the Josephson diode effect in our JJs. We measured the field strength dependent diode signals (Fig. 2a−c) by applying \({\mu }_{0}{H}_{\parallel }\) along a given \(\theta\) direction. The angle dependent diode signals (Fig. 3a–c) were measured at a constant \({\mu }_{0}{H}_{\parallel }\) using a vector field magnet.
Atomic force microscopy
To characterize the thickness of each WTe2 barrier, we conducted atomic force microscopy (AFM) measurements on the fabricated vdW vertical JJs. The measured AFM image and height of each WTe2 barrier layer are shown together with the corresponding optical micrograph of the JJs in Fig. S1.
Data availability
The data that support the findings of this study are provided in main text and the Supplementary Information. The original data available from the corresponding authors upon request.
References
Sze, S. M. & Kwok, K. N. in Physics of Semiconductor Devices 793–815 (John Wiley & Sons, 2006).
Neamen, D. A. Semiconductor Physics and Devices: Basic Principles. Vol. 528 (McGraw-Hill, 2012).
Onsager, L. Reciprocal relations in irreversible processes. I. Phys. Rev. 37, 405–426 (1931).
Kubo, R. Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems. J. Phys. Soc. Jpn. 12, 570–586 (1957).
Rikken, G. L. J. A., Fölling, J. & Wyder, P. Electrical magnetochiral anisotropy. Phys. Rev. Lett. 87, 236602 (2001).
Tokura, Y. & Nagaosa, N. Nonreciprocal responses from non-centrosymmetric quantum materials. Nat. Commun. 9, 3740 (2018).
Baumgartner, C. et al. Supercurrent rectification and magnetochiral effects in symmetric Josephson junctions. Nat. Nanotechnol. 17, 39–44 (2022).
Lyu, Y.-Y. et al. Superconducting diode effect via conformal-mapped nanoholes. Nat. Commun. 12, 2703 (2021).
Wakatsuki, R. et al. Nonreciprocal charge transport in noncentrosymmetric superconductors. Sci. Adv. 3, e1602390 (2017).
Ando, F. et al. Observation of superconducting diode effect. Nature 584, 373–376 (2020).
Bauriedl, L. et al. Supercurrent diode effect and magnetochiral anisotropy in few-layer NbSe2. Nat. Commun. 13, 4266 (2022).
Jeon, K.-R. et al. Zero-field polarity-reversible Josephson supercurrent diodes enabled by a proximity-magnetized Pt barrier. Nat. Mater. 21, 1008–1013 (2022).
Pal, B. et al. Josephson diode effect from cooper pair momentum in a topological semimetal. Nat. Phys. 18, 1228–1233 (2022).
Gupta, M. et al. Gate-tunable superconducting diode effect in a three-terminal Josephson device. Nat. Commun. 14, 3078 (2023).
Wu, H. et al. The field-free Josephson diode in a van der Waals heterostructure. Nature 604, 653–656 (2022).
Baumgartner, C. et al. Effect of Rashba and Dresselhaus spin–orbit coupling on supercurrent rectification and magnetochiral anisotropy of ballistic Josephson junctions. J. Phys. Condens. Matter 34, 154005 (2022).
Mazur G. P. et al. The gate-tunable Josephson diode. arXiv https://doi.org/10.48550/arXiv.2211.14283 (2022).
Xi, X. et al. Ising pairing in superconducting NbSe2 atomic layers. Nat. Phys. 12, 139–143 (2016).
Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).
Choi, Y.-B. et al. Evidence of higher-order topology in multilayer WTe2 from Josephson coupling through anisotropic hinge states. Nat. Mater. 19, 974–979 (2020).
Wu, S. et al. Observation of the quantum spin Hall effect up to 100 kelvin in a monolayer crystal. Science 359, 76–79 (2018).
Kang, K., Li, T., Sohn, E., Shan, J. & Mak, K. F. Nonlinear anomalous Hall effect in few-layer WTe2. Nat. Mater. 18, 324–328 (2019).
Xu, S.-Y. et al. Electrically switchable Berry curvature dipole in the monolayer topological insulator WTe2. Nat. Phys. 14, 900–906 (2018).
Buzdin, A. Direct coupling between magnetism and superconducting current in the Josephson φ0 Junction. Phys. Rev. Lett. 101, 107005 (2008).
Konschelle, F., Tokatly, I. V. & Bergeret, F. S. Theory of the spin-galvanic effect and the anomalous phase shift φ0 in superconductors and Josephson junctions with intrinsic spin-orbit coupling. Phys. Rev. B 92, 125443 (2015).
Bergeret, F. S. & Tokatly, I. V. Theory of diffusive φ0 Josephson junctions in the presence of spin-orbit coupling. Europhys. Lett. 110, 57005 (2015).
Kononov, A. et al. One-dimensional edge transport in few-layer WTe2. Nano Lett. 20, 4228–4233 (2020).
Soluyanov, A. A. et al. Type-II Weyl semimetals. Nature 527, 495–498 (2015).
Chen, C.-Z. et al. Asymmetric Josephson effect in inversion symmetry breaking topological materials. Phys. Rev. B 98, 075430 (2018).
Souto, R. S., Leijnse, M. & Schrade, C. Josephson diode effect in supercurrent interferometers. Phys. Rev. Lett. 129, 267702 (2022).
Qian, X., Liu, J., Fu, L. & Li, J. Quantum spin hall effect in two-dimensional transition metal dichalcogenides. Science 346, 1344–1347 (2014).
Huang, C. et al. Edge superconductivity in multilayer WTe2 Josephson junction. Natl Sci. Rev. 7, 1468–1475 (2020).
Li, P. et al. Evidence for topological type-II Weyl semimetal WTe2. Nat. Commun. 8, 2150 (2017).
Kochan, D., Costa, A., Zhumagulov, I. & Žutić, I. J. a. e.-p. Phenomenological theory of the supercurrent diode effect: the lifshitzi Invariant. arXiv 2303, 11975 (2023).
Ilić, S. & Bergeret, F. S. Theory of the supercurrent diode effect in rashba superconductors with arbitrary disorder. Phys. Rev. Lett. 128, 177001 (2022).
Ribeiro-Palau, R. et al. Twistable electronics with dynamically rotatable heterostructures. Science https://doi.org/10.1126/science.aat6981 (2018).
Novoselov, K. S., Mishchenko, A., Carvalho, A. & Castro Neto, A. H. 2D materials and van der Waals heterostructures. Science 353, 6298 (2016).
Díez-Mérida, J. et al. Symmetry-broken Josephson junctions and superconducting diodes in magic-angle twisted bilayer graphene. Nat. Commun. 14, 2396 (2023).
Lin, J.-X. et al. Zero-field superconducting diode effect in small-twist-angle trilayer graphene. Nat. Phys. 18, 1221–1227 (2022).
Barone, A. P., G. in Physics and Applications of the Josephson Effect 2nd edn, 525–529 (John Wiley & Sons, 1982).
Acknowledgements
SSPP acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—project no. 443406107, Priority Programme (SPP) 2244. K.-R.J. acknowledges that this work was supported by Chung-Ang University Research Grant in 2022.
Funding
Open Access funding enabled and organized by Projekt DEAL.
Author information
Authors and Affiliations
Contributions
J.-K.K. and S.S.P.P. conceived of and designed the experiments with the help of K.-R.J. J.-K.K. fabricated the van der Waals Josephson junctions and carried out the transport measurements with the help of K.-R.J., P.K.S. and J.J. J.-K.K. performed the Raman measurement with the help of C.K. and G.W. J.-K.K analyzed the data with the guidance of K.-R.J. J.-K.K., K.-R.J and S.S.P.P. wrote the manuscript with input from all the other authors.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Kim, JK., Jeon, KR., Sivakumar, P.K. et al. Intrinsic supercurrent non-reciprocity coupled to the crystal structure of a van der Waals Josephson barrier. Nat Commun 15, 1120 (2024). https://doi.org/10.1038/s41467-024-45298-9
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s41467-024-45298-9