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Andrei Kudriashov, Xiangyu Zhou, Razmik A. Hovhannisyan, Alexander S. Frolov, Leonid Elesin, Yi Bo Wang, Ekaterina V. Zharkova, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Zheng Liu, Kostya S. Novoselov, Lada V. Yashina, Xin Zhou, Denis A. Bandurin
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[Non-Majorana origin of anomalous current-phase relation and Josephson diode effect in Bi 2 Se 3 /NbSe 2 Josephson junctions](https://mdr.nims.go.jp/datasets/056648ee-ee5c-466c-9482-66837ec8f22a)
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Non-Majorana origin of anomalous current-phase relation and Josephson diode effect in Bi2Se3/NbSe2 Josephson junctionsKudriashov et al., Sci. Adv. 11, eadw6925 (2025) 13 June 2025S c i e n c e A d v a n c e s | R e s e ar c h A r t i c l e1 of 9C O N D E N S E D M AT T E R P H Y S I C SNon-Majorana origin of anomalous current-phase relation and Josephson diode effect in Bi2Se3/NbSe2 Josephson junctionsAndrei Kudriashov1,2*†, Xiangyu Zhou1,2†, Razmik A. Hovhannisyan3, Alexander S. Frolov4,5, Leonid Elesin1,2,6, Yi Bo Wang2, Ekaterina V. Zharkova5,6, Takashi Taniguchi7, Kenji Watanabe8, Zheng Liu9, Kostya S. Novoselov2, Lada V. Yashina4,5, Xin Zhou2*, Denis A. Bandurin1,2*Josephson junctions (JJs) are key to superconducting quantum technologies and the search for self-conjugate quasiparticles potentially useful for fault-tolerant quantum computing. In topological insulator (TI)–based JJs, measuring the current-phase relation (CPR) can reveal unconventional effects such as Majorana bound states (MBS) and nonreciprocal transport. However, reconstructing CPR as a function of magnetic field has not been attempted. Here, we present a platform for field-dependent CPR measurements in planar JJs made of NbSe2 and few-layer Bi2Se3. When a flux quantum Φ0 threads the junction, we observe anomalous peak-dip CPR structure and nonreciprocal supercurrent flow. We show that these arise from a nonuniform supercurrent distribution that also leads to a robust and tunable Josephson diode effect. Furthermore, despite numerous previous studies, we find no evidence of MBS. Our results establish magnetic field–dependent CPR as a powerful probe of TI-based superconducting devices and offer design strategies for nonreciprocal superconducting electronics.INTRODUCTIONCharacterizing and controlling supercurrent flow in Josephson junc-tions (JJs) is critical for advancing both fundamental research and practical applications, from superconducting classical and quantum technologies (1–4) to the discovery of exotic quasiparticles (5–11). While conventional methods, such as measuring the critical current between dissipationless and resistive states, have been instrumental in studying JJs, they often provide limited insight into fundamen-tal mechanisms like spin-orbit coupling (SOC) (12), quantum-geometric effects (13), and pairing symmetry (14) that govern their superconducting properties. At the same time, spectroscopic tech-niques probing the amplitude of the superconducting wave function (15) lack direct access to phase-dependent phenomena such as current-induced hidden states (16) and screening currents in super-conductor/ferromagnet hybrids (17) that were uncovered only re-cently with the advent of sensitive noninvasive scanning probes. These limitations are amplified in JJs with topologically nontrivial weak links (18–21), where multiple confounding factors (22–30) can mimic transport signatures of Majorana bound states (MBSs) (31–34), pivotal for fault-tolerant quantum computing (5, 35, 36). Phase-sensitive information is also crucial for understanding nonreciprocal supercurrent transport and the Josephson diode effect (JDE), a re-search focus in superconducting nanoelectronics (37). While JDE has been observed in various systems (17, 37–41), directly probing the direction and amplitude of nonreciprocal supercurrent in topo-logical insulator (TI)–based JJs as a function of external tuning knobs (42)—such as a magnetic field—and uncovering its possible relation to MBS (43, 44) have remained experimentally difficult. These challenges have resulted in a proliferation of studies making unsubstantiated claims about MBS signatures in some TIs and the nature of the JDE in related systems. To circumvent the limitations of the transport and spectroscopic approaches and get access to the internals of the topological JJs, an alternative methodology frame-work is needed.Here, we propose and realize such a framework that is based on accurate field-dependent reconstruction of the current-phase relation (CPR) in a lateral JJ made of a superconducting NbSe2 and one of the most-known TI—Bi2Se3 (45, 46). Although several studies have investi-gated the zero-field CPR of TI-based JJs (47–52), none of them reported the exploration of the critical regime near Φ0 , where MBSs are antici-pated to dominate the supercurrent (32, 33). At the same time, the CPR of conventional and topological JJs in the regime of JDE has remained largely unexplored. We fabricated lateral van der Waals (vdW) hetero-junctions and incorporated them into superconducting quantum inter-ference devices (SQUIDs). By controlling the flux through the SQUID using a superconducting local flux line, we performed precise CPR measurements of individual JJs and its dependence on the external magnetic field. Near Φ0 , we observe unconventional CPR characteris-tics and nonreciprocal supercurrent flow, which we show to stem from the nonuniform supercurrent distribution (SD). The latter generates distinctive nonreciprocal CPR, giving rise to a robust and tunable JDE with 30% efficiency. Finally, we observe no signatures of MBS near a single flux quantum conditions in the CPR data, thereby challenging dozens of theoretical and experimental studies on superconductor-proximitized Bi2Se3.1Department of Materials Science and Engineering, National University of Singapore, Singapore, Singapore. 2Institute for Functional Intelligent Materials, National Uni-versity of Singapore, Singapore, Singapore. 3Department of Physics, Stockholm University, AlbaNova University Center, SE-10691 Stockholm, Sweden. 4Chemistry Department, M.V. Lomonosov Moscow State University, Moscow, Russia. 5Moscow Center for Advanced Studies, Moscow, Russia. 6Programmable Functional Materials Lab, Center for Neurophysics and Neuromorphic Technologies, Moscow 127495, Russia. 7International Center for Materials Nanoarchitectonics, National Institute of Material Science, Tsukuba 305-0044, Japan. 8Research Center for Functional Materials, National Institute of Material Science, Tsukuba, Japan. 9School of Materials Science and Engineering, Nanyang Technological University, Singapore, Singapore.*Corresponding author. Email: andrei.kudriashov.97@gmail.com (A.K.); xin_zhou@nus.edu.sg (X.Z.); dab@nus.edu.sg (D.A.B.)†These authors contributed equally to this work.Copyright © 2025 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY). Downloaded from https://www.science.org at National Institute for Materials Science on June 17, 2025mailto:andrei.kudriashov.97@gmail.commailto:xin_zhou@nus.edu.sgmailto:xin_zhou@nus.edu.sgmailto:dab@nus.edu.sghttp://crossmark.crossref.org/dialog/?doi=10.1126%2Fsciadv.adw6925&domain=pdf&date_stamp=2025-06-13Kudriashov et al., Sci. Adv. 11, eadw6925 (2025) 13 June 2025S c i e n c e A d v a n c e s | R e s e ar c h A r t i c l e2 of 9RESULTSPlanar vdW JJsOur devices consist of planar JJs formed by two superconducting 2H-NbSe2 electrodes coupled through a 5-nm-thick TI Bi2Se3 (Fig. 1A) (53). Device fabrication was performed using a standard dry transfer method within an argon-filled glovebox to prevent surface degrada-tion of the constituent materials (54). The fabrication process began with mechanical exfoliation of thin Bi2Se3 flakes onto a Si/SiO2 sub-strate. Subsequently, an atomically flat NbSe2 flake, containing an intrinsic crack (55, 56), was transferred onto the Bi2Se3, forming two superconducting electrodes separated by a narrow gap of L ≈ 150 nm (Fig. 1B). Unlike conventional thin-film deposition techniques that typically involve sputtering superconducting electrodes onto TIs—a process known to introduce structural and compositional disorder (57)—our method ensures atomically sharp interface between the materials critical for superconducting proximity (58–60). High-resolution high-angle annular dark-field scanning transmission elec-tron microscopy (HAADF-STEM) imaging (Fig. 1, C and G to I, and Supplementary Materials) reveals the structural characteristics of the heterostructure, confirming the exceptional interface quality, which is important for JJ experiments. The heterostructure was further cov-ered by a relatively thick (40 nm) slab of hexagonal boron nitride (hBN) to protect the device during subsequent patterning using elec-tron beam lithography (see Materials and Methods and the Supple-mentary Materials).We fabricated three different samples, all featuring robust prox-imity effect (Supplementary Materials). The data in the main text are shown for one of them. This device contains two junctions, which we will refer to as JJ1 and JJ2, shown in the optical image in Fig. 1D. We intentionally oriented NbSe2 crack in a way to ensure different junc-tion widths and patterned the device in a SQUID geometry, which is required for CPR measurements (details below). While we first mea-sured the as-fabricated SQUID, for convenience, we initially present data from the individual junctions, obtained after etching the SQUID into two independent devices. The current-voltage ( I-V ) curve of JJ1, shown in Fig. 1E, is typical for proximity JJs. It displays a zero-voltage state for currents below the critical current Ic , followed by a sharp transition to the resistive state as the current exceeds Ic . Upon de-creasing the current, the junction remains in the resistive state until the current drops below the retrapping current Ir , leading to hyster-esis in the curve. Hysteresis is typical for this type of device and is likely caused by a combination of self-heating effects (61) and an increased McCumber parameter, which can become large due to the enhanced capacitance from the gate electrodes (62).Since the transition from superconducting to normal state is very sharp, it allows us to define a critical current Ic and a retrapping cur-rent Ir using the threshold method and accurately determine its de-pendence on the magnetic field, B. Figure 1F shows Ic as a function of B for both JJ1 and JJ2. It exhibits a characteristic Fraunhofer-like pattern, where the critical current Ic oscillates as a function of the applied magnetic field B , reaching minimum (nonzero) values when the magnetic flux through the junctions is close to integer multiples of the magnetic flux quantum, Φ1,2 = nΦ0 , where 1,2 indices corre-spond to JJ1 and JJ2, respectively, and n is integer.Fig. 1. Planar vdW NbSe2/Bi2Se3 JJs. (A) Schematic illustration of a single JJ. A few-layer Bi2Se3 film is covered by a cracked NbSe2 flake, with Ti/Au electrodes contacting the NbSe2 regions. The device is fabricated on an oxidized Si substrate. (B) Atomic force microscopy topography of the cracked NbSe2 region. White solid line indicates the height profile across the crack. Measurements performed in an Ar-filled glovebox. (C) Representative high-resolution HAADF-STEM image across the NbSe2/Bi2Se3 inter-face. (D) Optical micrograph of an hBN-encapsulated NbSe2/Bi2Se3 stack comprising two Bi2Se3 flakes that form two JJs (JJ1 and JJ2). (E) Characteristic I -V curve of JJ1 measured at base temperature T = 8 mK. Arrows indicate the bias current sweep direction. I+,−c and I+,−r denote critical and retrapping currents for positive (+) and negative (−) current directions, respectively. (F) Magnetic field dependence of the critical current Ic for JJ1 (blue) and JJ2 (red) at the specified temperature. (G) Typical STEM image of the device cross section. (H) Zoomed-in STEM image of the NbSe2/Bi2Se3 interface at the end of the NbSe2 flake. (I) STEM image of the atomic planes in NbSe2.Downloaded from https://www.science.org at National Institute for Materials Science on June 17, 2025Kudriashov et al., Sci. Adv. 11, eadw6925 (2025) 13 June 2025S c i e n c e A d v a n c e s | R e s e ar c h A r t i c l e3 of 9CPR measurementsSince the widths of the two junctions were intentionally made differ-ent, their Ic(B) patterns also differ (as shown in Fig. 1, D and F). Im-portantly, when B ≈ 0.75 mT (which corresponds to the interference pattern minimum), I JJ1c≈ 60 nA and I JJ2c≈ 1 μA. By redesigning the asymmetric SQUID technique (51, 63, 64) with an additional flux bias, we leveraged this order-of-magnitude asymmetry in critical cur-rent to enable measurements of the CPR of JJ1 as a function of exter-nal magnetic field, a capability previously unattained in TI-based JJs.The idea behind this technique is the following. The supercurrent through the SQUID is the sum of supercurrents through individual JJs: ISQUIDs= I JJ1s(φ1)+ I JJ2s(φ2) , where φ1 and φ2 are the phase differences in JJ1 and JJ2, respectively. Assuming negligible induc-tance L of the SQUID (in our geometry L ⋅ Ic ∕Φ0 ∼ 10−3 ), the phase differences are related by the magnetic flux through the SQUID, Φ , as φ1 − φ2 = 2πΦ∕Φ0.When the critical current of JJ2 is notably larger than that of JJ1, φ2 = φ∗ , where φ∗ is the phase at which the critical current of JJ2 is achieved and it is almost independent of Φ . As a result, the critical current of the SQUID can be expressed aswhere φ1(Φ) = φ∗ + 2πΦ∕Φ0 . Therefore, the desired CPR, I JJ1s(φ1) , can be reconstructed from Eq. 1 through the accurate measure-ments of ISQUIDc(Φ) (51).To perform such experiment, we used a SQUID made of JJ1 and JJ2 shown in Fig. 2A. Figure 2B reveals fast ISQUIDc(B) oscillations modulated by the combination of interference patterns from indi-vidual JJs, highlighting the typical SQUID pattern. When B ≈ 0.746 mT, the amplitude of the oscillations is suppressed (Fig. 2C), reflecting that JJ1 is close to the Fraunhofer minimum—the point of interest in our study. For an accurate control of Φ while maintaining magnetic field through JJ1 constant, we endowed our device with an alumi-num flux line located relatively far from the JJs (Fig. 2A). By applying the current through the flux line and accounting for the superposition of both magnetic fields, we mapped the full depen-dence of ISQUIDc on Φ and B shown in Fig. 2D.Next, using these data and Eq. 1, we obtained the CPR I JJ1s(φ1) at selected values of B in the vicinity of the first interference pattern minimum, as shown in Fig. 2E. This is the central plot of our study. At B = 0.708 mT and B = 0.782 mT, the CPRs are 2π-periodic func-tions oscillating in anti-phase with respect to each other. This phase shift is expected since the JJs experience 0-π transition when cross-ing the integer number of flux quanta (25). At B = 0.746 mT, the periodic pattern undergoes a notable transformation, developing an anomalous peak-dip structure (highlighted by the yellow rectangle) that notably deviates from the anticipated CPR behavior where the critical current through JJ1 is expected to be fully suppressed (see below).For further analysis of the observed anomalies, we characterize these features phenomenologically and fit the data with a two-harmonic expansion: I JJ1s(φ1)= I0 + I1sin(φ1+θ1)+ I2sin(2φ1+θ2) (solid lines in Fig. 2E). Here, I1,2 and θ1,2 represent the amplitudes and phases of the first and second harmonics, respectively, and I0 is the offset introduced by the asymmetric SQUID technique (see Eq. 1). The amplitude of the first harmonic I1 decreases, reaching a mini-mum nonzero value at B = 0.746 mT, before increasing again, while the phase θ1 undergoes a smooth 0-π transition, as shown in Fig. 2 (F and G). In contrast, the amplitude of the second harmonic I2 gradually decreases over the entire measurement interval, showing no features associated with B = 0.746 mT, while the phase θ2 re-mains close to zero, as shown in Fig. 2 (H and I). Therefore, there is a magnetic field–dependent phase shift between first and second harmonics, which leads to another notable characteristic of the ob-served CPR: its directional asymmetry (the amplitudes of positive and negative supercurrents differ at certain magnetic fields, as marked in Fig. 2E). This asymmetry implies that the junction exhib-its a nonreciprocal transport, where the magnitude of the critical current depends on its direction through the JJ.Nonreciprocal CPR and Josephson diodeTo demonstrate and analyze the nonreciprocal behavior, we return to the data obtained on JJ1. Figure 3A shows examples of two I-V curves for JJ1 measured at B = ± 0.7 mT and reveals the anticipated nonreciprocity: I+c≠ I−c , indicating the manifestation of JDE (37). Figure 3B details this observation further by showing I+c and I−c as a function of B in the vicinity of the single flux quantum. The clear in-equivalence between the two persists for ∣B∣ < 0.8 mT and abruptly disappears for larger ∣B∣.For further analysis, we quantify the strength of the diode effect by introducing a diode efficiency factor Q =(I+c−∣I−c∣)∕(I+c+∣I−c∣). Figure 3C shows the tunability of Q on magnetic field B , revealing a distinctive tooth-like structure. The efficiency ∣Q∣ exhibits periodic behavior, vanishing at integer numbers of flux quanta Φ0 through the junction, followed by sharp increases with increasing B . In our devices, the maximum achieved efficiency ∣Q∣ reached approxi-mately 30%.These large values of ∣Q∣ allow us to demonstrate a robust recti-fication effect (Fig. 3D). To this end, we applied square-wave cur-rent oscillations (black line) across the junction with the amplitude 0.2 μA, which is between ∣I−c∣ = 0.18 μA and I+c= 0.3 μA. The result-ing voltage drop appears only during half of the excitation period, and its sign can be controlled by the direction of B (see blue and red curves in Fig. 3D).Theoretical modelingTo understand the origin of the observed anomalous CPR and the JJ diode effect, we use the standard expression (26, 30, 65) that de-scribes the supercurrent flow through the narrow JJ, i.e., when W < λJ , where W is the width of the junction and λJ is the Josephson penetration length (see the Supplementary Materials)Here, y is the coordinate along the junction, with y = 0 being the center of the junction, Jc(y) is the SD at B = 0 , js is the local CPR, φ1 is the Josephson free phase, α = 2πLeff ∕Φ0 , and Leff is the effective length of the junction, which is determined by the geometry of the superconducting leads in the case of a planar JJ (66). Since Is(φ1) describes the total supercurrent through the junction as a function of the phase difference between the superconducting leads φ1 , we will refer to this dependence as a global CPR, the desired property of the Bi2Se3/NbSe2 JJ that we investigate in our study. Equation 2 ISQUIDc(Φ) = I JJ2c+ I JJ1s[φ1(Φ)](1)Is(φ1)=W∕2∫−W∕2Jc(y)js(αBy+φ1)dy (2)Downloaded from https://www.science.org at National Institute for Materials Science on June 17, 2025Kudriashov et al., Sci. Adv. 11, eadw6925 (2025) 13 June 2025S c i e n c e A d v a n c e s | R e s e ar c h A r t i c l e4 of 9allows to calculate the magnetic field dependence of the CPR as well as of the critical currents I+c=maxIs(φ1) and I−c=minIs(φ1).First, we apply Eq. 2 to the simplest case of uniform supercurrent flow Jc(y)= 1 and sinusoidal local CPR js(φ) = sin(φ) . The results are shown in Fig. 4A (bottom) that maps Is against B and φ1 . The map reveals a sudden change of Is sign at Φ1 = Φ0 that is achieved when B = 0.85 mT, demonstrating the standard 0-π transition. The cal-culated dependence is drastically different from the experimentally obtained CPR (see Fig. 2D), highlighting the distinctive supercurrent transport mechanism in our devices.The obtained I+,−c(B) dependencies, shown in Fig. 4A (top), describe conventional Fraunhofer pattern Ic= Ic0∣sin(πΦ∕Φ0)∕(πΦ∕Φ0)∣ for ideal JJs, which notably deviate from experimentally measured Ic(B) (Fig. 5). This implies that our device features a nonuniform SD Jc(y) along the junction that needs to be accounted for in further analysis. To this end, we determine the SD Jc(y) using a standard Fig. 2. NbSe2/Bi2Se3 SQUID and CPR measurements. (A) Optical micrograph of the SQUID incorporating two JJs (JJ1 and JJ2) with measurement configuration overlay. Direct current flows between contacts 1 and 2, while voltage is measured across contacts 3 and 4. A perpendicular magnetic field is applied externally, and a supercon-ducting Al line controls the magnetic flux through the SQUID. (B) Critical current ISQUIDc as a function of magnetic field, measured at base temperature T = 8 mK. (C) Magni-fied view of the region near one magnetic flux quantum through JJ1. (D) ISQUIDc plotted against magnetic field ( B ) and magnetic flux through SQUID ( Φ ), normalized to Φ0 . (E) CPR of JJ1 extracted along vertical dashed lines in (D). Symbols represent experimental data; solid lines show best fits to IJJ1s(φ1)= I0 + I1sin(φ1+θ1)+ I2sin(2φ1+θ2) . Dashed lines represent I0 . Data are shifted vertically for clarity. (F) Amplitude I1 of the first harmonic plotted versus magnetic field B . (G) Phase θ1 of the first harmonic plot-ted versus magnetic field B . (H) Amplitude I2 of the second harmonic plotted versus magnetic field B . (I) Phase θ2 of the second harmonic plotted versus magnetic field B.Downloaded from https://www.science.org at National Institute for Materials Science on June 17, 2025Kudriashov et al., Sci. Adv. 11, eadw6925 (2025) 13 June 2025S c i e n c e A d v a n c e s | R e s e ar c h A r t i c l e5 of 9Fig. 3. Josephson diode in TI-based JJs. (A) I -V curves of JJ1 measured at specified magnetic fields B . (B) Positive ( I+c ) and negative ( I−c ) critical currents for JJ1 as a function of B . Vertical dotted lines correspond to B = ± 0.7 mT. (C) Superconducting diode efficiency, Q , as a function of B . (D) Rectified voltage across JJ1 (right axis) measured by its excitation with the square-wave current (left axis) with the amplitude 0.2 μA for B = 0.7 mT (red curve) and B = −0.7 mT (blue curve). T = 8 mK.Fig. 4. Theoretical modeling of the CPR. (A to C) Calculated positive I+c and negative I−c critical currents of the JJ as a function of magnetic field B (top) and calculated supercurrent Is as a function of phase difference φ1 and magnetic field B (bottom). (A) Case of sinusoidal CPR and uniform SD. (B) Case of sinusoidal CPR and nonuniform SD. Black line in the top is the same as red and blue curves in (A). (C) Case of nonsinusoidal CPR and nonuniform SD. Black line in the top is the same as red and blue curves in (B). (D) Calculated Is(φ1) for different magnetic fields B around Fraunhofer minima for the case shown in (C). The case of nonsinusoidal js(φ1) combined with a uniform current distribution is shown in the Supplementary Materials. Downloaded from https://www.science.org at National Institute for Materials Science on June 17, 2025Kudriashov et al., Sci. Adv. 11, eadw6925 (2025) 13 June 2025S c i e n c e A d v a n c e s | R e s e ar c h A r t i c l e6 of 9method that calculates the Fourier transform of the measured Ic(B) dependencies (22). The results are shown by the red line in the inset of Fig. 5 that reveals (i) increased Jc at the end of the JJ and (ii) the linear slope of Jc(y) across the whole junction.To take into account the nonuniform SD, for simplicity, we approximate the extracted Jc(y) with a model dependence (black curve in Fig. 5) and use it in Eq. 2. The resulting Ic(B) and Is(B,φ1) dependencies are shown in Fig. 4B. Compared with the previous case, nonuniform SD leads to the shift of the Fraunhofer minima, prevents the critical current from dropping to zero, and causes the global CPR to experience a gradual phase shift from 0 to π state. However, accounting for nonuniform SD alone cannot explain the complex Is(B,φ1) pattern observed in Fig. 2D. In particular, this model fails to account for the prominent second harmonic compo-nent present in the experimental global CPR (Fig. 2E), suggesting an intrinsic nonsinusoidal js(φ1) relation that we incorporate in our subsequent analysis.Although the exact js(φ1) relation for our JJ cannot be mea-sured directly, since our SQUID is not in the asymmetric regime at zero B , we assume js(φ) = I1sin(φ) + I2sin(2φ) , where I1 and I2 are the amplitudes of the first and second harmonics, respectively. To illustrate how it affects the evolution of the global CPR, in Fig. 4 (C and D), we show the global CPR and Ic(B) results for js(φ) = 1.3sin(φ) − 0.3sin(2φ) . The resulting model accurately re-produces all experimentally observed features, namely, (i) nonre-ciprocal CPR (marked in Fig. 4D), (ii) JDE (Fig. 4C, top), (iii) gradual (nonsharp) 0-π transition, and (iv) peak-dip CPR struc-ture close to the single flux quantum (yellow shaded area). The excellent agreement between our model and the experimental data confirms that the observed effects arise from the interplay between spatial distribution of the supercurrent, combined with nonsinusoidal js(φ1) dependence.DISCUSSIONOur theoretical analysis demonstrates that the observed anomalous CPR in our devices, its nonreciprocity, and JJ diode effect can be explained by the interplay of nonuniform current distribution and higher-harmonic contributions. A key prerequisite for the explana-tion is a distinct shape of Jc(y) shown in the inset of Fig. 5. The shape is characterized by (i) its linear gradient and (ii) increased Jc at the ends of the JJ. Although the exact origin of the observed Jc(y) distri-bution remains unknown, we attribute these features to the follow-ing mechanisms. First, the slope can stem from a nonuniform gap between two superconducting NbSe2 parts. Taking into account a steep dependence of the critical current on the distance between the superconductors, even a small asymmetry in the junction geometry can lead to the gradient in Jc(y) . Another possible mechanism involves Abrikosov vortices penetrating into the superconducting leads and creating nonuniform stray fields. However, trapped Abrikosov vortices would break time-reversal symmetry, violating the condition Ic(B) = −Ic(−B) that is satisfied in our experiments excluding this interpretation. Second, the increased Jc at the ends of the junction is likely related to current crowding. In our devices, the width of the superconducting NbSe2 leads exceeds the width of the Bi2Se3 flake, which can lead to the supercurrent streaming effect, thereby squeezing its density toward the edges (16, 67). An alterna-tive explanation involves long superconducting leads, which result in a nonlinear φ(y) dependence (66). In this case, the Fourier analy-sis of the interference pattern can produce spurious effects that mimic an apparent enhancement of supercurrent flow near the edges. Both scenarios capture the main experimental features of our data: a nonreciprocal CPR, an anomalous peak-dip structure, and the superconducting diode effect.Next, the nonsinusoidal js(φ1) dependence can, in principle, re-sult from both SOC and high-transparency junction. For instance, the superposition of currents from spin-dependent Andreev bound states—arising due to SOC (68)—can generate higher harmonics in the js(φ1) dependence (47). Similarly, high-transparency interfaces between the superconductor and the weak link material can also lead to nonsinusoidal behavior (69). Previous studies have shown that SOC has little effect on the CPR in Bi2Se3 JJ in the absence of an applied in-plane magnetic field (50), which is the case in our ex-periment. In contrast, our analysis—based on the Galaktionov-Zaikin formalism (70) (Supplementary Materials)—indicates that the interfaces in our device have high transparency. Therefore, the prominent second harmonic observed in the local CPR is likely re-lated to the high transparency of the NbSe2/Bi2Se3 interface, which we ascribe to its atomically smooth nature achieved through our fabrication process.It is also instructive to place the observed JDE in a broader context of nonreciprocity in superconducting systems [see (37) for recent review]. Originally predicted to emerge in superconducting materials with intrinsically broken inversion and time-reversal symmetries, su-perconducting diodes can also be engineered artificially [e.g., (16, 38–41)]. Among numerous approaches, recently proposed SQUID-based diodes particularly stand out in terms of ease of fabrication, large diode efficiency, and remarkable tunability (71, 72). The SD in our JJ1, name-ly, its increase at the edges, effectively mimics that of a typical SQUID loop. Together with nonsinusoidal CPR and asymmetry between the edges, this gives rise to the JDE of a conceptually similar nature as in the proposed asymmetric higher-harmonic SQUIDs (71, 72).Fig. 5. Reconstruction of the SD. Critical current Ic of JJ1 as a function of magnetic field B . The inset shows the SD, which was reconstructed from Ic(B) , by the red line, and the SD, which was used for modeling, by the black line.Downloaded from https://www.science.org at National Institute for Materials Science on June 17, 2025Kudriashov et al., Sci. Adv. 11, eadw6925 (2025) 13 June 2025S c i e n c e A d v a n c e s | R e s e ar c h A r t i c l e7 of 9Finally, we compare our system with the model assumed by Potter and Fu in their original prediction of the peculiar CPR structure near the flux quantum due to MBS hybridization (32). The theory considered a JJ based on a TI thin film in the short ( L < ξn ) and narrow ( W < λJ ) limit, where both top and bottom surfaces are proximitized by a superconductor, where ξn is the superconducting coherence length in Bi2Se3. Our junction satisfies these constraints, as detailed in the Supplementary Materials. Furthermore, the thin Bi2Se3 flake ( ≈5 nm) minimizes contributions from the side sur-faces, while its high n-doping enables superconductivity to propa-gate from the top to the bottom surface through bulk states (58). Thus, our experimental system closely matches the conditions re-quired by the theoretical proposal. The observed peak-dip structure (Fig. 2E) in some sense resembles the anomalous CPR due to MBS hybridizing at the edge of the junction predicted in (32) and can be naively attributed to their presence. Moreover, the supercurrent in this regime is expected to be close to the maximal Josephson current carried by a single quantum channel Δ∕Φ0 ≈ 75 nA for the super-conducting gap of Δ ∼ 1 meV that is fortuitously close to our ex-perimental value at the Fraunhofer minimum—60 nA (see Fig. 2E, black curve). However, despite apparent similarity of the anomalous peak-dip CPR in the Potter-Fu model to the experimental data, there are two key differences that rule out this interpretation. First, the theoretical peak-dip structure is predicted to emerge around φ1 = π but not at π∕2 as in the case of our experiment. Second, the width of the experimental peak-dip structure is notably larger com-pared to the theoretical prediction (32). Should the MBSs be present in the Bi2Se3-based JJs, the resolution of our technique would be sufficient to reveal their signatures.To conclude, we have demonstrated a platform for precise CPR measurements in lateral JJs composed of NbSe2 and few-layer Bi2Se3, enabling the reconstruction of the CPR as a function of mag-netic flux. Our findings reveal unconventional CPR characteristics and a robust, tunable JDE in the vicinity of the flux quantum, stem-ming from nonuniform SD and nonsinusoidal local CPR. Notably, we find no evidence of MBSs near a single flux quantum, challeng-ing previous claims in Bi2Se3-based JJs. These results establish CPR measurements as a powerful tool for probing nonreciprocal trans-port phenomena in superconducting systems and provide design principles for superconducting quantum devices. It would be natu-ral to extend our approach of CPR measurements in planar vdW JJs using cracked, atomically flat superconductors to investigate other topologically nontrivial materials such as Sn-doped Bi1.1Sb0.9Te2S (73), WTe2 (74, 75), or MnBi2Te4 (76) that are unstable under stan-dard nanofabrication processing.MATERIALS AND METHODSSample fabricationDevice fabrication was performed using a dry transfer technique in an argon-filled glovebox with controlled H2O and O2 levels (<0.5 parts per million). The fabrication process began with oxygen plas-ma cleaning of Si/SiO2 substrates to optimize the subsequent exfolia-tion of thin Bi2Se3 flakes. hBN, NbSe2, and Bi2Se3 were mechanically exfoliated onto the prepared Si/SiO2 substrates using adhesive tape. The heterostructure assembly proceeded by first picking up an hBN flake using a PDMS/PC (polydimethylsiloxane/polycarbonate) stamp, which was then used to pick up a cracked NbSe2 flake, followed by transferring the assembled stack onto the exfoliated Bi2Se3 flake.Electrical contacts were fabricated using standard electron beam lithography, followed by CHF3/O2 reactive ion etching (RIE) of the hBN layer and electron beam evaporation of Ti/Au contacts (5 nm/65 nm). A magnetic flux line was subsequently created by depositing Ti (3 nm) followed by Al (97 nm). The SQUID loop geometry was then defined using CHF3/O2 RIE. After performing initial transport measurements on the complete SQUID, the device was divided into two separate JJs using CHF3/O2 RIE, enabling indi-vidual junction characterization after cooling. See the Supplemen-tary Materials for details.Scanning transmission electron microscopyA cross-sectional specimen of the nanodevice was prepared using a focused ion beam (FEI Versa 3D Dual Beam) after depositing a 30-nm-thick platinum layer on the surface as a protective coating. Cross-sectional STEM imaging was then performed ex situ using a JEOL ARM200F microscope equipped with an ASCOR aberra-tion corrector, operating at 200 kV. Elemental mapping was con-ducted with an Oxford X-Max 100TLE EDS detector integrated with the microscope.Low-noise measurementsElectrical measurements were performed in a BlueFors dilution refrigerator at a base temperature of 8 mK, equipped with a 12-T superconducting solenoid. The solenoid was controlled using a Yokogawa GS610 source-measure unit. The devices were mounted on a QDevil QBoard sample holder using the BlueFors fast sample ex-change system. The measurement setup incorporated two distinct wir-ing configurations to optimize different measurement requirements.For precise I-V measurements, we used a low-current measure-ment line featuring a cryogenic filtering system consisting of a Basel Precision Instruments MFT25-100 Ohm microwave filter and thermalizer at the mixing chamber plate, complemented by a QDevil QFilter at the still plate. The setup was designed to effec-tively eliminate 50-Hz interference, allowing for fast and high-precision measurements. The devices were biased with a sinusoidal current (frequency: few hertz) generated by a QDevil qDAC-II and converted through a CS580 voltage-to-current converter. Both the sample voltage drop and applied voltage were amplified using a battery-powered SR560 amplifier and digitized synchronously with an NI-3232 system. Critical current determination was performed using custom LabView-based software (MeXpert) implementing a threshold method, with CS580 current offset compensation (see the Supplementary Materials for details).For high-current applications, specifically the magnetic flux line control requiring currents up to several milliamperes, we imple-mented a separate configuration optimized to minimize heating ef-fects. This setup utilized only a superconducting MFT25-25 mOhm filter at the mixing chamber, bypassing the QFilter. The circuit used aluminum superconducting bonds (additionally, QBoard resistors were removed), with current supplied by a QDevil qDAC-II through a 1-kilohm resistor.Supplementary MaterialsThis PDF file includes:Supplementary TextFigs. S1 to S11ReferencesDownloaded from https://www.science.org at National Institute for Materials Science on June 17, 2025Kudriashov et al., Sci. 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Ritchie, Probing the topological surface state in Bi2Se3 thin films using temperature-dependent terahertz spectroscopy. ACS Photonics 4, 2711–2718 (2017).Acknowledgments: We thank K. Laubscher, M. Feigelman, and Y. Fominov for valuable discussions. Funding: The work is supported by MOE Tier 2 grant award T2EP50123-0020 (sample fabrication) awarded to D.A.B. We acknowledge the Electron Microscopy Facility (EMF) at the National University of Singapore for providing access to the FIB and STEM equipment. K.S.N. is grateful to the Ministry of Education, Singapore (Research Centre of Excellence award to the Institute for Functional Intelligent Materials, I-FIM, project no. EDUNC-33-18-279-V12) and to the Royal Society (UK, grant number RSRP R 190000) for support. E.V.Z. and L.E. were supported by internal funding programme from the Center for Neurophysics and Neuromorphic Technologies. L.V.Y. acknowledges the support of RSF grant no. 23-72- 00020. Z.L. acknowledges the support from the National Research Foundation, Singapore, under its Competitive Research Programme (CRP) (NRF-CRP22-2019-0007 and NRF-CRP22-2019-0004) and also the support by the Ministry of Education, Singapore, under its Research Centre of Excellence award to the Institute for Functional Intelligent Materials (project no. EDUNC-33-18-279-V12). Author contributions: A.K. and D.A.B. designed the project. Xiangyu Zhou, A.K., and L.E. fabricated the devices. A.K. performed the transport measurements. R.A.H. and A.K. performed the theoretical analysis. T.T. and K.W. provided the hBN crystals. L.V.Y. and A.S.F. provided the Bi2Se3 crystals. Xin Zhou performed STEM measurements. A.K. and D.A.B. wrote the manuscript with inputs from R.A.H. All authors contributed to the discussions. D.A.B. supervised the project. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. The data shown in Figs. 1 to 5 are available on Zenodo (https://doi.org/10.5281/zenodo.15149021). The hBN single crystals can be provided by the National Institute for Materials Science (NIMS), Japan, pending scientific review and a completed material transfer agreement. Requests for the hBN crystals should be submitted to: TANIGUCHI.Takashi@nims.go.jp and bncrystals.office@ml.nims.go.jp.Submitted 12 February 2025 Accepted 12 May 2025 Published 13 June 2025 10.1126/sciadv.adw6925Downloaded from https://www.science.org at National Institute for Materials Science on June 17, 2025https://doi.org/10.5281/zenodo.15149021mailto:TANIGUCHI.Takashi@nims.go.jpmailto:bncrystals.office@ml.nims.go.jpmailto:bncrystals.office@ml.nims.go.jp Non-Majorana origin of anomalous current-phase relation and Josephson diode effect in Bi2Se3/NbSe2 Josephson junctions INTRODUCTION RESULTS Planar vdW JJs CPR measurements Nonreciprocal CPR and Josephson diode Theoretical modeling DISCUSSION MATERIALS AND METHODS Sample fabrication Scanning transmission electron microscopy Low-noise measurements Supplementary Materials This PDF file includes: REFERENCES AND NOTES Acknowledgments