Abstract
The transmission of Cooper pairs between two weakly coupled superconductors produces a superfluid current and a phase difference; the celebrated Josephson effect. Because of timereversal and parity symmetries, there is no Josephson current without a phase difference between two superconductors. Reciprocally, when those two symmetries are broken, an anomalous supercurrent can exist in the absence of phase bias or, equivalently, an anomalous phase shift φ_{0} can exist in the absence of a superfluid current. We report on the observation of an anomalous phase shift φ_{0} in hybrid Josephson junctions fabricated with the topological insulator Bi_{2}Se_{3} submitted to an inplane magnetic field. This anomalous phase shift φ_{0} is observed directly through measurements of the currentphase relationship in a Josephson interferometer. This result provides a direct measurement of the spinorbit coupling strength and open new possibilities for phasecontrolled Josephson devices made from materials with strong spinorbit coupling.
Introduction
In Josephson junctions^{1}, the CurrentPhase relationship (CPR) is given by the first Josephson equation^{2}, I_{J}(φ) = I_{0} sin (φ + φ_{0}). Timereversal and spatial parity symmetries^{3}, P_{x},P_{y},P_{z} impose the equality I_{J}(φ → 0) = 0 and so only two states for the phase shift φ_{0} are possible. φ_{0} = 0 in standard junctions and φ_{0} = π in presence of a large Zeeman field, as obtained in hybrid superconductingferromagnetic junctions^{4,5,6} or in large gfactor materials under magnetic field^{7,8}.
To observe an anomalous phase shift φ_{0} intermediate between 0 and π, both timereversal and parity symmetries must be broken^{9,10,11,12,13,14,15,16,17,18,19,20,21,22}. This can be obtained in systems with both a Zeeman field and a Rashba spinorbit coupling term \({\mathrm{H}}_{\mathrm{R}} = \frac{\alpha }{\hbar }({\mathbf{p}} \times {\mathbf{e}}_z).\sigma\) in the Hamiltonian^{11,20}, where α is the Rashba coefficient, e_{z} the direction of the Rashba electric field and σ a vector of Pauli matrices describing the spin. Physically, these terms lead to a spininduced dephasing of the superconducting wavefunction.
This anomalous phase shift is related to the inverse Edelstein effect observed in metals or semiconductors with strong spinorbit coupling. While the Edelstein effect consists in the generation of a spin polarization in response to an electric field^{23}, the inverse Edelstein effect^{24}, also called spingalvanic effect, consists in the generation of a charge current by an outofequilibrium spin polarization. These two magnetoelectric effects are predicted also to occur in superconductors as a consequence of a Lifshitz type term in the free energy^{25,26}. Thus, in a superconductor with a strong Rashba coupling, a Zeeman field induces an additional term in the supercurrent. In Josephson junctions this term leads to the anomalous phase shift^{20}.
Several designs of Josephson junctions leading to an anomalous phase shift have been proposed theoretically where the Zeeman field can be obtained from an applied magnetic field^{14,16,20} or by using a magnetic element^{11}. These designs include the use of atomic contacts^{12}, quantum dots^{13,27}, nanowires^{17,18}, topological insulator^{19,28,29,30}, diffusive junction^{20}, magnetic impurity^{21}, ferromagnetic barrier^{11}, and diffusive superconductingferromagnetic junctions with noncoplanar magnetic texture^{31}.
Experimentally, the anomalous phase shift φ_{0} can be detected in a Josephson Interferometer (JI) through measurements of the CPR. Anomalous phase shifts have been identified recently in JIs fabricated from the parallel combination of a normal ‘0’ and ‘π’ junction^{22} that breaks the parity symmetries.
Because of its large gfactor g = 19.5^{32} and large Rashba coefficient, Bi_{2}Se_{3} is a promising candidate for observing the anomalous Josephson effect due to the interplay of the Zeeman field and spinorbit interaction. In this topological insulator^{33,34}, the effective Rashba coefficient of the topological Dirac states is about α ≃ 3 eVÅ^{35}, while the Rashba coefficient of the bulk states, induced by the broken inversion symmetry at the surface, has a value in the range 0.3–1.3 eVÅ as measured by photoemission^{36,37}.
As detailed in refs. ^{20,26} the amplitude of the anomalous phase depends on the amplitude of the Rashba coefficient α, the transparency of the interfaces, the spin relaxation terms such as the DyakonovPerel coefficient and whether the junction is in the ballistic or diffusive regime. At small α, the anomalous phase is predicted proportional to α^{3}, at large α, it should be proportional to α.
In the ballistic regime^{11} and for large α, the anomalous phase shift is given by \(\varphi _0 = \frac{{4E_{\mathrm{Z}}\alpha L}}{{(\hbar v_{\mathrm{F}})^2}}\) for a magnetic field of magnitude B and perpendicular to the Rashba electric field, where \(E_{\mathrm{Z}} = \frac{1}{2}g\mu _BB\) is the Zeeman energy, L is the distance between the superconductors and v_{F} is the Fermi velocity of the barrier material. For the Rashba spinsplit conduction band with α ≈ 0.4 eVÅ, v_{F} = 3.2×10^{5} ms^{−1} and junction length L = 150 nm, a magnetic field B = 100 mT generates an anomalous phase \(\varphi _0 \simeq 0.01 \pi\), while for Dirac states^{35} with v_{F} = 4.5×10^{5} ms^{−1}, \(\varphi _0 \simeq 0.005 \pi\).
In the diffusive regime, the expected anomalous phase shift has been calculated in ref. ^{20}. For weak α, highly transparent interfaces and neglecting spinrelaxation, the anomalous phase shift is given by the relation:
where τ = 0.13 ps is the elastic scattering time, \(D = \frac{1}{3}v_{\mathrm{F}}^2\tau = 40\,{\mathrm{cm}}^2\,{\mathrm{s}}^{  1}\) is the diffusion constant and m^{*} = 0.25 m_{e} is the effective electron mass^{38}.
To test these theoretical predictions, we fabricated single Josephson junctions and JIs from Bi_{2}Se_{3} thin films of 20 quintuple layers thick, ~20 nm, grown by Molecular Beam Epitaxy and protected by a Se layer, see Supplementary Note 1 and Supplementary Figure 1. As described in Supplementary Figure 2, these junctions are in the diffusive regime. From the measurement of the relative phase shift between two JIs with different orientations of the Josephson junctions with respect to the inplane magnetic field, we observed unambiguously the anomalous phaseshift predicted by Eq. (1).
Results
Currentphase relationship and Shapiro steps
The JI shown in Fig. 1a consists of two junctions in parallel of widths W_{1} = 600 nm and W_{2} = 60 nm, respectively. The phase differences φ_{1} and φ_{2} for the two junctions are linked by the relation \(\varphi _1  \varphi _2 = 2\pi \frac{\phi }{{\phi _0}}\), where ϕ = B_{z}S is the magnetic flux enclosed in the JI of surface S, B_{z} is a small magnetic field perpendicular to the sample, i.e. along e_{z}, and ϕ_{0} is the flux quantum. In this situation, the Zeeman energy is negligible and oriented along the Rashba electric field, which implies that φ_{0} = 0. As the critical current \(I_{{\mathrm{c}}_1}\) is much higher than \(I_{{\mathrm{c}}_2}\), then φ_{1} = π/2 and \(I_{\mathrm{c}} = I_{{\mathrm{c}}_1} + I_{{\mathrm{c}}_2}{\mathrm{cos}}(\omega B_z)\) with ω = 2πS/ϕ_{0}^{39}. Thus, a measurement of the critical current I_{c} as function of B_{z} provides a measure of the current \(I_{{\mathrm{c}}_2}\) as function of φ_{2}, i.e. the CPR. From the voltage map as a function of current I and B_{z}, shown Fig. 1b, the critical current I_{c} is extracted when the voltage across the device exceeds the value V_{switch} = 4 μV, as shown in Fig. 1c. We find that the CPR displays a conventional sinusoidal form I_{J} = I_{c} sin (φ), as shown by the fit in Fig. 1d. Furthermore, under microwave irradiation, the JI displays a conventional, 2π periodic, Shapiro pattern, as shown Fig. 2, and detailed discussion in Supplementary Note 2.
Asymmetric Fraunhofer pattern with inplane magnetic field
Figure 3b–d show resistance maps dV/dI of a single junction, Fig. 3a, as function of current I and B_{z} for different values of an inplane magnetic field, B_{y}. Figure 3e shows the corresponding critical current curves. A Fraunhofer pattern is observed with the first node located at \(B_0 \simeq 1.2\,{\mathrm{mT}}\). This value is consistent with the theoretical value \(B_0 = \frac{{\phi _0}}{{W(L + 2\lambda _z)}}\), using the effective magnetic penetration depth λ_{z} = 175 nm and taking into account fluxfocusing effects, see Supplementary Note 3. While for B_{y} = 0, the Fraunhofer pattern is symmetric with respect to B_{z}, this pattern becomes asymmetric upon increasing the amplitude of B_{y}. This evolution is shown in the critical current map as a function of B_{z} and B_{y} in Fig. 3f. We observed a much less pronounced asymmetry when we apply the magnetic field in the x direction as shown in Supplementary Figure 5. Similar behavior has been observed recently in InAs^{40} interpreted as the consequence of a combination of spinorbit, Zeeman and disorder effects. As described in ref. ^{3}, the generation of an anomalous phase shift requires breaking all symmetry operations U leaving UH(φ)U^{†} = H(−φ), where H is the full Hamiltonian of the system including spinorbit interactions. These symmetry operations are shown in Table 1 together with the parameters breaking those symmetries. This table shows that for a system with a finite spinorbit coefficient α, finite B_{y} is sufficient to generate an anomalous phase shift. However, additional symmetry operations U leaving UH(B_{z}, φ)U^{†} = H(−B_{z}, φ) must be broken to generate an asymmetric Fraunhofer pattern, as shown in Supplementary Table 1. In addition to nonzero values for α and B_{y}, disorder along y direction, i.e. nonzero V_{y}, is required to generate an asymmetric Fraunhofer pattern. AFM images, as in shown in Supplementary Figure 6g, show that the MBE films present atomic steps. Due to the dependence of the Rashba coefficient on film thickness^{35}, phase jumps along the y direction of the junction can be produced by jumps in the Rashba coefficient and explains the polarity asymmetry of the Fraunhofer pattern. As detailed in Supplementary Note 4, using a simple model, the asymmetric Fraunhofer pattern measured experimentally can be simulated, as shown in Fig. 3g.
Currentphase relationship with inplane magnetic field
To unambiguously demonstrate that an anomalous phase shift φ_{0} can be generated by finite spinorbit coefficient α and finite magnetic field B_{y} alone, a direct measurement of the CPR with inplane magnetic field is required. To that end, we measured simultaneously two JIs, oriented as sketched in Fig. 4a, differing only by the orientation of the small junctions with respect to the inplane magnetic field.
The CPRs for the two JIs are measured as function of a magnetic field making a small tilt θ with the sample plane, which produces an inplane B_{y} = B cos (θ) and a perpendicular B_{z} = B sin (θ) magnetic field, as sketched in Fig. 4c. In this situation, the critical current for the reference JI changes as I_{c} ∝ cos (ω_{ref} B) with \(\omega _{{\mathrm{ref}}} = \frac{{2\pi S_{{\mathrm{ref}}}}}{{\phi _0}}{\mathrm{sin}}(\theta )\) where S_{ref} is the surface of the JI. For the anomalous JI, the critical current changes as I_{c} ∝ cos (ωB) with:
where \(C_{\varphi _0} = \frac{{\tau m^{ \ast 2}g\mu _{\mathrm{B}}(\alpha L)^3}}{{6\hbar ^6D}}\) in the diffusive regime.
In Eq. (2), the first term arises from the flux within the JI of area S, the second term arises from the anomalous phase shift \(\varphi _0 = C_{\varphi _0}B\,{\mathrm{cos}}\,(\theta )\).
Figure 4b shows voltage maps for two different orientations θ, Fig. 4c. At low B, the two JIs are inphase and become outofphase at higher magnetic field, indicating that the frequency ω of the anomalous JI is slightly larger than the reference JI. This is also visible on the critical current plot, Fig. 5a, extracted from these voltage maps. To see this more clearly, the average critical current, shown as a continuous line in Fig. 5a, is removed from the critical current curve and the result shown in Fig. 5b for the two JIs. On these curves, the nodes at π(2n + 1/2), n = 0,1,.., are indicated by large red (blue) dots for the reference (anomalous) curve. At low magnetic field, the two JIs are inphase as indicated by the blue and red dots being located at the same field position. Upon increasing the inplane magnetic field, the two JIs become outofphase with the anomalous JI oscillating at a higher frequency than the reference JI, as indicated by the blue dot shifting to lower magnetic field position with respect to the red dot. This increased frequency for the anomalous device is expected from Eq. (2) as a consequence of the anomalous phase shift. Supplementary Figure 7a,b shows additional data taken from negative to positive magnetic field, across zero magnetic field. A plot of the phase difference between the two JIs as function of inplane magnetic field, shown in Supplementary Figure 7c, demonstrates that the two JIs are inphase at zero magnetic field and reach a dephasing approaching about π/2 for an inplane magnetic field of ≃80 mT.
One also sees that the oscillation period of both JIs increase with increasing B. As detailed in Supplementary Note 3, this is due to flux focusing that makes the effective area of the JIs larger at low magnetic field. As the effect of flux focusing decreases with the increasing penetration depth at higher magnetic field, the effective areas of the JIs decreases upon increasing the magnitude of the magnetic field and so the period of oscillations increases.
While the two JIs have been fabricated with nominally identical areas, to exclude that the observed difference in frequencies between the two JIs is due to a difference of areas, we plot in Fig. 5c, the frequency ratio \(\frac{\omega }{{\omega _{{\mathrm{ref}}}}}(\theta )\) measured at different angles θ. Because each curve contains several periods T_{i}, the frequency ratio is obtained from the average between the N periods ratio as \(\omega /\omega _{{\mathrm{ref}}} = \frac{1}{N}\mathop {\sum}\nolimits_{i = 1}^N \frac{{T_{i,{\mathrm{ref}}}}}{{T_i}}\), where T_{i,ref} and T_{i} are the i^{th} oscillation period for the reference and for the anomalous device respectively. This method enables ignoring the flux focusing effect because the ratio is only taken between two periods measured at about the same magnetic field. We find that the experimental data follows the relation:
At large θ, this ratio is equal to the ratio of areas \(S/S_{{\mathrm{ref}}} \simeq 1\), however, for small θ, this ratio increases as 1/tan(θ), indicating the presence of an anomalous phase shift φ_{0}.
Another way of extracting the frequency is described in the Supplementary Note 5 and leads to the same result, as shown in Supplementary Figure 8.
Discussion
A fit of the experimental data with Eq. (3), Fig. 5c, enables extracting the coefficient \(\frac{{C_{\varphi _0}\phi _0}}{{2\pi S_{{\mathrm{ref}}}}} = 41 \pm 5 10^{  5}\). Using the expression of \(C_{\varphi _0}\) in the diffusive regime given above, we calculate a spinorbit coefficient α = 0.38 ± 0.015 eVÅ. This value of the Rashba coefficient is consistent with the value extracted from Rashbasplit conduction band observed by photoemission measurements^{36,37}. Table 2 gives the anomalous phase shift extracted from the critical current oscillations at the largest magnetic field about 80–100 mT. The phase shift is extracted from the magnetic field difference between the last nodes of the oscillations, indicated by blue and red dots on Fig. 5. At this largest magnetic field, we find an anomalous phase shift \(\varphi _0 \simeq 0.9\pi\) for all three tilt angles θ. This shows that the anomalous phase shift depends only on the parallel component of the magnetic field as expected. This experimental value is compared with the theoretical values calculated in the ballistic regime, for the Rashbasplit conduction states and Dirac states, and in the diffusive regime, for the Rashbasplit conduction states. This table shows that the Dirac states provide only a phase shift of 0.005π and so cannot explain the experimental data. The table also shows that the Rashbasplit conduction states provide a phase shift of only 0.01π in the ballistic regime while they provide an anomalous shift of 0.94π in the diffusive regime, close to the experimental value, confirming that the junctions are indeed in the diffusive regime and demonstrating the validity of the theory leading to Eq. (1).
A detailed look at Table 1 shows that the anomalous shift observed here must be the consequence of finite Rashba coefficient and inplane magnetic field. While Table 1 shows that disorder alone V_{y} is sufficient to generate an anomalous phase shift, this disorderinduced anomalous phase shift should exist even at zero magnetic field and should not change with magnetic field. In contrast, as discussed above, we have seen that the two JIs are inphase near zero magnetic field and become out of phase only for at finite magnetic field. Thus, this observation implies that disorder V_{y} is absent, which is plausible as the small Josephson junction is only 150 nm × 150 nm. In the absence of disorder V_{y}, Table 1 shows that the only way for an anomalous phase shift to be present is that the coefficient α be nonzero. Indeed, if α were zero, the first and third symmetry operations of Table 1 would not be broken even with finite B_{y}.
To summarize the result of this work, the simultaneous measurements of the CPR in two JIs making an angle of 90° with respect to the inplane magnetic field enabled the identification of the anomalous phase shift φ_{0} induced by the combination of the strong spinorbit coupling in Bi_{2}Se_{3} and Zeeman field. This anomalous phase shift can be employed to fabricate a phase battery, a quantum device of intense interest for the design and fabrication of superconducting quantum circuits^{41,42}.
Methods
Sample preparation
The Bi_{2}Se_{3} samples were grown by Molecular Beam Epitaxy. The crystalline quality of the films was monitored insitu by reflection high energy electron diffraction and ex situ by xray diffraction, and by post growth verification of the electronic structure though the observation of the Dirac cone fingerprint in angleresolved photoemission spectra as described in ref. ^{43}. Following growth, the samples were capped with a Se protective layer. The Josephson junctions are fabricated on these thin films with standard ebeam lithography, ebeam deposition of Ti(5 nm)/Al(20–50 nm) electrodes and liftoff. The Se capping layer is removed just before metal evaporation by dipping the samples in a NMF solution of Na_{2}S. In the evaporator chamber, the surface is cleaned by moderate insitu ion beam cleaning of the film surface before metal deposition. While for standard junctions, an aluminum layer 50 nm thick is usually deposited, we also fabricated junctions with 20nmthick electrodes to increase their upper critical field as required by the experiments with inplane magnetic field. See Supplementary Figure 3 for a lateral sketch of the devices. After microfabrication, the carrier concentration is about 10^{19} cm^{−3} and the resistivity about 0.61 mΩ.cm, as shown in Supplementary Figure 2. A comparison between the normal state junction resistance of the order of 20–50 Ω and the resistivity of the films indicates negligible contact resistance, i.e. the junction resistance is due to the Bi_{2}Se_{3} film between the electrodes.
Measurements details
The values for the normal resistance and critical current values measured on 20 devices are found to be highly reproducible, demonstrating the reliability of our procedure for surface protection and preparation before evaporation of the electrodes. The devices are measured in a dilution fridge with a base temperature of 25 mK. The IV curves are measured with standard current source and low noise instrumentation amplifiers for detecting the voltage across the junctions. The measurement lines are heavily filtered with π filters at room temperature at the input connections of the cryostat. They are also filtered on the sample stage at low temperature with 1 nF capacitances connecting the measurements lines to the ground.
References
Josephson, B. D. Possible new effects in superconductive tunnelling. Phys. Lett. 1, 251–253 (1962).
Golubov, A. A., Kupriyanov, M. Y. & Il’ichev, E. The currentphase relation in josephson junctions. Rev. Mod. Phys. 76, 411–469 (2004).
Rasmussen, A. et al. Effects of spinorbit coupling and spatial symmetries on the josephson current in SNS junctions. Phys. Rev. B Condens. Matter 93, 155406 (2016).
Kontos, T., Aprili, M., Lesueur, J. & Grison, X. Inhomogeneous superconductivity induced in a ferromagnet by proximity effect. Phys. Rev. Lett. 86, 304–307 (2001).
Guichard, W. et al. Phase sensitive experiments in ferromagneticbased josephson junctions. Phys. Rev. Lett. 90, 167001 (2003).
Buzdin, A. I. Proximity effects in superconductorferromagnet heterostructures. Rev. Mod. Phys. 77, 935–976 (2005).
Hart, S. et al. Controlled finite momentum pairing and spatially varying order parameter in proximitized HgTe quantum wells. Nat. Phys. 13, 87 (2016).
Li, C. et al. 4πperiodic andreev bound states in a dirac semimetal. Nat. Mater. 17, 875–880 (2018).
Bezuglyi, E. V., Rozhavsky, A. S., Vagner, I. D. & Wyder, P. Combined effect of zeeman splitting and spinorbit interaction on the josephson current in a superconductor–twodimensional electron gas–superconductor structure. Phys. Rev. B Condens. Matter 66, 1011 (2002).
Braude, V. & Nazarov, Y. V. Fully developed triplet proximity effect. Phys. Rev. Lett. 98, 077003 (2007).
Buzdin, A. Direct coupling between magnetism and superconducting current in the josephson phi0 junction. Phys. Rev. Lett. 101, 107005 (2008).
Reynoso, A. A., Usaj, G., Balseiro, C. A., Feinberg, D. & Avignon, M. Anomalous josephson current in junctions with spin polarizing quantum point contacts. Phys. Rev. Lett. 101, 107001 (2008).
Zazunov, A., Egger, R., Jonckheere, T. & Martin, T. Anomalous josephson current through a spinorbit coupled quantum dot. Phys. Rev. Lett. 103, 147004 (2009).
Grein, R., Eschrig, M., Metalidis, G. & Schön, G. Spindependent cooper pair phase and pure spin supercurrents in strongly polarized ferromagnets. Phys. Rev. Lett. 102, 227005 (2009).
Mal’shukov, A. G., Sadjina, S. & Brataas, A. Inverse spin hall effect in superconductor/normalmetal/superconductor josephson junctions. Phys. Rev. B Condens. Matter 81, 060502 (2010).
Liu, J.F. & Chan, K. S. Anomalous josephson current through a ferromagnetic trilayer junction. Phys. Rev. B Condens. Matter 82, 184533 (2010).
Yokoyama, T., Eto, M. & Nazarov, Y. V. Anomalous josephson effect induced by spinorbit interaction and zeeman effe Phys. Rev. B Condens. Matter 89, 195407 (2014).
Campagnano, G., Lucignano, P., Giuliano, D. & Tagliacozzo, A. Spinorbit coupling and anomalous josephson effect in nanowires. J. Phys. Condens. Matter 27, 205301 (2015).
Dolcini, F., Houzet, M. & Meyer, J. S. Topological josephson junctions. Phys. Rev. B Condens. Matter 92, 035428 (2015).
Bergeret, F. S. & Tokatly, I. V. Theory of diffusive φ _{0} josephson junctions in the presence of spinorbit coupling. EPL 110, 57005 (2015).
Pershoguba, S. S., Björnson, K., BlackSchaffer, A. M. & Balatsky, A. V. Currents induced by magnetic impurities in superconductors with spinorbit coupling. Phys. Rev. Lett. 115, 116602 (2015).
Szombati, D. B. et al. Josephson 0junction in nanowire quantum dots. Nat. Phys. 12, 568 (2016).
Edelstein, V. M. Spin polarization of conduction electrons induced by electric current in twodimensional asymmetric electron systems. Solid State Commun. 73, 233–235 (1990).
Shen, K., Vignale, G. & Raimondi, R. Microscopic theory of the inverse edelstein effect. Phys. Rev. Lett. 112, 096601 (2014).
Yip, S. K. Twodimensional superconductivity with strong spinorbit interaction. Phys. Rev. B Condens. Matter 65, 144508 (2004).
Konschelle, F., Tokatly, I. V. & Bergeret, F. S. Theory of the spingalvanic effect and the anomalous phase shift in superconductors and josephson junctions with intrinsic spinorbit coupling. Phys. Rev. B Condens. Matter 92, 125443 (2015).
Dell’Anna, L., Zazunov, A., Egger, R. & Martin, T. Josephson current through a quantum dot with spinorbit coupling. Phys. Rev. B Condens. Matter 75, 085305 (2007).
Alidoust, M. & Hamzehpour, H. Spontaneous supercurrent and φ _{0} phase shift parallel to magnetized topological insulator interfaces. Phys. Rev. B Condens. Matter 96, 165422 (2017).
Zyuzin, A., Alidoust, M. & Loss, D. Josephson junction through a disordered topological insulator with helical magnetization. Phys. Rev. B Condens. Matter 93, 214502 (2016).
Bobkova, I. V., Bobkov, A. M., Zyuzin, A. A. & Alidoust, M. Magnetoelectrics in disordered topological insulator josephson junctions. Phys. Rev. B Condens. Matter 94, 134506 (2016).
Silaev, M. A., Tokatly, I. V. & Bergeret, F. S. Anomalous current in diffusive ferromagnetic josephson junctions. Phys. Rev. B Condens. Matter 95, 184508 (2017).
Wolos, A. et al. gfactors of conduction electrons and holes in Bi2Se3 threedimensional topological insulator. Phys. Rev. B Condens. Matter 93, 3023 (2016).
Zhang, H. et al. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single dirac cone on the surface. Nat. Phys. 5, 438 (2009).
Hasan, M. Z. & Kane, C. L. Colloquium. Rev. Mod. Phys. 82, 3045–3067 (2010).
Zhang, Y. et al. Crossover of the threedimensional topological insulator Bi2Se3 to the twodimensional limit. Nat. Phys. 6, 584 (2010).
Zhu, Z.H. et al. Rashba spinsplitting control at the surface of the topological insulator Bi2Se3. Phys. Rev. Lett. 107, 186405 (2011).
King, P. D. C. et al. Large tunable rashba spin splitting of a twodimensional electron gas in Bi2Se3. Phys. Rev. Lett. 107, 096802 (2011).
Hyde, G. R. et al. Shubnikovde haas effects in Bi2Se3 with high carrier concentrations. Solid State Commun. 13, 257–263 (1973).
Della Rocca, M. L. et al. Measurement of the currentphase relation of superconducting atomic contacts. Phys. Rev. Lett. 99, 127005 (2007).
Suominen, H. J. et al. Anomalous fraunhofer interference in epitaxial superconductorsemiconductor josephson junctions. Phys. Rev. B Condens. Matter 95, 035307 (2017).
Ortlepp, T. et al. Flipflopping fractional flux quanta. Science 312, 1495–1497 (2006).
Feofanov, A. K. et al. Implementation of superconductor/ferromagnet/ superconductor πshifters in superconducting digital and quantum circuits. Nat. Phys. 6, 593 (2010).
Vidal, F. et al. Photon energy dependence of circular dichroism in angleresolved photoemission spectroscopy of Bi_{2}Se_{3} dirac states. Phys. Rev. B Condens. Matter 88, 241410 (2013).
Acknowledgements
The devices have been made within the consortium Salle Blanche Paris Centre. We acknowledge fruitful discussions with S. Bergeret and J. Danon. This work was supported by French state funds managed by the ANR within the Investissements d’Avenir programme under reference ANR11IDEX000402, and more specifically within the framework of the Cluster of Excellence MATISSE. We also thanks L. Largeau (C2N: Centre de Nanosciences et de NanotechnologiesUniversit ParisSud) and D. Demaille (INSP: Institut des NanoSciences de ParisSorbonne Univerit)) for the atomicresolved HAADFSTEM images.
Author information
Authors and Affiliations
Contributions
H.A. proposed and supervised the project. M.E. and P.A. have grown the Bi_{2}Se_{3} thin films by MBE and did the structural characterization (AFM, XRay, and TEM). A.A. designed and microfabricated the samples with the help of C.F.P., T.Z., A.M., A.Z., E.L., M.A., and H.A.; A.A., M.A., and H.A made the measurements with the help of C.F.P. and N.B.; A.A., M.A., and H.A. analyzed the data and wrote the manuscript.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Journal peer review information: Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. Peer reviewer reports are available.
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 license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license 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 license, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Assouline, A., FeuilletPalma, C., Bergeal, N. et al. SpinOrbit induced phaseshift in Bi_{2}Se_{3} Josephson junctions. Nat Commun 10, 126 (2019). https://doi.org/10.1038/s4146701808022y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s4146701808022y
This article is cited by

Zerofield polarityreversible Josephson supercurrent diodes enabled by a proximitymagnetized Pt barrier
Nature Materials (2022)

Josephson diode effect from Cooper pair momentum in a topological semimetal
Nature Physics (2022)

Supercurrent rectification and magnetochiral effects in symmetric Josephson junctions
Nature Nanotechnology (2022)

Gate controlled anomalous phase shift in Al/InAs Josephson junctions
Nature Communications (2020)

Fermiarc supercurrent oscillations in Dirac semimetal Josephson junctions
Nature Communications (2020)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.