Although signatures of superconductivity in Dirac semimetals have been reported, for instance by applying pressure or using point contacts, our understanding of the topological aspects of Dirac semimetal superconductivity is still developing. Here, we utilize nanoscale phase-sensitive junction technology to induce superconductivity in the Dirac semimetal Bi1−xSbx. Our radiofrequency irradiation experiments then reveal a significant contribution of 4π-periodic Andreev bound states to the supercurrent in Nb–Bi0.97Sb0.03–Nb Josephson junctions. The conditions for a substantial 4π contribution to the supercurrent are favourable because of the Dirac cone’s very broad transmission resonances and a measurement frequency faster than the quasiparticle poisoning rate. In addition, we show that a magnetic field applied in the plane of the junction allows tuning of the Josephson junctions from 0 to π regimes. Our results open the technologically appealing avenue of employing the topological bulk properties of Dirac semimetals for topological superconductivity research and topological quantum computer development.
Subscribe to Journal
Get full journal access for 1 year
only $16.58 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
The data that support the findings of this study are available from the corresponding author on request.
Liu, Z. K. et al. Discovery of a three-dimensional topological Dirac semimetal, Na3Bi. Science 343, 864–867 (2014).
Neupane, M. et al. Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd3As2. Nat. Commun. 5, 3786 (2014).
Borisenko, S. et al. Experimental realization of a three-dimensional Dirac semimetal. Phys. Rev. Lett. 113, 027603 (2014).
Kim, H. J. et al. Dirac versus Weyl fermions in topological insulators: Adler–Bell–Jackiw anomaly in transport phenomena. Phys. Rev. Lett. 111, 246603 (2013).
Shin, D. et al. Violation of Ohm’s law in a Weyl metal. Nat. Mater. 16, 1096–1099 (2017).
Qi, X. L. & Zhang, S. C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).
Fu, L. & Kane, C. L. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008).
Das Sarma, S., Freedman, M. & Nayak, C. Majorana zero modes and topological quantum computation. npj Quant. Inf. 1, 15001 (2015).
Mourik, V. et al. Signatures of Majorana fermions in hybrid superconductor–semiconductor nanowire devices. Science 336, 1003–1007 (2012).
Rokhinson, L. P., Liu, X. & Furdyna, J. K. The fractional a.c. Josephson effect in a semiconductor-superconductor nanowire as a signature of Majorana particles. Nat. Phys. 8, 795–799 (2012).
Albrecht, S. M. et al. Exponential protection of zero modes in Majorana islands. Nature 531, 206–209 (2016).
Nadj-Perge, S. et al. Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor. Science 31, 602–607 (2014).
Wiedenmann, J. et al. 4π-Periodic Josephson supercurrent in HgTe-based topological Josephson junctions. Nat. Commun. 7, 10303 (2016).
Sun, H. H. et al. Majorana zero mode detected with spin selective Andreev reflection in the vortex of a topological superconductor. Phys. Rev. Lett. 116, 257003 (2016).
He, L. et al. Pressure-induced superconductivity in the three-dimensional topological Dirac semimetal Cd3As2. npj Quant. Mater. 1, 16014 (2016).
Aggarwal, L. et al. Unconventional superconductivity at mesoscopic point contacts on the 3D Dirac semimetal Cd3As2. Nat. Mater. 15, 32–37 (2016).
Wang, H. et al. Observation of superconductivity induced by a point contact on 3D Dirac semimetal Cd3As2 crystals. Nat. Mater. 15, 38–42 (2016).
Parameswaran, S. A., Grover, T., Abanin, D. A., Pesin, D. A. & Vishwanath, A. Probing the chiral anomaly with nonlocal transport in three dimensional topological semimetals. Phys. Rev. X 4, 031035 (2014).
Snelder, M., Veldhorst, M., Golubov, A. A. & Brinkman, A. Andreev bound states and current–phase relations in three-dimensional topological insulators. Phys. Rev. B 87, 104507 (2013).
Badiane, D. M., Houzet, M. & Meyer, J. S. Nonequilibrium Josephson effect through helical edge states. Phys. Rev. Lett. 107, 177002 (2011).
Wolff, P. A. Matrix elements and selection rules for the two-band model of bismuth. J. Phys. Chem. Solids 25, 1057–1068 (1964).
Tichovoisky, E. J. & Mavroides, J. G. Magnetoreflection studies on the band structure of bismuth-antimony alloys. Solid State Commun. 7, 927–931 (1969).
Yang, B. J. & Nagaosa, N. Classification of stable three-dimensional Dirac semimetals with nontrivial topology. Nat. Commun. 5, 4898 (2014).
Hsieh, D. et al. A topological Dirac insulator in a quantum spin Hall phase. Nature 452, 970–974 (2008).
Hsieh, D. et al. Observation of unconventional quantum spin textures in topological insulators. Science 323, 919–922 (2009).
Xiong, J. et al. Evidence for the chiral anomaly in the Dirac semimetal Na3Bi. Science 350, 413–416 (2015).
Dominguez, F., Hassler, F. & Platero, G. Dynamical detection of Majorana fermions in current-biased nanowires. Phys. Rev. B 86, 140503 (2012).
Bocquillon, E. et al. Gapless Andreev bound states in the quantum spin Hall insulator HgTe. Nat. Nanotech. 12, 13743 (2017).
Pico-Cortes, J., Dominguez, F. & Platero, G. Signatures of a 4π-periodic supercurrent in the voltage response of capacitively shunted topological Josephson junctions. Phys. Rev. B 96, 125438 (2017).
Fu, L. & Kane, C. L. Josephson current and noise at a superconductor/quantum-spin-Hall-insulator/superconductor junction. Phys. Rev. B 79, 161408 (2009).
Beenakker, C. W. J., Pikulin, D. I., Hyart, T., Schomerus, H. & Dahlhaus, J. P. Fermion-parity anomaly of the critical supercurrent in the quantum spin-Hall effect. Phys. Rev. Lett. 110, 017003 (2013).
Zhang, F. & Kane, C. L. Anomalous topological pumps and fractional Josephson effects. Phys. Rev. B 90, 020501 (2014).
Zhang, F. & Kane, C. L. Time-reversal-invariant Z 4 fractional Josephson effect. Phys. Rev. Lett. 113, 036401 (2014).
Peng, Y., Pientka, F., Berg, E., Oreg, Y. & Von Oppen, F. Signatures of topological Josephson junctions. Phys. Rev. B 94, 085409 (2016).
Houzet, M., Meyer, J. S., Badiane, D. M. & Glazman, L. I. Dynamics of Majorana states in a topological Josephson junction. Phys. Rev. Lett. 111, 046401 (2013).
Zhu, Z., Fauqué, B., Fuseya, Y. & Behnia, K. Angle-resolved Landau spectrum of electrons and holes in bismuth. Phys. Rev. B 84, 115137 (2011).
Ryazanov, V. V. et al. Coupling of two superconductors through a ferromagnet: evidence for a π junction. Phys. Rev. Lett. 86, 2427–2430 (2001).
Kontos, T. et al. Josephson junction through a thin ferromagnetic layer: negative coupling. Phys. Rev. Lett. 89, 137007 (2002).
Blum, Y., Tsukernik, A., Karpovski, M. & Palevski, A. Oscillations of the superconducting critical current in Nb–Cu–Ni–Cu–Nb junctions. Phys. Rev. Lett. 89, 187004 (2002).
Hart, S. et al. Controlled finite momentum pairing and spatially varying order parameter in proximitized HgTe quantum wells. Nat. Phys. 13, 87–93 (2017).
Demler, E. A., Arnold, G. B. & Beasley, M. R. Superconducting proximity effects in magnetic metals. Phys. Rev. B 55, 15174–15182 (1997).
Li, C. et al. Zeeman effect induced 0−π transitions in ballistic Dirac semimetal Josephson junctions (2018). Preprint at https://arXiv.org/abs/1807.07725
Yu, W. et al. π and 4π Josephson effects mediated by a Dirac semimetal. Phys. Rev. Lett. 120, 177704 (2018).
Tang, S. & Dresselhaus, M. S. Constructing a large variety of Dirac-cone materials in the Bi1−xSbx thin film system. Nanoscale 4, 7786–7790 (2012).
Zhu, Z., Collaudin, A., Fauqué, B., Kang, W. & Behnia, K. Field-induced polarization of Dirac valleys in bismuth. Nat. Phys. 8, 89–94 (2012).
The authors thank the Diamond Light Source for access to beamline I05 (proposal no. 12969), which contributed to the results presented here, and A. Schiphorst, T. Kim and M. Hoesch for assistance with ARPES experiments. The authors thank R. Lier for numerical calculations. This work was financially supported by the Foundation for Fundamental Research on Matter (FOM), associated with the Netherlands Organization for Scientific Research (NWO), and the European Research Council (ERC) through a Consolidator Grant.
The authors declare no competing interests.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Li, C., de Boer, J.C., de Ronde, B. et al. 4π-periodic Andreev bound states in a Dirac semimetal. Nature Mater 17, 875–880 (2018). https://doi.org/10.1038/s41563-018-0158-6
Physical Review B (2020)
Communications Materials (2020)
Nature Communications (2020)
Annalen der Physik (2020)
Experimental study of ac Josephson effect in gate-tunable (Bi1−xSbx)2Te3 thin-film Josephson junctions
Physical Review B (2020)