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Optimal conditions for observing fractional Josephson effect in topological Josephson junctions

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Abstract

Topological Josephson junctions (JJs), which contain Majorana bound states, are expected to exhibit 4π-periodic current–phase relation, thereby resulting in doubled Shapiro steps under microwave irradiation. We performed numerical calculations of dynamical properties of topological JJs using a modified resistively and capacitively shunted junction model and extensively investigated the progressive evolution of Shapiro steps as a function of the junction parameters and microwave power and frequency. Our calculation results indicate that the suppression of odd-integer Shapiro steps, i.e., evidence of the fractional ac Josephson effect, is enhanced significantly by the increase in the junction capacitance and IcRn product as well as the decrease in the microwave frequency even for the same portion of the 4π-periodic supercurrent. Our study provides the optimal conditions for observing the fractional ac Josephson effect; furthermore, our new model can be used to precisely quantify the topological supercurrent from the experimental data of topological JJs.

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References

  1. L. Fu, C.L. Kane, Phys. Rev. Lett. 100, 096407 (2008)

    Article  ADS  Google Scholar 

  2. X.-L. Qi, S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011)

    Article  ADS  Google Scholar 

  3. S. D. Sarma, M. Freedman, and C. Nayak, npj Quantum Information 1, 15001 (2015).

  4. M. Houzet, J.S. Meyer, D.M. Badiane, L.I. Glazman, Phys. Rev. Lett. 111, 046401 (2013)

    Article  ADS  Google Scholar 

  5. H.-J. Kwon, K. Sengupta, V.M. Yakovenko, Eur. Phys. J. B Condens. Matter Complex Syst. 37, 349 (2004)

    Article  Google Scholar 

  6. S. Shapiro, Phys. Rev. Lett. 11, 80 (1963)

    Article  ADS  Google Scholar 

  7. Y.-J. Doh, J.A. van Dam, A.L. Roest, E.P.A.M. Bakkers, L.P. Kouwenhoven et al., Science 309, 272 (2005)

    Article  ADS  Google Scholar 

  8. Y.-J. Doh, A.L. Roest, E.P.A.M. Bakkers, S. De Franceschi, L.P. Kouwenhoven, J. Korean Phys. Soc. 54, 135 (2009)

    Article  ADS  Google Scholar 

  9. H.-S. Kim, H.S. Shin, J.S. Lee, C.W. Ahn, J.Y. Song et al., Curr. Appl. Phys. 16, 51 (2016)

    Article  ADS  Google Scholar 

  10. H.-S. Kim, T.-H. Hwang, N.-H. Kim, Y. Hou, D. Yu et al., ACS Nano 14, 14118 (2020)

    Article  Google Scholar 

  11. J. Kim, A. Hwang, S.-H. Lee, S.-H. Jhi, S. Lee et al., ACS Nano 10, 3936 (2016)

    Article  Google Scholar 

  12. J. Kim, B.-K. Kim, H.-S. Kim, A. Hwang, B. Kim et al., Nano Lett. 17, 6997 (2017)

    Article  ADS  Google Scholar 

  13. L.P. Rokhinson, X. Liu, J.K. Furdyna, Nat. Phys. 8, 795 (2012)

    Article  Google Scholar 

  14. J. Wiedenmann, E. Bocquillon, R.S. Deacon, S. Hartinger, O. Herrmann et al., Nat. Commun. 7, 10303 (2016)

    Article  ADS  Google Scholar 

  15. E. Bocquillon, R.S. Deacon, J. Wiedenmann, P. Leubner, T.M. Klapwijk et al., Nat. Nanotechnol. 12, 137 (2017)

    Article  ADS  Google Scholar 

  16. C. Li, J.C. de Boer, B. de Ronde, S.V. Ramankutty, E. van Heumen et al., Nat. Mater. 17, 875 (2018)

    Article  ADS  Google Scholar 

  17. A.-Q. Wang, C.-Z. Li, C. Li, Z.-M. Liao, A. Brinkman et al., Phys. Rev. Lett. 121, 237701 (2018)

    Article  ADS  Google Scholar 

  18. M. Veldhorst, M. Snelder, M. Hoek, T. Gang, V.K. Guduru et al., Nat. Mater. 11, 417 (2012)

    Article  ADS  Google Scholar 

  19. C.G. Molenaar, D.P. Leusink, X.L. Wang, A. Brinkman, Supercond. Sci. Technol. 27, 104003 (2014)

    Article  ADS  Google Scholar 

  20. C.-Z. Li, C. Li, L.-X. Wang, S. Wang, Z.-M. Liao et al., Phys. Rev. B 97, 115446 (2018)

    Article  ADS  Google Scholar 

  21. Y. Takeshige, S. Matsuo, R.S. Deacon, K. Ueda, Y. Sato et al., Phys. Rev. B 101, 115410 (2020)

    Article  ADS  Google Scholar 

  22. F. Domínguez, O. Kashuba, E. Bocquillon, J. Wiedenmann, R.S. Deacon et al., Phys. Rev. B 95, 195430 (2017)

    Article  ADS  Google Scholar 

  23. K. Le Calvez, L. Veyrat, F. Gay, P. Plaindoux, C.B. Winkelmann et al., Commun. Phys. 2, 4 (2019)

    Article  Google Scholar 

  24. M. Tinkham, Introduction to Superconductivity (McGraw-Hill, New York, 1975).

    Google Scholar 

  25. D. Jeong, J.-H. Choi, G.-H. Lee, S. Jo, Y.-J. Doh et al., Phys. Rev. B 83, 094503 (2011)

    Article  ADS  Google Scholar 

  26. F. Domínguez, F. Hassler, G. Platero, Phys. Rev. B 86, 140503 (2012)

    Article  ADS  Google Scholar 

  27. H.H. Zappe, J. Appl. Phys. 44, 1371 (1973)

    Article  ADS  Google Scholar 

  28. J. Picó-Cortés, F. Domínguez, G. Platero, Phys. Rev. B 96, 125438 (2017)

    Article  ADS  Google Scholar 

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Acknowledgements

We are grateful to Ryundon Kim, Youngmin Cho, Sang-Jun Choi, and H.-S. Sim for the useful discussions. This research was supported by the NRF of Korea through the Basic Science Research Program (2018R1A3B1052827).

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  1. Department of Physics and Photon Science, Gwangju Institute of Science and Technology (GIST), Gwangju, 61005, Korea

    Yeongmin Jang & Yong-Joo Doh

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  1. Yeongmin Jang
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  2. Yong-Joo Doh
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Correspondence to Yong-Joo Doh.

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Jang, Y., Doh, YJ. Optimal conditions for observing fractional Josephson effect in topological Josephson junctions. J. Korean Phys. Soc. 78, 58–63 (2021). https://doi.org/10.1007/s40042-020-00035-5

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  • DOI: https://doi.org/10.1007/s40042-020-00035-5

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