Skip to main content
Log in

Shape-Resonant Superconductivity in Nanofilms: from Weak to Strong Coupling

  • Original Paper
  • Published:
Journal of Superconductivity and Novel Magnetism Aims and scope Submit manuscript

Abstract

Ultrathin superconductors of different materials are becoming a powerful platform to find mechanisms for enhancement of superconductivity, exploiting shape resonances in different superconducting properties. Here, we evaluate the superconducting gap and its spatial profile, the multiple gap components, and the chemical potential, of generic superconducting nanofilms, considering the pairing attraction and its energy scale as tunable parameters, from weak to strong coupling, at fixed electron density. Superconducting properties are evaluated at mean field level as a function of the thickness of the nanofilm, in order to characterize the shape resonances in the superconducting gap. We find that the most pronounced shape resonances are generated for weakly coupled superconductors, while approaching the strong coupling regime the shape resonances are rounded by a mixing of the subbands due to the large energy gaps extending over large energy scales. Finally, we find that the spatial profile, transverse to the nanofilm, of the superconducting gap acquires a flat behavior in the shape resonance region, indicating that a robust and uniform multigap superconducting state can arise at resonance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Ge, J.F., Liu, Z. L., Liu, C., Gao, C.L., Qian, D., Xue, O.K., Liu, Y., Jia, J. F.: Superconductivity above 100 K in single-layer FeSe films on doped S r T i O 3. Nat. Mater. 14(5pp) (2015)

  2. Xue, M., Chen, G., Yang, H., Zhu, Y., Wang, D., He, J., Cao, T.: Superconductivity in Potassium-Doped Few-Layer Graphene. J. Am. Chem. Soc 134(4pp), 15 (2012)

    Google Scholar 

  3. Shi, X., Han, Z.-Q., Peng, X.-L., Richard, P., Qian, T., Wu, X.-X., Qiu, M.-W., Wang, S.C., Hu, J.P., Sun, Y.-J., Ding, H.: Enhanced superconductivity accompanying a Lifshitz transition in electron-doped FeSe monolayer. arXiv:1606.01470 (2016)

  4. Perali, A., Pieri, P., Strinati, G.C.: Extracting the condensate density from projection experiments with Fermi gases. Phys. Rev. Lett. 95(4pp), 010407 (2005)

    Article  ADS  Google Scholar 

  5. Palestini, F., Perali, A., Pieri, P., Strinati, G.C.: Dispersions, weights, and widths of the single-particle spectral function in the normal phase of a Fermi gas. Phys. Rev. B 85(17pp), 024517 (2012)

    Article  ADS  Google Scholar 

  6. Lubashevsky, Y., Lahoud, E., Chashka, K., Podolsky, D., Kanigel, A.: Shallow pockets and very strong coupling superconductivity in FeSe x Te 1−x . Nat. Phys. 8(4pp) (2012)

  7. Kasahara, S., Watashige, T., Hanaguri, T., Kohsaka, Y., Yamashita, T., Shimoyama, Y., Mizukami, Y., Endo, R., Ikeda, H., Aoyama, K., Terashima, T., Uji, S., Wolf, T., Lhneysenn, H.v., Shibauchi, T., Matsuda, Y.: Field-induced superconducting phase of FeSe in the BCS-BEC cross-over. PNAS 111(5pp), 46 (2014)

    Google Scholar 

  8. Okazaki, K., Ito, Y., Ota, Y., Kotani, Y., Shimojima, T., Kiss, T., Watanabe, S., Chen, C.-T., Niitaka, S., Hanaguri, T., Takagi, H., Chainani, A., Shin, S.: Superconductivity in an electron band just above the Fermi level: possible route to BCS-BEC superconductivity. Sci. Rep. 4(6pp), 4109 (2014)

    ADS  Google Scholar 

  9. Guidini, A., Perali, A.: Band-edge BCS-BEC crossover in a two-band superconductor: physical properties and detection parameters. Supercond. Sci. Technol. 27(10pp), 124002 (2014)

    Article  ADS  Google Scholar 

  10. Guo, Y., Zhang, Y.-F., Bao, X.-Y., Han, T.-Z., Tang, Z., Zhang, L.-X., Zhu, W.-G., Wang, E.G., Niu, Q., Qiu, Z.Q., Jia, J.-F., Zhao, Z.-X., Xue, Q.-K.: Superconductivity modulated by quantum size effects. Science 306(3pp), 1915 (2004)

    Article  ADS  Google Scholar 

  11. Eom, D., Qin, S., Chou, M.-Y., Shih, C.-K.: Persistent superconductivity in ultrathin Pb films: a scanning tunneling spectroscopy study. Phys. Rev. Lett. 96(4pp), 027005 (2006)

    Article  ADS  Google Scholar 

  12. Qin, S., Kim, J., Niu, Q., Shih, C.-K.: Superconductivity at the two-dimensional limit. Science 324 (4pp), 1314 (2009)

    Article  ADS  Google Scholar 

  13. Shanenko, A.A., Croitoru, M.D., Zgirski, M., Peeters, F.M., Arutyunov, K.: Size-dependent enhancement of superconductivity in nanowires. Phys. Rev. B 74(4pp), 052502 (2006). And reference therein

    Article  ADS  Google Scholar 

  14. Altomare, F., Chang, A.M.: One-Dimensional Superconductivity in Nanowires, WILEY-VCH. Weinheim, Germany (2013)

    Book  Google Scholar 

  15. Shanenko, A.A., Croitoru, M.D., Peeters, F.M.: Nanoscale superconductivity: nanowires and nanofilms. Physica C 468(6pp) (2008)

  16. Blatt, J.M., Thompson, C.J.: Shape resonances in superconducting thin films. Phys. Rev. Lett. 10(3pp), 8 (1963)

    Google Scholar 

  17. Thompson, C.J., Blatt, J.M.: Shape resonances in superconductors - II simplified theory. Phys. Lett. 5 (4pp), 1 (1963)

    ADS  Google Scholar 

  18. Shanenko, A.A., Aguiar, J.A., Vagov, A., Croitoru, M.D., Milošević, M.V.: Atomically flat superconducting nanofilms: multiband properties and mean-field theory. Supercond. Sci. Technol. 28(16pp), 05001 (2015)

    Google Scholar 

  19. Milosevic, M.V., Perali, A.: Emergent phenomena in multicomponent superconductivity: an introduction to the focus issue. Supercond. Sci. Tech. 28(4pp), 060201 (2015)

    Article  ADS  Google Scholar 

  20. Perali, A., Bianconi, A., Lanzara, A., Saini, N.L.: The gap amplification at a shape resonance in a superlattice of quantum stripes: a mechanism for high Tc. Solid State Comm 100(6pp), 3 (1996)

    Google Scholar 

  21. García-García, A.M., Urbina, J.D., Yuzbashyan, E.A., Richter, K., Altshuler, B.L.: Bardeen-Cooper-Schrieffer Theory of finite-size superconducting metallic grains. Phys. Rev. Lett. 100(4pp), 187001 (2008)

    Article  ADS  Google Scholar 

  22. Bose, S., García-García, A.M., Ugeda, M.M., Urbina, J.D., Michaelis, C.H., Brihuega, I., Kern, K.: Observation of shell effects in superconducting nanoparticles of Sn. Nat. Mater. 9(5pp) (2010)

  23. Mayoh, J., García-García, A.M.: Strong enhancement of bulk superconductivity by engineered nanogranularity. Phys. Rev. B 90(10pp), 134513 (2014)

    Article  ADS  Google Scholar 

  24. Mayoh, J., García-García, A. M.: Number theory, periodic orbits, and superconductivity in nanocubes. Phys. Rev. B 90(9pp), 014509 (2014)

    Article  ADS  Google Scholar 

  25. Bianconi, A., Valletta, A., Perali, A., Saini, N.L.: High Tc superconductivity in a superlattice of quantum stripes. Solid State Comm. 102(6pp), 5 (1997)

    Google Scholar 

  26. Bianconi, A., Valletta, A., Perali, A., Saini, N.L.: Superconductivity of a striped phase at the atomic limit. Physica C 296(12pp) (1998)

  27. Bianconi, A.: Quantum materials: shape resonances in superstripes. Nature Phys. 9(2pp) (2013)

  28. Fretto, M., Enrico, E., De Leo, N., Boarino, L., Rocci, R., Lacquaniti, V.: Nano SNIS Junctions Frabicated by 3D FIB Sculpting for Application to Digital Electronics. IEEE Trans. Appl. Supercond. 23, 1101104 (2013)

    Article  Google Scholar 

  29. Doria, M.M., Cariglia, M., Perali, A.: Multigap superconductivity and interaction driven resonances in superconducting nanofilms with an inner potential barrier. arXiv:1606.06018 (2016)

  30. Innocenti, D., Poccia, N., Ricci, A., Valletta, A., Caprara, S., Perali, A., Bianconi, A.: Resonant and crossover phenomena in a multiband superconductor: tuning the chemical potential near a band edge. Phys. Rev. B 82(12pp), 184528 (2010)

    Article  ADS  Google Scholar 

  31. Perali, A., Innocenti, D., Valletta, A., Bianconi, A.: Anomalous isotope effect near a 2.5 Lifshitz transition in a multi-band multi-condensate superconductor made of a superlattice of stripes. Supercond. Sci. Technol. 25(7pp), 124002 (2012)

    Article  ADS  Google Scholar 

  32. Chen, Y.J., Shanenko, A.A., Perali, A., Peeters, F.M.: Superconducting nanofilms: molecule-like pairing induced by quantum confinement. J. Phys. Condens. Matter 24(8pp), 185701 (2012)

    Article  ADS  Google Scholar 

  33. Shanenko, A.A., Croitoru, M.D., Vagov, A.V., Axt, V.M., Perali, A., Peeters, F.M.: Atypical BCS-BEC crossover induced by quantum-size effects. Phys. Rev. A 86(7pp), 033612 (2012)

    Article  ADS  Google Scholar 

  34. Guidini, A., Flammia, L., Milošević, M.V., Perali, A.: BCS-BEC crossover in quantum confined superconductors. J. Supercond. Nov. Magn. 29(5pp), 711 (2016)

    Article  Google Scholar 

  35. Perali, A., Castellani, C., Di Castro, C., Grilli, M., Piegari, E., Varlamov, A.A.: Two-gap model for underdoped cuprate superconductors. Phys. Rev. B 62(4pp), R9295(R) (2000)

    Article  ADS  Google Scholar 

  36. Marsiglio, F., Pieri, P., Perali, A., Palestini, F., Strinati, G.C.: Pairing effects in the normal phase of a two-dimensional Fermi gas. Phys. Rev. B 91(10pp), 054509 (2015)

    Article  ADS  Google Scholar 

  37. Anderson, P.W.: Theory of dirty superconductors. J. Phys. Chem. Solids 11(5pp), 26 (1959)

    Article  ADS  MATH  Google Scholar 

  38. De Gennes, P.G.: Superconductivity of Metals and Alloys. Benjamin, New York (1966)

    MATH  Google Scholar 

  39. Tanaka, K., Marsiglio, F.: Anderson prescription for surfaces and impurities. Phys. Rev. B 62, 5345 (2000)

    Article  ADS  Google Scholar 

  40. Suhl, H., Matthias, B.T., Walker, L.R.: Bardeen-Cooper-Schrieffer theory of superconductivity in the case of overlapping bands. Phys. Rev. Lett. 3(3pp), 12 (1959)

    MATH  Google Scholar 

  41. Valentinis, D., van der Marel, D., Berthod, C.: Rise and fall of shape resonances in thin films of BCS superconductors. arXiv:1601.04927v1 (2016)

  42. Valentinis, D., van der Marel, D., Berthod, C.: BCS superconductivity near the band edge: exact results for one and several bands. Phys. Rev. B 94(11pp), 024511 (2016)

    Article  ADS  Google Scholar 

  43. Bendele, M., Barinov, A., Joseph, B., Innocenti, D., Iadecola, A., Bianconi, A., Takeya, H., Mizuguchi, Y., Takano, Y., Noji, T., Hatakeda, T., Koike, Y., Horio, M., Fujimori, A., Ootsuki, D., Mizokawa, T., Saini, N. L.: Spectromicroscopy of electronic phase separation in KxFe2ySe2 superconductor. Sci. Rep. 4(5pp), 5592 (2014)

    ADS  Google Scholar 

  44. Razado-Colambo, I., Avila, J., Nys, J.P., Chen, C., Wallart, X., Asensio, M.C., Vignaud, D.: NanoARPES of twisted bilayer graphene on SiC: absence of velocity renormalization for small angles. Sci. Rep. 6 (7pp), 27261 (2016)

    Article  ADS  Google Scholar 

  45. Brur, J., Maggio-Aprile, I., Jenkins, N., Risti, Z., Erb, A., Berthod, C., Fischer, O., Renner, C.: Revisiting the vortex-core tunnelling spectroscopy in YBa2Cu3O7 −δ. Nature Commun. 7(6pp), 11139 (2016)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

We acknowledge D. Valentinis, D. Van der Marel, and C. Berthod for useful discussions. A. Ricci is also acknowledged for his comments on the experimental detection of the predictions of this paper. A. Bianconi acknowledges financial support from Superstripes non-profit organization. M. Cariglia acknowledges CNPq support from project (205029 / 2014-0) and FAPEMIG support from project APQ-02164-14. M.M. Doria acknowledges CNPq support from funding (23079.014992 / 2015-39). M.V. Milošević acknowledges support from Research Foundation - Flanders (FWO). A. Perali acknowledges financial support from the University of Camerino under the project FAR “Control and enhancement of superconductivity by engineering materials at the nanoscale”. All authors acknowledge the collaboration within the MultiSuper Network (http://www.multisuper.org) for exchange of ideas and suggestions.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Andrea Perali.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cariglia, M., Vargas-Paredes, A., Doria, M.M. et al. Shape-Resonant Superconductivity in Nanofilms: from Weak to Strong Coupling. J Supercond Nov Magn 29, 3081–3086 (2016). https://doi.org/10.1007/s10948-016-3673-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10948-016-3673-1

Keywords

Navigation