Journal of Superconductivity and Novel Magnetism

, Volume 26, Issue 12, pp 3423–3435 | Cite as

Gate Voltage Tuned Quantum Superconductor to Insulator Transition in an Ultrathin Bismuth Film Revisited

  • T. Schneider
  • S. Weyeneth
Original Paper


We explore the implications of Berezinskii–Kosterlitz–Thouless (BKT) critical behavior and variable-range hopping on the two-dimensional (2D) quantum superconductor–insulator (QSI) transition driven by tuning the gate voltage. To illustrate the potential and the implications of this scenario we analyze sheet resistance data of Parendo et al. taken on a gate voltage tuned ultrathin amorphous bismuth film. The finite size scaling analysis of the BKT-transition uncovers a limiting length L preventing the correlation length to diverge and to enter the critical regime deeply. Nevertheless the attained BKT critical regime reveals consistency with two parameter quantum scaling and an explicit quantum scaling function determined by the BKT correlation length. The two parameter scaling yields for the zero temperature critical exponents of the QSI-transition the estimates \(z\overline{\nu }\simeq 3/2\), z≃3 and \(\overline{\nu} \simeq 1/2\), revealing that hyperscaling is violated and in contrast to finite temperature disorder is relevant at zero temperature. Furthermore, \(z\overline{\nu }\simeq 3/2\) is also consistent with the two variable quantum scaling form associated with a variable-range hopping controlled insulating ground state.


Superconducting films Quantum phase transition Two parameter scaling Superconductor insulator transition 


  1. 1.
    Sondhi, S.L., Girvin, S.M., Carini, J.P., Shahar, D.: Continuous quantum phase transitions. Rev. Mod. Phys. 69, 315–333 (1997) CrossRefADSGoogle Scholar
  2. 2.
    Schneider, T., Singer, J.M.: Phase Transition Approach to High Temperature Superconductivity. Imperial College Press, London (2000) CrossRefGoogle Scholar
  3. 3.
    Schneider, T.: In: Bennemann, K.H., Ketterson, J.B. (eds.) The Physics of Superconductors, p. 111. Springer, Berlin (2002) Google Scholar
  4. 4.
    Marcović, N., Christiansen, C., Mack, A., Goldman, A.M.: Superconductor–insulator transitions in 2D: the experimental situation. Phys. Status Solidi B 218, 221–227 (2000) CrossRefADSGoogle Scholar
  5. 5.
    Gantmakher, V.F., Dolgopolov, V.T.: Superconductor–insulator quantum phase transition. Phys. Usp. 53, 1–49 (2010) CrossRefADSGoogle Scholar
  6. 6.
    Parendo, K.A., Tan, K.H., Sarwa, B., Bhattacharya, A., Eblen-Zayas, M., Staley, N.E., Goldman, A.M.: Electrostatic tuning of the superconductor–insulator transition in two dimensions. Phys. Rev. Lett. 94, 197004 (2005) CrossRefADSGoogle Scholar
  7. 7.
    Parendo, K.A., Tan, K.H., Sarwa, B., Goldman, A.M.: Electrostatic and parallel-magnetic-field tuned two-dimensional superconductor–insulator transitions. Phys. Rev. B 73, 174527 (2006) CrossRefADSGoogle Scholar
  8. 8.
    Berezinskii, V.L.: Destruction of long-range order in one dimensional and 2-dimensional systems having a continuous symmetry group: 1-classical systems. Sov. Phys. JETP 32, 493 (1971) MathSciNetADSGoogle Scholar
  9. 9.
    Kosterlitz, J.M., Thouless, D.J.: Ordering, metastability and phase-transitions in 2 dimensional systems. J. Phys. C 6, 1181–1203 (1973) CrossRefADSGoogle Scholar
  10. 10.
    Harris, A.B.: Effect of random defects on critical behavior of Ising models. J. Phys. C 7, 1671–1692 (1974) CrossRefADSGoogle Scholar
  11. 11.
    Aharony, A., Harris, A.B.: Absence of self-averaging and universal fluctuations in random systems near critical points. Phys. Rev. Lett. 77, 3700–3703 (1996) CrossRefADSGoogle Scholar
  12. 12.
    Pearl, J.: Current distribution in superconducting films carrying quantized fluxoids. Appl. Phys. Lett. 5, 65 (1964) CrossRefADSGoogle Scholar
  13. 13.
    Beasley, M.R., Mooij, J.E., Orlando, T.P.: Possibility of vortex–antivortex pair dissociation in 2-dimensional superconductors. Phys. Rev. Lett. 42, 1165–1168 (1979) CrossRefADSGoogle Scholar
  14. 14.
    Nelson, D.R., Kosterlitz, J.M.: Universal jump in superfluid density of 2-dimensional superfluids. Phys. Rev. Lett. 39, 1201–1205 (1977) CrossRefADSGoogle Scholar
  15. 15.
    Privman, V. (ed.): Finite-Size Scaling and Numerical Simulations of Statistical Systems. World Scientific, Singapore (1990) Google Scholar
  16. 16.
    Schneider, T., Caviglia, A.D., Gariglio, S., Reyren, N., Triscone, J.-M.: Electrostatically-tuned superconductor-metal-insulator quantum transition at the LaAlO3/SrTiO3 interface. Phys. Rev. B 79, 184502 (2009) CrossRefADSGoogle Scholar
  17. 17.
    Schneider, T., Weyeneth, S.: Quantum superconductor–insulator transition: Implications of BKT-critical behavior. arXiv:1212.1330v1 (unpublished)
  18. 18.
    Hertz, J.A.: Quantum critical phenomena. Phys. Rev. B 14, 1165–1184 (1976) CrossRefADSGoogle Scholar
  19. 19.
    Bollinger, A.T., Dubuis, G., Yoon, J., Pavuna, D., Misewich, J., Božoviĉ, I.: Superconductor–insulator transition in La2−xSrxCuO4 at the pair quantum resistance. Nature (London) 472, 458–460 (2011) CrossRefADSGoogle Scholar
  20. 20.
    Marcano, N., Sangiao, S., Plaza, M., Pérez, L., Pacheco, A.F., Córdoba, R., Sánchez, M.C., Morellón, L., Ibarra, M.R., De Teresa, J.M.: Weak-antilocalization signatures in the magnetotransport properties of individual electrodeposited Bi Nanowires. Appl. Phys. Lett. 96, 082110 (2010) CrossRefADSGoogle Scholar
  21. 21.
    Bergmann, G.: Weak anti-localization—an experimental proof for the destructive interference of rotated spin 1/2. Solid State Commun. 42, 815–817 (1982) CrossRefADSGoogle Scholar
  22. 22.
    Mott, N.F.: Conduction in non-crystalline materials. 3. Localized states in a pseudogap and near extremities of conduction and valence bands. Philos. Mag. 19, 835 (1969) CrossRefADSGoogle Scholar
  23. 23.
    Fisher, M.P.A.: Quantum phase transitions in disordered two-dimensional superconductors. Phys. Rev. Lett. 65, 923–926 (1990) CrossRefADSGoogle Scholar
  24. 24.
    Weichman, P.B.: Dirty bosons: twenty years later. Mod. Phys. Lett. B 22, 2623–2647 (2008) CrossRefADSMATHGoogle Scholar
  25. 25.
    Fisher, M.P.A., Weichman, P.B., Grinstein, G., Fisher, D.S.: Boson localization and the superfluid-insulator transition. Phys. Rev. B 40, 546–570 (1989) CrossRefADSGoogle Scholar
  26. 26.
    Maekawa, S., Fukuyama, H.: Localization effects in two-dimensional superconductors. J. Phys. Soc. Jpn. 51, 1380–1385 (1982) CrossRefADSGoogle Scholar
  27. 27.
    Finkel’shtein, A.M.: Superconducting transition-temperature in amorphous films. Sov. Phys. JETP 45, 46–49 (1987) Google Scholar
  28. 28.
    Fisher, M.P.A., Grinstein, G., Girvin, S.M.: Presence of quantum diffusion in two dimensions: universal resistance at the superconductor–insulator transition. Phys. Rev. Lett. 64, 587–590 (1990) CrossRefADSGoogle Scholar
  29. 29.
    Dahm, A.J.: Further comment on “Dislocations and melting in two dimensions: the critical region”. Phys. Rev. B 29, 484–486 (1984) CrossRefADSGoogle Scholar
  30. 30.
    Steele, L.M., Yeager, C.J., Finotello, D.: Precision specific-heat studies of thin superfluid films. Phys. Rev. Lett. 71, 3673–3676 (1993) CrossRefADSGoogle Scholar
  31. 31.
    Cho, H., Williams, G.A.: Vortex core size in submonolayer superfluid 4He films. Phys. Rev. Lett. 75, 1562–1565 (1995) CrossRefADSGoogle Scholar
  32. 32.
    Pierson, S.W., Friesen, M., Ammirata, S.M., Hunnicutt, J.C., Gorham, L.A.: Dynamic scaling for two-dimensional superconductors, Josephson-junction arrays, and superfluids. Phys. Rev. B 60, 1309–1325 (1999) CrossRefADSGoogle Scholar
  33. 33.
    Schneider, T.: Estimation of the critical dynamics and thickness of superconducting films and interfaces. Phys. Rev. B 80, 214507 (2009) CrossRefADSGoogle Scholar
  34. 34.
    Medvedyeva, K., Kim, B.J., Minnhagen, P.: Analysis of current-voltage characteristics of two-dimensional superconductors: finite-size scaling behavior in the vicinity of the Kosterlitz–Thouless transition. Phys. Rev. B 62, 14531–14540 (2000) CrossRefADSGoogle Scholar
  35. 35.
    Aslamosov, L.G., Larkin, A.I.: Effect of fluctuations on properties of a superconductor above critical temperature. Sov. Phys., Solid State 10, 875 (1968) Google Scholar
  36. 36.
    Lee, P.A., Ramakrishnan, T.V.: Disordered electronic systems. Rev. Mod. Phys. 57, 287–337 (1985) CrossRefADSGoogle Scholar
  37. 37.
    McLachlan, D.S.: Weak-localization, spin-orbit, and electron-electron interaction effects in two- and three-dimensional bismuth films. Phys. Rev. B 28, 6821–6832 (1983) CrossRefADSGoogle Scholar
  38. 38.
    Blanter, Y.M., Vinokur, V.M., Glazman, L.I.: Weak localization in metallic granular media. Phys. Rev. B 73, 165322 (2006) CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Physik-Institutder Universität ZürichZürichSwitzerland

Personalised recommendations