Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Quantum oscillations in an overdoped high-Tc superconductor


The nature of the metallic phase in the high-transition-temperature (high-Tc) copper oxide superconductors, and its evolution with carrier concentration, has been a long-standing mystery1. A central question is how coherent electronic states, or quasiparticles, emerge from the antiferromagnetic insulator with doping. Recent quantum oscillation experiments on lightly doped copper oxides have shown evidence for small pockets of Fermi surface2,3,4,5, the formation of which has been associated with the opening of the pseudogap—an anisotropic gap in the normal state excitation spectrum of unknown origin1. As the doping is increased, experiments suggest that the full Fermi surface is restored6,7, although the doping level at which the pseudogap closes and the nature of the electronic ground state beyond this point have yet to be determined. Here we report the observation of quantum oscillations in the overdoped superconductor Tl2Ba2CuO6+δ that show the existence of a large Fermi surface of well-defined quasiparticles covering two-thirds of the Brillouin zone. These measurements confirm that, in overdoped superconducting copper oxides, coherence is established at all Fermi wavevectors, even near the zone boundary where the pseudogap is maximal and electronic interactions are strongest; they also firmly establish the applicability of a generalized Fermi-liquid picture on the overdoped side of the superconducting phase diagram.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Quantum oscillations in Tl2201.
Figure 2: Features of the oscillation data.


  1. 1

    Timusk, T. & Statt, B. The pseudogap in high temperature superconductors: An experimental survey. Rep. Prog. Phys. 62, 61–122 (2000)

    ADS  Article  Google Scholar 

  2. 2

    Doiron-Leyraud, N. et al. Quantum oscillations and the Fermi surface in an underdoped high-T c superconductor. Nature 447, 565–568 (2007)

    CAS  ADS  Article  Google Scholar 

  3. 3

    Yelland, E. A. et al. Quantum oscillations in the underdoped cuprate YBa2Cu4O8 . Phys. Rev. Lett. 100, 047003 (2008)

    CAS  ADS  Article  Google Scholar 

  4. 4

    Bangura, A. F. et al. Small Fermi surface pockets in underdoped high temperature superconductors: Observation of Shubnikov-de Haas oscillations in YBa2Cu4O8 . Phys. Rev. Lett. 100, 047004 (2008)

    CAS  ADS  Article  Google Scholar 

  5. 5

    Jaudet, C. et al. de Haas–van Alphen oscillations in the underdoped high-temperature superconductor YBa2Cu3O6.5 . Phys. Rev. Lett. 100, 187005 (2008)

    ADS  Article  Google Scholar 

  6. 6

    Hussey, N. E. et al. A coherent three-dimensional Fermi surface in a high transition temperature superconductor. Nature 425, 814–817 (2003)

    CAS  ADS  Article  Google Scholar 

  7. 7

    Platé, M. et al. Fermi surface and quasiparticle excitations of overdoped Tl2Ba2CuO6+δ . Phys. Rev. Lett. 95, 077001 (2005)

    ADS  Article  Google Scholar 

  8. 8

    Andersen, O. K., Liechtenstein, A. I., Jepsen, O. & Paulsen, F. LDA energy bands, low energy Hamiltonians, t’, t’’, t (k) and J . J. Phys. Chem. Solids 56, 1573–1591 (1995)

    CAS  ADS  Article  Google Scholar 

  9. 9

    Singh, D. J. & Pickett, W. E. Electronic characteristics of Tl2Ba2CuO6 . Physica C 203, 193–199 (1992)

    CAS  Article  Google Scholar 

  10. 10

    Kanigel, A. et al. Evolution of the pseudogap from Fermi arcs to the nodal metal. Nature Phys. 2, 447 (2006)

    CAS  ADS  Article  Google Scholar 

  11. 11

    Mackenzie, A. P., Julian, S. R., Sinclair, D. C. & Lin, C. T. Normal state magnetotransport in superconducting Tl2Ba2CuO6+δ to millikelvin temperatures. Phys. Rev. B 53, 5848–5854 (1996)

    CAS  ADS  Article  Google Scholar 

  12. 12

    Yusof, Z. M. et al. Quasiparticle liquid in the highly overdoped Bi2Sr2CaCu2O8+δ . Phys. Rev. Lett. 88, 167006 (2002)

    CAS  ADS  Article  Google Scholar 

  13. 13

    Tyler, A. W. An Investigation into the Magnetotransport Properties of Layered Superconducting Perovskites. Ph.D. thesis, Univ. Cambridge. (1997)

    Google Scholar 

  14. 14

    Abdel-Jawad, M. et al. Anisotropic scattering and anomalous normal state transport in a high temperature superconductor. Nature Phys. 2, 821–825 (2006)

    CAS  ADS  Article  Google Scholar 

  15. 15

    Mackenzie, A. P. et al. Calculation of thermodynamic and transport properties of Sr2RuO4 at low temperatures using known Fermi surface parameters. Physica C 263, 510–515 (1996)

    CAS  ADS  Article  Google Scholar 

  16. 16

    Loram, J. W. et al. The electronic specific heat of cuprate superconductors. Physica C 235–240, 134–137 (1994)

    ADS  Article  Google Scholar 

  17. 17

    Alexandrov, A. S. Theory of quantum magneto-oscillations in underdoped cuprate superconductors. J. Phys. Condens. Matter 20, 192202 (2008)

    ADS  Article  Google Scholar 

  18. 18

    Proust, C., Boaknin, E., Hill, R. W., Taillefer, L. & Mackenzie, A. P. Heat transport in a strongly overdoped cuprate: Fermi liquid and a pure d-wave BCS superconductor. Phys. Rev. Lett. 89, 147003 (2002)

    ADS  Article  Google Scholar 

  19. 19

    Dell’Anna, L. & Metzner, W. Electrical resistivity near Pomeranchuk instability in two dimensions. Phys. Rev. Lett. 98, 136402 (2007)

    ADS  Article  Google Scholar 

  20. 20

    Zhu, L., Aji, V., Shekhter, A. & Varma, C. M. Universality of single-particle spectra of cuprate superconductors. Phys. Rev. Lett. 100, 057001 (2008)

    ADS  Article  Google Scholar 

  21. 21

    Ossadnik, M., Honerkamp, C., Rice, T. M. & Sigrist, M. Breakdown of Landau theory in overdoped cuprates near the onset of superconductivity. Preprint at 〈〉 (2008)

  22. 22

    Wasserman, A., Springford, M. & Han, F. The de Haas-van Alphen effect in a marginal Fermi liquid. J. Phys. Condens. Matter 3, 5335–5339 (1991)

    ADS  Article  Google Scholar 

  23. 23

    Wasserman, A. & Springford, M. The influence of many-body interactions on the de Haas-van Alphen effect. Adv. Phys. 45, 471–503 (1996)

    CAS  ADS  Article  Google Scholar 

  24. 24

    McCollam, A., Julian, S. R., Rourke, P. M. C., Aoki, D. & Flouquet, J. Anomalous de Haas-van Alphen oscillations in CeCoIn5 . Phys. Rev. Lett. 94, 186401 (2005)

    CAS  ADS  Article  Google Scholar 

  25. 25

    Tallon, J. L. & Loram, J. W. The doping dependence of T* — what is the true high-T c phase diagram? Physica C 349, 53–68 (2001)

    CAS  ADS  Article  Google Scholar 

  26. 26

    Lin, J. & Millis, A. J. Theory of low-temperature Hall effect in electron-doped cuprates. Phys. Rev. B 72, 214506 (2005)

    ADS  Article  Google Scholar 

  27. 27

    Chakravarty, S. et al. Hidden order in the cuprates. Phys. Rev. B 63, 094503 (2001)

    ADS  Article  Google Scholar 

  28. 28

    Millis, A. J. & Norman, M. R. Antiphase stripe order as the origin of electron pockets observed in 1/8-hole-doped cuprates. Phys. Rev. B 76, 220503 (2007)

    ADS  Article  Google Scholar 

  29. 29

    Schoenberg, D. Magnetic Oscillations in Metals (Cambridge Univ. Press, 1984)

    Book  Google Scholar 

  30. 30

    Bergemann, C., Mackenzie, A. P., Julian, S. R., Forsythe, D. & Ohmichi, E. Quasi-two-dimensional Fermi-liquid properties of the unconventional superconductor Sr2RuO4 . Adv. Phys. 52, 639–725 (2003)

    CAS  ADS  Article  Google Scholar 

Download references


We acknowledge technical and scientific assistance from A. Audouard, M. Nardone, N. Shannon and D. C. Sinclair. This work was supported by EPSRC, LNCMP, the French ANR IceNET and EuroMagNET.

Author Contributions The crystals were grown by A.P.M. and screened by M.M.J.F. and N.E.H. The experiments were carried out by B.V., A.C., R.A.C., C.P., C.J., D.V. and N.E.H., and the analysis performed by B.V., A.C., M.M.J.F., C.P. and N.E.H.

Author information



Corresponding author

Correspondence to N. E. Hussey.

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Vignolle, B., Carrington, A., Cooper, R. et al. Quantum oscillations in an overdoped high-Tc superconductor. Nature 455, 952–955 (2008).

Download citation

Further reading


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.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing