Skip to main content

Thank you for visiting nature.com. 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.

  • Letter
  • Published:

A coherent three-dimensional Fermi surface in a high-transition-temperature superconductor

Nature volume 425, pages 814–817 (2003)Cite this article

Abstract

All conventional metals are known to possess a three-dimensional Fermi surface, which is the locus in reciprocal space of the long-lived electronic excitations that govern their electronic properties at low temperatures. These excitations should have well-defined momenta with components in all three dimensions. The high-transition-temperature (high-Tc) copper oxide superconductors have unusual, highly two-dimensional properties above the superconducting transition1. This, coupled with a lack of unambiguous evidence for a three-dimensional Fermi surface, has led to many new and exotic models for the underlying electronic ground state2. Here we report the observation of polar angular magnetoresistance oscillations3 in the overdoped superconductor Tl2Ba2CuO6+δ in high magnetic fields, which firmly establishes the existence of a coherent three-dimensional Fermi surface. Analysis of the oscillations reveals that at certain symmetry points, however, this surface is strictly two-dimensional. This striking form of the Fermi surface topography, long-predicted by electronic band structure calculations4, provides a natural explanation for a wide range of anisotropic properties both in the normal5,6 and superconducting states7,8,9. Our data reveal that, despite their extreme electrical anisotropy, the high-Tc materials at high doping levels can be understood within a framework of conventional three-dimensional metal physics.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Polar AMRO sweeps in an overdoped Tl2201 single crystal (Tc ≈ 20 K).
Figure 2: Reconstruction of the FS in Tl2201 from polar AMRO data.
Figure 3: Projection of the deduced FS of Tl2201 onto the ab-plane.

Similar content being viewed by others

References

  1. Ong, N. P. Non-Fermi-liquid aspects of charge-transport in cuprate superconductors. Physica C 235, 221–224 (1994)

    Article  ADS  Google Scholar 

  2. Orenstein, J. & Millis, A. J. Advances in the physics of high temperature superconductivity. Science 288, 468–474 (2000)

    Article  ADS  CAS  Google Scholar 

  3. Yamaji, K. On the angle dependence of the magnetoresistance in quasi-two-dimensional organic superconductors. J. Phys. Soc. Jpn 58, 1520–1522 (1989)

    Article  ADS  CAS  Google Scholar 

  4. 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)

    Article  ADS  CAS  Google Scholar 

  5. Ioffe, L. B. & Millis, A. J. Zone-diagonal-dominated transport in high-Tc cuprates. Phys. Rev. B 58, 11631–11637 (1998)

    Article  ADS  CAS  Google Scholar 

  6. van der Marel, D. Anisotropy of the optical conductivity of high-Tc cuprates. Phys. Rev. B 60, R765–R769 (1999)

    Article  ADS  CAS  Google Scholar 

  7. Xiang, T. & Wheatley, J. M. c-axis superfluid response of copper oxide superconductors. Phys. Rev. Lett. 77, 4632–4635 (1996)

    Article  ADS  CAS  Google Scholar 

  8. Wu, C., Xiang, T. & Su, Z.-B. Absence of the zero bias peak in vortex tunneling spectra of high-temperature superconductors. Phys. Rev. B 62, 14427–14430 (2000)

    Article  ADS  CAS  Google Scholar 

  9. Franz, M. & Tesanovic, Z. Quasiparticle spectra in the vicinity of a d-wave vortex. Phys. Rev. B 60, 3581–3588 (1999)

    Article  ADS  CAS  Google Scholar 

  10. Kartsovnik, M. V., Laukhin, V. N., Pesotskii, S. I., Schegolev, I. F. & Yakovenko, V. M. Angular magnetoresistance oscillations and the shape of the Fermi surface in β- (ET)2IBr2 . J. Phys. I 2, 89–99 (1992)

    CAS  Google Scholar 

  11. Wosnitza, J. et al. The Fermi surfaces of β-(BEDT-TTF)2X. J. Phys. I 6, 1597–1608 (1996)

    CAS  Google Scholar 

  12. 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)

    Article  ADS  CAS  Google Scholar 

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

    Google Scholar 

  14. Tyler, A. W. et al. High field study of normal state magnetotransport in Tl2Ba2CuO6+δ . Phys. Rev. B 57, R728–R731 (1998)

    Article  ADS  CAS  Google Scholar 

  15. Mackenzie, A. P. et al. Resistance upper critical field in Tl2Ba2CuO6 at low temperatures and high magnetic fields. Phys. Rev. Lett. 71, 1238–1241 (1993)

    Article  ADS  CAS  Google Scholar 

  16. Hussey, N. E. et al. Angular dependence of the c-axis normal state magnetoresistance in single crystal Tl2Ba2CuO6+δ . Phys. Rev. Lett. 76, 122–125 (1996)

    Article  ADS  CAS  Google Scholar 

  17. Dragulescu, A., Yakovenko, V. M. & Singh, D. J. Theory of angular magnetoresistance oscillations in Tl2Ba2CuO6 . Phys. Rev. B 60, 6312–6315 (1999)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  19. Bergemann, C., Julian, S. R., Mackenzie, A. P., NishiZaki, S. & Maeno, Y. Detailed topography of the Fermi surface of Sr2RuO4 . Phys. Rev. Lett. 84, 2662–2665 (2000)

    Article  ADS  CAS  Google Scholar 

  20. Ziman, J. M. Principles of the Theory of Solids (Cambridge Univ. Press, Cambridge, 1972)

    Book  Google Scholar 

  21. Pavarini, E., Dasgupta, I., Saha-Dasgupta, T., Jepsen, O. & Andersen, O. K. Band-structure trend in hole-doped cuprates and correlation with Tcmax . Phys. Rev. Lett. 87, 047003 (2001)

    Article  ADS  CAS  Google Scholar 

  22. McKenzie, R. H. & Moses, P. Incoherent interlayer transport and angular-dependent magneto-resistance oscillations in layered metals. Phys. Rev. Lett. 81, 4492–4495 (1998)

    Article  ADS  CAS  Google Scholar 

  23. Kumar, N. & Jayannavar, A. M. Temperature dependence of the c-axis resistivity of high-Tc layered oxides. Phys. Rev. B 45, 5001–5004 (1992)

    Article  ADS  CAS  Google Scholar 

  24. Tamasaku, K., Ito, T., Takagi, H. & Uchida, S. Interplane charge dynamics in La2-xSrxCuO4 . Phys. Rev. Lett. 72, 3088–3091 (1994)

    Article  ADS  CAS  Google Scholar 

  25. Damascelli, A., Hussain, Z. & Shen, Z.-X. Angle-resolved photoemission studies of the cuprate superconductors. Rev. Mod. Phys. 75, 473–541 (2003)

    Article  ADS  CAS  Google Scholar 

  26. Hussey, N. E. The normal state scattering rate in high-Tc cuprates. Eur. Phys. J. B 31, 495–507 (2003)

    Article  ADS  CAS  Google Scholar 

  27. Hussey, N. E. Low-energy quasi-particles in high-Tc cuprates. Adv. Phys. 51, 1685–1771 (2002)

    Article  ADS  CAS  Google Scholar 

  28. Nakamae, S. et al. Electronic ground state of heavily overdoped non-superconducting La2-xSrxCuO4 . Phys. Rev. B 68, 100502 (2003)

    Article  ADS  Google Scholar 

  29. 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)

    Article  ADS  Google Scholar 

  30. Bergemann, C. et al. Quasi-two-dimensional Fermi liquid properties of the unconventional superconductor Sr2RuO4 . Adv. Phys. (in the press)

Download references

Acknowledgements

We acknowledge technical support from S. Hannahs, and discussions with O. K. Andersen, C. Bergemann, S. J. Blundell, B. L. Gyorrfy, R. Hlubina, A. J. Leggett, G. Santi and J. A. Wilson. We also acknowledge J. R. Cooper for first recognizing the potential of AMRO studies in Tl2201. This work was supported by EPSRC, the Leverhulme Trust and by a cooperative agreement between the State of Florida and NSF. The crystals were grown by A.P.M., the experiments carried out by M.A.-J., L.B., A.C. and N.E.H., and the analysis performed by M.A.-J. and N.E.H. in discussion with A.P.M.

Author information

Authors and Affiliations

  1. H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, UK

    N. E. Hussey, M. Abdel-Jawad & A. Carrington

  2. School of Physics and Astronomy, University of St Andrews, St Andrews, Fife, KY16 9SS, UK

    A. P. Mackenzie

  3. National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida, 32306, USA

    L. Balicas

Authors
  1. N. E. Hussey
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Abdel-Jawad
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Carrington
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. P. Mackenzie
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. L. Balicas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. E. Hussey.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hussey, N., Abdel-Jawad, M., Carrington, A. et al. A coherent three-dimensional Fermi surface in a high-transition-temperature superconductor. Nature 425, 814–817 (2003). https://doi.org/10.1038/nature01981

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature01981

This article is cited by

Comments

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.

Search

Advanced search

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