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


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.

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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.


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

    ADS  Article  Google Scholar 

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

    ADS  CAS  Article  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)

    ADS  CAS  Article  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)

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  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)

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  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)

    ADS  CAS  Article  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)

    ADS  CAS  Article  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)

    ADS  CAS  Article  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)

    ADS  CAS  Article  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)

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  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)

    ADS  CAS  Article  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)

    ADS  CAS  Article  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)

    ADS  CAS  Article  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)

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  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)

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  Article  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)

    ADS  Article  Google Scholar 

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

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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.

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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).

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