Despite twenty years of research, the phase diagram of high-transition-temperature superconductors remains enigmatic1,2. A central issue is the origin of the differences in the physical properties of these copper oxides doped to opposite sides of the superconducting region. In the overdoped regime, the material behaves as a reasonably conventional metal, with a large Fermi surface3,4. The underdoped regime, however, is highly anomalous and appears to have no coherent Fermi surface, but only disconnected ‘Fermi arcs’5,6. The fundamental question, then, is whether underdoped copper oxides have a Fermi surface, and if so, whether it is topologically different from that seen in the overdoped regime. Here we report the observation of quantum oscillations in the electrical resistance of the oxygen-ordered copper oxide YBa2Cu3O6.5, establishing the existence of a well-defined Fermi surface in the ground state of underdoped copper oxides, once superconductivity is suppressed by a magnetic field. The low oscillation frequency reveals a Fermi surface made of small pockets, in contrast to the large cylinder characteristic of the overdoped regime. Two possible interpretations are discussed: either a small pocket is part of the band structure specific to YBa2Cu3O6.5 or small pockets arise from a topological change at a critical point in the phase diagram. Our understanding of high-transition-temperature (high-Tc) superconductors will depend critically on which of these two interpretations proves to be correct.
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Orenstein, J. & Millis, A. J. Advances in the physics of high-temperature superconductivity. Science 288, 468–474 (2000)
Norman, M. R., Pines, D. & Kallin, C. The pseudogap: friend or foe of high Tc? Adv. Phys. 54, 715–733 (2005)
Hussey, N. E. et al. Observation of a coherent three-dimensional Fermi surface in a high-transition temperature superconductor. Nature 425, 814–817 (2003)
Platé, M. et al. Fermi surface and quasiparticle excitations of overdoped Tl2Ba2CuO6+δ by ARPES. Phys. Rev. Lett. 95, 077001 (2005)
Norman, M. et al. Destruction of the Fermi surface in underdoped high-Tc superconductors. Nature 392, 157–160 (1998)
Shen, K. et al. Nodal quasiparticles and antinodal charge ordering in Ca2-xNaxCuO2Cl2 . Science 307, 901–904 (2005)
Wosnitza, J. et al. Shubnikov-de Haas effect in the superconducting state of an organic superconductor. Phys. Rev. B 62, 11973–11976 (2000)
Fowler, C. M. et al. de Haas-van Alphen effect and Fermi surface of YBa2Cu3O6. 97 . Phys. Rev. Lett. 68, 534–537 (1992)
Kido, G., Komorita, K., Katayama-Yoshida, H. & Takahashi, T. de Haas-van Alphen measurement of YBa2Cu3O7 . J. Phys. Chem. Solids 52, 1465–1470 (1991)
Haanappel, E. G. et al. The de Haas-van Alphen effect in YBa2Cu3O7-δ . J. Phys. Chem. Solids 54, 1261–1267 (1993)
Springford, M., Harrison, N., Meeson, P. & Probst, P.-A. Comment on “de Haas-van Alphen effect and Fermi surface of YBa2Cu3O6. 97”. Phys. Rev. Lett. 69, 2453 (1992)
Pickett, W. E., Cohen, R. E. & Krakauer, H. Precise band structure and Fermi-surface calculation for YBa2Cu3O7: Importance of three-dimensional dispersion. Phys. Rev. B 42, 8764–8767 (1990)
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)
Campuzano, J. C. et al. Fermi surfaces of YBa2Cu3O6. 9 as seen by angle-resolved photoemission. Phys. Rev. Lett. 64, 2308–2311 (1990)
Nakayama, K. et al. Bulk and surface low-energy excitations in YBa2Cu3O7-δ studied by high-resolution angle-resolved photoemission spectroscopy. Phys. Rev. B 75, 014513 (2007)
Bascones, E. et al. Optical conductivity of ortho-II YBa2Cu3O6. 5 . Phys. Rev. B 71, 012505 (2005)
Lin, J. & Millis, A. J. Theory of low-temperature Hall effect in electron-doped cuprates. Phys. Rev. B 72, 214506 (2005)
Mackenzie, A. P., Julian, S. R., Sinclair, D. C. & Lin, C. T. Normal-state magneto-transport in superconducting Tl2Ba2CuO6+y to millikelvin temperatures. Phys. Rev. B 53, 5848–5855 (1996)
Pereg-Barnea, T. et al. Absolute values of the London penetration depth in YBa2Cu3O6+y measured by zero field ESR spectroscopy on Gd doped single crystals. Phys. Rev. B 69, 184513 (2004)
Loram, J. W. et al. Specific heat evidence on the normal state pseudogap. J. Phys. Chem. Solids 59, 2091–2094 (1998)
Chakravarty, S., Laughlin, R. B., Morr, D. K. & Nayak, C. Hidden order in the cuprates. Phys. Rev. B 63, 094503 (2001)
Lee, P. A. & Wen, X.-G. Vortex structure in underdoped cuprates. Phys. Rev. B 63, 224517 (2001)
Oganesyan, V., Kivelson, S. A. & Fradkin, E. Quantum theory of a nematic Fermi fluid. Phys. Rev. B 64, 195109 (2001)
Yang, K.-Y., Rice, T. M. & Zhang, F.-C. Phenomenological theory of the pseudogap state. Phys. Rev. B 73, 174501 (2006)
Stanescu, T. D. & Kotliar, G. Fermi arcs and hidden zeros of the Green function in the pseudogap state. Phys. Rev. B 74, 125110 (2006)
Kyung, B. et al. Pseudogap induced by short-range spin correlations in a doped Mott insulator. Phys. Rev. B 73, 165114 (2006)
Liang, R., Bonn, D. A. & Hardy, W. N. Preparation and X-ray characterization of highly ordered ortho-II phase YBa2Cu3O6. 50 single crystals. Physica C 336, 57–62 (2000)
Liang, R., Bonn, D. A. & Hardy, W. N. Evaluation of CuO2 plane hole doping in YBa2Cu3O6+x single crystals. Phys. Rev. B 73, 180505 (2006)
Portugall, O. et al. The LNCMP: a pulsed-field user-facility in Toulouse. Physica B 346–347, 668–672 (2004)
We thank R. T. Brisson, G. G. Lonzarich, G. L. J. A. Rikken and A.-M. S. Tremblay for discussions, and M. Nardone and A. Audouard for their help with the experiment and analysis. We acknowledge support from the Canadian Institute for Advanced Research and the LNCMP, and funding from NSERC, FQRNT and a Canada Research Chair. Part of this work was supported by the French ANR IceNET and EuroMagNET.
Author Contributions N.D.-L. and C.P. contributed equally to this work.
Reprints and permissions information is available at www.nature.com/reprints. The authors declare no competing financial interests.
About this article
Cite this article
Doiron-Leyraud, N., Proust, C., LeBoeuf, D. et al. Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor. Nature 447, 565–568 (2007). https://doi.org/10.1038/nature05872
Physical Review B (2020)
New Journal of Physics (2020)
Journal of Physics: Condensed Matter (2020)
Proceedings of the National Academy of Sciences (2020)
Fermion dynamical symmetry and strongly-correlated electrons: A comprehensive model of high-temperature superconductivity
Frontiers of Physics (2020)