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Signature of optimal doping in Hall-effect measurements on a high-temperature superconductor

Abstract

High-temperature superconductivity is achieved by doping copper oxide insulators with charge carriers. The density of carriers in conducting materials can be determined from measurements of the Hall voltage—the voltage transverse to the flow of the electrical current that is proportional to an applied magnetic field. In common metals, this proportionality (the Hall coefficient) is robustly temperature independent. This is in marked contrast to the behaviour seen in high-temperature superconductors when in the ‘normal’ (resistive) state1,2,3,4,5; the departure from expected behaviour is a key signature of the unconventional nature of the normal state, the origin of which remains a central controversy in condensed matter physics6. Here we report the evolution of the low-temperature Hall coefficient in the normal state as the carrier density is increased, from the onset of superconductivity and beyond (where superconductivity has been suppressed by a magnetic field). Surprisingly, the Hall coefficient does not vary monotonically with doping but rather exhibits a sharp change at the optimal doping level for superconductivity. This observation supports the idea that two competing ground states underlie the high-temperature superconducting phase.

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The authors declare that they have no competing financial interests.

References

  1. 1

    Clayhold, J., Ong, N. P., Wang, Z. Z., Tarascon, J. M. & Barboux, P. Hall-effect anomaly in the high-T c copper-based perovskites. Phys. Rev. B 39, 7324–7327 (1989)

  2. 2

    Anderson, P. W. Hall-effect in the 2-dimensional Luttinger liquid. Phys. Rev. Lett. 67, 2092–2094 (1991)

  3. 3

    Chien, T. R., Wang, Z. Z. & Ong, N. P. Effect of Zn impurities on the normal-state Hall angle in single-crystal YBa2Cu3-xZnxO7-δ . Phys. Rev. Lett. 67, 2088–2091 (1991)

  4. 4

    Hwang, H. Y. et al. Scaling of the temperature dependent Hall effect in La2-xSrxCuO4 . Phys. Rev. Lett. 72, 2636–2639 (1994)

  5. 5

    Ando, Y. & Murayama, T. Nonuniversal power law of the Hall scattering rate in a single-layer cuprate Bi2Sr2-xLaxCuO6 . Phys. Rev. B 60, 6991–6994 (1999)

  6. 6

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

  7. 7

    Ono, S. & Ando, Y. Evolution of the resistivity anisotropy in Bi2Sr2-xLaxCuO6+δ single crystals for a wide range of hole doping. Phys. Rev. B 67, 104512 (2003)

  8. 8

    Ono, S. et al. Metal-to-insulator crossover in the low-temperature normal state of Bi2Sr2-xLaxCuO6+δ . Phys. Rev. Lett. 85, 638–641 (2000)

  9. 9

    Ando, Y. et al. Carrier concentrations in Bi2Sr2-zLazCuO6+δ single crystals and their relation to the Hall coefficient and thermopower. Phys. Rev. B 61, 14956–14959 (2000)

  10. 10

    Wang, Y. et al. Dependence of upper critical field and pairing strength on doping in cuprates. Science 299, 86–89 (2003)

  11. 11

    Ando, Y., Murayama, T. & Ono, S. Systematic evolution of the magnetotransport properties of Bi2Sr2-xLaxCuO6 in a wide doping range. Physica C 341, 1913–1914 (2000)

  12. 12

    Sato, T. et al. High-resolution angle-resolved photoemission study of Pb-substituted Bi2201. J. Phys. Chem. Solids 62, 157–161 (2001)

  13. 13

    Sato, T. et al. Evidence for a hole-like Fermi surface of Bi2Sr2CuO6 from temperature-dependent angle-resolved photoemission spectroscopy. Phys. Rev. B 64, 054502 (2001)

  14. 14

    Hoffman, J. E. et al. Imaging quasiparticle interference in Bi2Sr2CaCu2O8+δ . Science 297, 1148–1151 (2002)

  15. 15

    Norman, M. R. et al. Destruction of the Fermi surface in underdoped high-Tc superconductors. Nature 392, 157–160 (1998)

  16. 16

    Pan, S. H. et al. Microscopic electronic inhomogeneity in the high-Tc superconductor Bi2Sr2CaCu2O8+x . Nature 413, 282–285 (2001)

  17. 17

    Uemura, Y. J. et al. Universal correlations between T c and n s/m* (carrier density over effective mass) in high-T c cuprate superconductors. Phys. Rev. Lett. 62, 2317–2320 (1989)

  18. 18

    Uemura, Y. J. et al. Basic similarities among cuprate, bismuthate, organic, chevrel-phase, and heavy-fermion superconductors shown by penetration-depth measurements. Phys. Rev. Lett. 66, 2665–2668 (1991)

  19. 19

    Tallon, J. L. et al. Critical doping in overdoped high-T c superconductors: a quantum critical point? Phys. Status Solidi B 215, 531–540 (1999)

  20. 20

    Chakravarty, S., Nayak, C., Tewari, S. & Yang, X. Sharp signature of d x2-y2 quantum critical point in the Hall coefficient of cuprate superconductors. Phys. Rev. Lett. 89, 277003 (2002)

  21. 21

    Sachdev, S. Quantum criticality: Competing ground states in low dimensions. Science 288, 475–480 (2000)

  22. 22

    Varma, C. M., Littlewood, P. B., Schmitt-Rink, S., Abrahams, E. & Ruckenstein, A. E. Phenomenology of the normal state of Cu-O high-temperature superconductors. Phys. Rev. Lett. 63, 1996–1999 (1989)

  23. 23

    Perali, A., Castellani, C., Di Castro, C. & Grilli, M. d-wave superconductivity near charge instabilities. Phys. Rev. B 54, 16216–16225 (1996)

  24. 24

    Kivelson, S. A., Fradkin, E. & Emery, V. J. Electronic liquid-crystal phases of a doped Mott insulator. Nature 393, 550–553 (1998)

  25. 25

    Lee, P. A. & Wen, X.-G. Vortex structure in underdoped cuprates. Phys. Rev. B 63, 224517 (2001)

  26. 26

    Yeh, A. et al. Quantum phase transition in a common metal. Nature 419, 459–462 (2002)

  27. 27

    Mathur, N. D. et al. Magnetically mediated superconductivity in heavy fermion compounds. Nature 394, 39–43 (1998)

  28. 28

    Yamauchi, T., Ueda, Y. & Mori, N. Pressure-induced superconductivity in β-Na0.33V2O5 beyond charge ordering. Phys. Rev. Lett. 89, 057002 (2002)

  29. 29

    Grigera, S. A. et al. Magnetic field-tuned quantum criticality in the metallic ruthenate Sr3Ru2O7 . Science 294, 329–332 (2001)

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Acknowledgements

The work at the National High Magnetic Field Laboratory was supported by the National Science Foundation and the DOE Office of Science. We thank S. Chakravarty, S. A. Kivelson, P.A. Lee, R. Ramazashvili, C. M. Varma, I. Vekhter and F.-C. Zhang for discussions.

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The authors declare that they have no competing financial interests.

Correspondence to Fedor F. Balakirev.

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Further reading

Figure 1: Hall resistivity versus magnetic field.
Figure 2: Temperature dependence of the Hall coefficient, RH.
Figure 3: Variation of Hall number with doping and Tc.

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