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.

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


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.

Your institute does not have access to this article

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

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.


  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)

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  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)

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  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)

    ADS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  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)

    ADS  Article  Google Scholar 

  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)

    ADS  CAS  Article  Google Scholar 

  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)

    ADS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  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)

    ADS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  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)

    ADS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  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)

    ADS  CAS  Article  Google Scholar 

  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)

    ADS  CAS  Article  Google Scholar 

  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)

    ADS  CAS  Article  Google Scholar 

  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)

    ADS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  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)

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

Download references


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.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Fedor F. Balakirev.

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

Balakirev, F., Betts, J., Migliori, A. et al. Signature of optimal doping in Hall-effect measurements on a high-temperature superconductor. Nature 424, 912–915 (2003).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

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