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The break-up of heavy electrons at a quantum critical point


The point at absolute zero where matter becomes unstable to new forms of order is called a quantum critical point (QCP). The quantum fluctuations between order and disorder1,2,3,4,5 that develop at this point induce profound transformations in the finite temperature electronic properties of the material. Magnetic fields are ideal for tuning a material as close as possible to a QCP, where the most intense effects of criticality can be studied. A previous study6 on the heavy-electron material YbRh2Si2 found that near a field-induced QCP electrons move ever more slowly and scatter off one another with ever increasing probability, as indicated by a divergence to infinity of the electron effective mass and scattering cross-section. But these studies could not shed light on whether these properties were an artefact of the applied field7,8, or a more general feature of field-free QCPs. Here we report that, when germanium-doped YbRh2Si2 is tuned away from a chemically induced QCP by magnetic fields, there is a universal behaviour in the temperature dependence of the specific heat and resistivity: the characteristic kinetic energy of electrons is directly proportional to the strength of the applied field. We infer that all ballistic motion of electrons vanishes at a QCP, forming a new class of conductor in which individual electrons decay into collective current-carrying motions of the electron fluid.

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Figure 1: Evolution of ɛ, the exponent in Δρ(T) = [ρ(T) - ρ0]Tɛ, within the temperature–field phase diagram of YbRh2(Si1-xGex)2 single crystals.
Figure 2: Low-temperature electronic specific heat of YbRh2(Si1-xGex)2 single crystals as Cel/T versus T in semi-logarithmic plots at zero field and at low values of the applied magnetic field B.
Figure 3: Field dependences of the Sommerfeld coefficient γ0, of the electronic specific heat (a) and of the ratio of the A coefficient in the T2 term of the electrical resistivity and γ02 (b) for YbRh2(Si0.95Si0.05)2.


  1. Hertz, J. A. Quantum critical phenomena. Phys. Rev. B 14, 1165–1184 (1976)

    ADS  CAS  Article  Google Scholar 

  2. Millis, A. J. Effect of a nonzero temperature on quantum critical points in itinerant fermion systems. Phys. Rev. B 48, 7183–7196 (1993)

    ADS  CAS  Article  Google Scholar 

  3. Continentino, M. A. Quantum scaling in many-body systems. Phys. Rep. 239, 179–213 (1994)

    ADS  Article  Google Scholar 

  4. Si, Q., Rabello, S., Ingersent, K. & Smith, J. L. Locally critical quantum phase transitions in strongly correlated metals. Nature 413, 804–808 (2001)

    ADS  CAS  Article  Google Scholar 

  5. Coleman, P. & Pépin, C. What is the fate of the heavy electron at a quantum critical point? Physica B 312, 383–389 (2002)

    ADS  Article  Google Scholar 

  6. Gegenwart, P. et al. Magnetic-field induced quantum critical point in YbRh2Si2 . Phys. Rev. Lett. 89, 056402 (2002)

    ADS  CAS  Article  Google Scholar 

  7. Heuser, K. et al. Inducement of non-Fermi-liquid behavior with a magnetic field. Phys. Rev. B 57, R4198–R4201 (1998)

    ADS  CAS  Article  Google Scholar 

  8. Stockert, O. et al. Pressure versus magnetic-field tuning of a magnetic quantum phase transition. Physica B 312-313, 458–460 (2002)

    ADS  Article  Google Scholar 

  9. Trovarelli, O. et al. YbRh2Si2: Pronounced non-Fermi-liquid effects above a low-lying magnetic phase transition. Phys. Rev. Lett. 85, 626–629 (2000)

    ADS  CAS  Article  Google Scholar 

  10. Kadowaki, K. & Woods, S. B. Universal relationship of the resistivity and specific heat in heavy-fermion compounds. Solid State Commun. 58, 507–509 (1986)

    ADS  CAS  Article  Google Scholar 

  11. Gegenwart, P. et al. Divergence of the heavy quasiparticle mass at the antiferromagnetic quantum critical point in YbRh2Si2 . Acta. Phys. Pol. B 34, 323–334 (2003)

    CAS  Google Scholar 

  12. Landau, L. D. The theory of a Fermi liquid. Sov. Phys. JETP 3, 920–925 (1957)

    MathSciNet  CAS  MATH  Google Scholar 

  13. Paul, I. & Kotliar, G. Thermoelectric behavior near the magnetic quantum critical point. Phys. Rev. B 64, 184414 (2001)

    ADS  Article  Google Scholar 

  14. Giamarchi, T., Varma, C. M., Ruckenstein, A. E. & Nozières, P. Singular low energy properties of an impurity model with finite range interactions. Phys. Rev. Lett. 70, 3967–3970 (1993)

    ADS  CAS  Article  Google Scholar 

  15. Schröder, A. et al. Onset of antiferromagnetism in heavy-fermion metals. Nature 407, 351–355 (2000)

    ADS  Article  Google Scholar 

  16. Mederle, S. et al. Unconventional metallic state in YbRh2(Si1-xGex)2—a high pressure study. J. Phys. Condens. Matter 14, 10731–10736 (2002)

    ADS  CAS  Article  Google Scholar 

  17. Plessel, J. et al. Unusual behavior of the low-moment mangetic ground-state of YbRh2Si2 under high pressure. Phys. Rev. B 67, 180303 (2003)

    Article  Google Scholar 

  18. Francois, M., Venturini, G., Marchêché, J. F., Malaman, B. & Roques, B. De Nouvelles séries de germaniures, isotopes de U4Re7Si6, ThCr2Si2 et CaBe2Ge2, dans les systèmes ternaires R-T-Ge où R est un élément des terres rares et T ≡ Ru, Os, Rh, Ir: supraconductivité de LaIr2Ge2 . J. Less Common Metals 113, 231–237 (1985)

    CAS  Article  Google Scholar 

  19. Carter, G. C., et al. in Metallic shifts in NMR. Progress in Materials Science Vol. 20, Part I, Ch. 9 (eds Chalmers, B., Christian, J. W. & Massalski, T. B.) 123–124 (Oxford, Pergamon, 1977)

    Google Scholar 

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We acknowledge discussions with J. Ferstl, C. Langhammer, S. Mederle, N. Oeschler, I. Zerec, G. Sparn, O. Stockert, M. Abd-Elmeguid, J. Hopkinson, A. I. Larkin and I. Paul. Work at Dresden is partially supported by the Fonds der Chemischen Industrie and by the FERLIN project of the European Science Foundation. P. C. is supported by the National Science Foundation. Y. T. is a Young Scientist Research Fellow supported by the Japan Society for the Promotion of Science.

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Correspondence to P. Coleman.

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Custers, J., Gegenwart, P., Wilhelm, H. et al. The break-up of heavy electrons at a quantum critical point. Nature 424, 524–527 (2003).

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