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Thermal and electrical transport across a magnetic quantum critical point


A quantum critical point (QCP) arises when a continuous transition between competing phases occurs at zero temperature. Collective excitations at magnetic QCPs give rise to metallic properties that strongly deviate from the expectations of Landau’s Fermi-liquid description1, which is the standard theory of electron correlations in metals. Central to this theory is the notion of quasiparticles, electronic excitations that possess the quantum numbers of the non-interacting electrons. Here we report measurements of thermal and electrical transport across the field-induced magnetic QCP in the heavy-fermion compound YbRh2Si2 (refs 2, 3). We show that the ratio of the thermal to electrical conductivities at the zero-temperature limit obeys the Wiedemann–Franz law for magnetic fields above the critical field at which the QCP is attained. This is also expected for magnetic fields below the critical field, where weak antiferromagnetic order and a Fermi-liquid phase form below 0.07 K (at zero field). At the critical field, however, the low-temperature electrical conductivity exceeds the thermal conductivity by about 10 per cent, suggestive of a non-Fermi-liquid ground state. This apparent violation of the Wiedemann–Franz law provides evidence for an unconventional type of QCP at which the fundamental concept of Landau quasiparticles no longer holds4,5,6. These results imply that Landau quasiparticles break up, and that the origin of this disintegration is inelastic scattering associated with electronic quantum critical fluctuations—these insights could be relevant to understanding other deviations from Fermi-liquid behaviour frequently observed in various classes of correlated materials.

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Figure 1: Phase diagram and thermal conductivity of YbRh2Si2.
Figure 2: Thermal and electrical resistivity curves at low temperatures.
Figure 3: Violation and validity of the Wiedemann–Franz law at B ≈ B c and B > B c, respectively.
Figure 4: The evolution of the quasiparticle weights across a Kondo-breakdown quantum critical point.


  1. Landau, L. D. The theory of a Fermi liquid. Sov. Phys. JETP 6, 920–925 (1957)

    MathSciNet  MATH  Google Scholar 

  2. 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 

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

    ADS  CAS  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., Si, Q. & Ramazashvili, R. How do Fermi liquids get heavy and die? J. Phys. Condens. Matter 13, R723–R738 (2001)

    ADS  CAS  Article  Google Scholar 

  6. Senthil, T., Vojta, M. & Sachdev, S. Weak magnetism and non-Fermi liquids near heavy-fermion critical points. Phys. Rev. B 69, 035111 (2004)

    ADS  Article  Google Scholar 

  7. Schofield, A. J. Quantum criticality and novel phases: summary and outlook. Phys. Status Solidi B 247, 563–569 (2010)

    ADS  CAS  Article  Google Scholar 

  8. Löhneysen, H. V. et al. Non-Fermi-liquid behavior in a heavy-fermion alloy at a magnetic instability. Phys. Rev. Lett. 72, 3262–3265 (1994)

    ADS  Article  Google Scholar 

  9. Aronson, M. C. et al. Non-Fermi-liquid scaling of the magnetic response in UCu5–x Pd x (x = 1, 1.5). Phys. Rev. Lett. 75, 725–728 (1995)

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  11. 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 

  12. Einstein, A. Theoretical remark on the superconductivity of metals.; translated from Gedenkboek aangeb. aan H. Kamerlingh Onnes (Leiden, 1922)

    Google Scholar 

  13. Wakeham, N. et al. Gross violation of the Wiedemann-Franz law in a quasi-one-dimensional conductor. Nature Commun. 2 396 10.1038/ncomms1406 (2011)

    ADS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  15. Moriya, T. Spin Fluctuations in Itinerant Electron Magnetism (Springer, 1985)

    Book  Google Scholar 

  16. 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 

  17. Wölfle, P. & Abrahams, E. Quasiparticles beyond the Fermi liquid and heavy fermion criticality. Phys. Rev. B 84, 041101(R) (2011)

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  19. Shishido, H., Settai, R., Harima, H. & Ōnuki, Y. A change of the Fermi surface at a critical pressure in CeRhIn5: dHvA study under pressure. J. Phys. Soc. Jpn 74, 1103–1106 (2005)

    ADS  CAS  Article  Google Scholar 

  20. Park, T. et al. Hidden magnetism and quantum criticality in the heavy fermion superconductor CeRhIn5 . Nature 440, 65–68 (2006)

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  22. Gegenwart, P., Si, Q. & Steglich, F. Quantum criticality in heavy-fermion metals. Nature Phys. 4, 186–197 (2008)

    ADS  CAS  Article  Google Scholar 

  23. Paschen, S. et al. Hall effect evolution at a heavy fermion quantum critical point. Nature 432, 881–885 (2004)

    ADS  CAS  Article  Google Scholar 

  24. Friedemann, S. et al. Fermi-surface collapse and dynamical scaling near a quantum critical point. Proc. Natl Acad. Sci. USA 107, 14547–14551 (2010)

    ADS  CAS  Article  Google Scholar 

  25. Tanatar, M. A., Paglione, J., Petrovic, C. & Taillefer, L. Anisotropic violation of the Wiedemann-Franz law at a quantum critical point. Science 316, 1320–1322 (2007)

    ADS  CAS  Article  Google Scholar 

  26. Zaum, S. et al. Towards the identification of a quantum critical line in the (p, B) phase diagram of CeCoIn5 with thermal-expansion measurements. Phys. Rev. Lett. 106, 087003 (2011)

    ADS  CAS  Article  Google Scholar 

  27. Smith, R. P. et al. Marginal breakdown of the Fermi-liquid state on the border of metallic ferromagnetism. Nature 455, 1220–1223 (2008)

    ADS  CAS  Article  Google Scholar 

  28. Smith, M. F. & McKenzie, R. H. Apparent violation of the Wiedemann-Franz law near a magnetic field tuned metal-antiferromagnetic quantum critical point. Phys. Rev. Lett. 101, 266403 (2008)

    ADS  CAS  Article  Google Scholar 

  29. Tomokuni, K. et al. Thermal transport properties and quantum criticality of heavy fermion YbRh2Si2 . J. Phys. Soc. Jpn 80, SA096 (2011)

    Article  Google Scholar 

  30. Casey, P. A., Koralek, J. D., Plumb, N. C., Dessau, D. S. & Anderson, P. W. Accurate theoretical fits to laser-excited photoemission spectra in the normal phase of high-temperature superconductors. Nature Phys. 4, 210–212 (2008)

    ADS  CAS  Article  Google Scholar 

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We thank P. Coleman, R. Daou, P. Gegenwart, N. E. Hussey, K. Ingersent, G. Kotliar, A. P. Mackenzie, H. von Löhneysen, J. Schmalian, A. J. Schofield, T. Senthil, S. Shastry and Z. Teśanovic for discussions. The work was in part supported by the DFG Research Unit 960 ‘Quantum Phase Transitions’, NSF grant DMR-1006985 and the Robert A. Welch Foundation grant C-1411. E.A., S.K., Q.S. and F.S. acknowledge support in part by the NSF under grant 1066293 and the hospitality of the Aspen Center for Physics.

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Correspondence to Frank Steglich.

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Pfau, H., Hartmann, S., Stockert, U. et al. Thermal and electrical transport across a magnetic quantum critical point. Nature 484, 493–497 (2012).

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