Letter | Published:

Multidimensional entropy landscape of quantum criticality

Nature Physics volume 13, pages 742745 (2017) | Download Citation

Abstract

The third law of thermodynamics states that the entropy of any system in equilibrium has to vanish at absolute zero temperature. At nonzero temperatures, on the other hand, matter is expected to accumulate entropy near a quantum critical point, where it undergoes a continuous transition from one ground state to another1,2. Here, we determine, based on general thermodynamic principles, the spatial-dimensional profile of the entropy S near a quantum critical point and its steepest descent in the corresponding multidimensional stress space. We demonstrate this approach for the canonical quantum critical compound CeCu 6−xAux near its onset of antiferromagnetic order2. We are able to link the directional stress dependence of S to the previously determined geometry of quantum critical fluctuations3. Our demonstration of the multidimensional entropy landscape provides the foundation to understand how quantum criticality nucleates novel phases such as high-temperature superconductivity.

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Acknowledgements

We thank C. Meingast, P. Wölfle and L. Zhu for valuable discussions and S. Drobnik for experimental help. The work at Karlsruhe was supported by the DFG Research Unit FOR960 ‘Quantum Phase Transitions’, work at Rice University by the ARO Grant No. W911NF-14-1-0525 and the Robert A. Welch Foundation Grant No. C-1411, with travel support provided by NSF Grant No. DMR-1611392. One of us (Q.S.) graciously acknowledges the support of the Alexander von Humboldt Foundation and the hospitality of the Karlsruhe Institute of Technology. This article was completed during stays of Q.S. and H.v.L. at the Kavli Institute for Theoretical Physics at University of California, Santa Barbara supported by the NSF Grant No. PHY-1066293, and the Aspen Center for Physics supported by the NSF grant No. PHY-1066293.

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Affiliations

  1. Institut für Festkörperphysik, Karlsruher Institut für Technologie, D-76021 Karlsruhe, Germany

    • K. Grube
    • , S. Zaum
    •  & H. v. Löhneysen
  2. Max-Planck-Institut für Chemische Physik fester Stoffe, D-01187 Dresden, Germany

    • O. Stockert
  3. Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA

    • Q. Si
  4. Physikalisches Institut, Karlsruher Institut für Technologie, D-76049 Karlsruhe, Germany

    • H. v. Löhneysen

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Contributions

K.G. and H.v.L. conceived the experiment, S.Z. and K.G. conducted the measurements, O.S. provided the samples, Q.S. carried out the scaling analysis, and H.v.L., Q.S. and K.G. interpreted the results and wrote the paper.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to K. Grube or H. v. Löhneysen.

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DOI

https://doi.org/10.1038/nphys4113

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