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Breakdown of the Bardeen–Cooper–Schrieffer ground state at a quantum phase transition

Nature volume 459, pages 405–409 (2009)Cite this article

Abstract

Advances in solid-state and atomic physics are exposing the hidden relationships between conventional and exotic states of quantum matter. Prominent examples include the discovery of exotic superconductivity proximate to conventional spin and charge order1,2, and the crossover from long-range phase order to preformed pairs achieved in gases of cold fermions3,4,5 and inferred for copper oxide superconductors5. The unifying theme is that incompatible ground states can be connected by quantum phase transitions. Quantum fluctuations about the transition are manifestations of the competition between qualitatively distinct organizing principles6,7, such as a long-wavelength density wave and a short-coherence-length condensate. They may even give rise to ‘protected’ phases, like fluctuation-mediated superconductivity that survives only in the vicinity of an antiferromagnetic quantum critical point8,9. However, few model systems that demonstrate continuous quantum phase transitions have been identified, and the complex nature of many systems of interest hinders efforts to more fully understand correlations and fluctuations near a zero-temperature instability. Here we report the suppression of magnetism by hydrostatic pressure in elemental chromium, a simple cubic metal that demonstrates a subtle form of itinerant antiferromagnetism10,11,12,13,14,15,16 formally equivalent to the Bardeen–Cooper–Schrieffer (BCS) state in conventional superconductors. By directly measuring the associated charge order in a diamond anvil cell at low temperatures, we find a phase transition at pressures of ∼10 GPa driven by fluctuations that destroy the BCS-like state but preserve the strong magnetic interaction between itinerant electrons and holes. Chromium is unique among stoichiometric magnetic metals studied so far in that the quantum phase transition is continuous, allowing experimental access to the quantum singularity and a direct probe of the competition between conventional and exotic order in a theoretically tractable material.

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Figure 1: Phase diagram and Brillouin zone schematic for magnetism in chromium.
Figure 2: Structure, CDW intensity and wavevector Q for T  < 8 K.
Figure 3: Dependence of Q on order parameter and band structure in the classical and quantum regimes.
Figure 4: Disparate routes to quantum criticality.

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Acknowledgements

We are grateful to J. Pluth for assistance with sample preparation, V. Prakapenka and GeoSoilEnviroCARS (Advanced Photon Source (APS), Argonne National Laboratory) for technical support and G. Aeppli for many discussions. The work at the University of Chicago was supported by the US National Science Foundation (NSF) Division of Materials Research. GeoSoilEnviroCARS is supported by the US NSF Earth Sciences and Department of Energy (DOE) Geosciences. Use of APS is supported by the US DOE Office of Basic Energy Sciences.

Author information

Authors and Affiliations

  1. The James Franck Institute and Department of Physics, The University of Chicago, Chicago, Illinois 60637, USA,

    R. Jaramillo, Yejun Feng & T. F. Rosenbaum

  2. The Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA ,

    Yejun Feng, J. C. Lang, Z. Islam & G. Srajer

  3. Cavendish Laboratory, University of Cambridge, Cambridge CB3 OHE, UK

    P. B. Littlewood

  4. Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA,

    D. B. McWhan

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  1. R. Jaramillo
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Correspondence to T. F. Rosenbaum.

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Jaramillo, R., Feng, Y., Lang, J. et al. Breakdown of the Bardeen–Cooper–Schrieffer ground state at a quantum phase transition. Nature 459, 405–409 (2009). https://doi.org/10.1038/nature08008

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