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Published October 2015 | Supplemental Material
Journal Article Open

Itinerant density wave instabilities at classical and quantum critical points


Charge ordering in metals is a fundamental instability of the electron sea, occurring in a host of materials and often linked to other collective ground states such as superconductivity. What is difficult to parse, however, is whether the charge order originates among the itinerant electrons or whether it arises from the ionic lattice. Here we employ high-resolution X-ray diffraction, combined with high-pressure and low-temperature techniques and theoretical modelling, to trace the evolution of the ordering wavevector Q in charge and spin density wave systems at the approach to both thermal and quantum phase transitions. The non-monotonic behaviour of Q with pressure and the limiting sinusoidal form of the density wave point to the dominant role of the itinerant instability in the vicinity of the critical points, with little influence from the lattice. Fluctuations rather than disorder seem to disrupt coherence.

Additional Information

© 2015 Macmillan Publishers Limited. Received 25 May 2015; accepted 26 June 2015; published online 27 July 2015. We are grateful for stimulating discussions with R. Jaramillo, C. V. Parker and M. R. Norman, and for NbSe_2 samples provided by Y. Liu and Z.-A. Xu. The work at the University of Chicago was supported by National Science Foundation Grant No. 1206519. The work at the Advanced Photon Source of Argonne National Laboratory was supported by the US Department of Energy Basic Energy Sciences under Contract No. NEAC02-06CH11357. J.v.W. acknowledges support from a VIDI grant financed by the Netherlands Organization for Scientific Research (NWO). Contributions: Y.F. and T.F.R. conceived the research. Y.F. and J.W. performed X-ray measurements. Y.F., D.M.S. and T.F.R. analysed the data. Y.F., J.v.W., F.F. and P.B.L. developed the theoretical framework. Y.F., J.v.W. and T.F.R. prepared the manuscript. All authors commented on the manuscript. Competing financial interests: The authors declare no competing financial interests.

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August 20, 2023
October 23, 2023