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Melting of the charge density wave by generation of pairs of topological defects in UTe2

Nature Physics (2024)Cite this article

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Abstract

Topological defects are singularities in an ordered phase that can have a profound effect on phase transitions and serve as a window into the order parameter. Examples of topological defects include dislocations in charge density waves and vortices in a superconductor or pair density wave, where the latter is a condensate of Cooper pairs with finite momentum. Here we demonstrate the role of topological defects in the magnetic-field-induced disappearance of a charge density wave in the heavy-fermion superconductor UTe2. We reveal pairs of topological defects of the charge density wave with positive and negative phase winding. The pairs are directly correlated with zeros in the charge density wave amplitude and increase in number with increasing magnetic field. A magnetic field generates vortices of the superconducting and pair density wave orders that can create topological defects in the charge density wave and induce the experimentally observed melting of this charge order at the upper critical field. Our work reveals the important role of magnetic-field-generated topological defects in the melting of the charge density wave order parameter in UTe2 and provides support for the existence of a pair density wave order on the surface.

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Fig. 1: Topological defects in the CDW in UTe2 and their relationship to the amplitude and phase of the CDW.
Fig. 2: Generation of topological defects in the phase of CDW and decay of the amplitude with increasing magnetic field.
Fig. 3: Strong positive cross-correlation between regions of zero-amplitude and location of topological defects.
Fig. 4: Increase in pairs of dislocations of the CDW with opposite vorticities as a function of increasing magnetic field.

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Data availability

The relevant data for the plots are available via the Illinois Databank at https://doi.org/10.13012/B2IDB-6515700_V1. Source data are provided with this paper.

Code availability

Data have been obtained using Nanonis software V5 and analysed following the procedure mentioned in the Methods section using standard functions in Python 3.9.

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Acknowledgements

We thank S. Kivelson, E.-A. Kim and D. Agterberg for useful discussions. We would also like to thank I. Hayes who provided the transport characterization of the crystals during the review process. STM work at the University of Illinois, Urbana-Champaign, was supported by the US Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences (BES), Materials Sciences and Engineering Division, under award no. DE-SC0022101. V.M. and J.P. acknowledge support from the Gordon and Betty Moore Foundation’s EPiQS Initiative through grants GBMF4860 and GBMF9071, respectively, as well as the Canadian Institute for Advanced Research Quantum Materials Program. Theoretical work was supported in part by the US National Science Foundation through grant DMR 2225920 at the University of Illinois (E.F.). Research at the University of Maryland was supported by the Department of Energy via award no. DE-SC-0019154 (sample characterization), the National Science Foundation under grant no. DMR-2105191 (sample preparation), the Maryland Quantum Materials Center and the National Institute of Standards and Technology. S.R.S. acknowledges support from the National Institute of Standards and Technology Cooperative Agreement 70NANB17H301.

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Authors and Affiliations

  1. Department of Physics and Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Anuva Aishwarya, Julian May-Mann, Avior Almoalem, Eduardo Fradkin & Vidya Madhavan

  2. Anthony J. Leggett Institute for Condensed Matter Theory, University of Illinois, Urbana, IL, USA

    Julian May-Mann & Eduardo Fradkin

  3. Maryland Quantum Materials Center, Department of Physics, University of Maryland, College Park, MD, USA

    Sheng Ran, Shanta R. Saha, Johnpierre Paglione & Nicholas P. Butch

  4. NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD, USA

    Sheng Ran & Nicholas P. Butch

  5. Department of Physics, Washington University in St Louis, St Louis, MO, USA

    Sheng Ran

  6. Canadian Institute for Advanced Research, Toronto, ON, Canada

    Johnpierre Paglione & Vidya Madhavan

Authors
  1. Anuva Aishwarya
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Contributions

A. Aishwarya and V.M. conceived the experiments. The single crystals were provided by S.R., S.R.S., J.P. and N.P.B. A. Aishwarya obtained the primary STM data with help from A. Almoalem during the review process. A. Aishwarya and V.M. performed the analysis and J.M.-M. and E.F. provided theoretical input on the interpretation of the data. A. Aishwarya, V.M., J.M.-M. and E.F. wrote the paper with input from all authors.

Corresponding author

Correspondence to Vidya Madhavan.

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Nature Physics thanks Minghu Pan, Yukio Hasegawa and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Information

Supplementary Figs. 1–9 and discussion.

Source data

Source Data Fig. 4

Polar plots for phase winding. The first column lists the angle of traversing around the defect (where the start angle is arbitrary) and the second column is the relative phase of the CDW.

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Aishwarya, A., May-Mann, J., Almoalem, A. et al. Melting of the charge density wave by generation of pairs of topological defects in UTe2. Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02429-9

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