Abstract
The intense interest in triplet superconductivity partly stems from theoretical predictions of exotic excitations such as non-Abelian Majorana modes, chiral supercurrents and half-quantum vortices1,2,3,4. However, fundamentally new and unexpected states may emerge when triplet superconductivity appears in a strongly correlated system. Here we use scanning tunnelling microscopy to reveal an unusual charge-density-wave (CDW) order in the heavy-fermion triplet superconductor UTe2 (refs. 5,6,7,8). Our high-resolution maps reveal a multi-component incommensurate CDW whose intensity gets weaker with increasing field, with the CDW eventually disappearing at the superconducting critical field Hc2. To understand the phenomenology of this unusual CDW, we construct a Ginzburg–Landau theory for a uniform triplet superconductor coexisting with three triplet pair-density-wave states. This theory gives rise to daughter CDWs that would be sensitive to magnetic field owing to their origin in a pair-density-wave state and provides a possible explanation for our data. Our discovery of a CDW state that is sensitive to magnetic fields and strongly intertwined with superconductivity provides important information for understanding the order parameters of UTe2.
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Data availability
All of the data for the main figures have been uploaded to the Illinois Databank (https://doi.org/10.13012/B2IDB-1713879_V1).
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Acknowledgements
We thank S. Kivelson and Q. Si for useful discussions. STM studies at the University of Illinois, Urbana-Champaign were supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under award number DE-SC0022101. V.M. acknowledges partial support from Gordon and Betty More Foundation’s EPiQS Initiative through grant GBMF4860 and the Quantum Materials Program at CIFAR where she is a Fellow. Theoretical work was supported in part by the US National Science Foundation through the grant DMR 1725401 and DMR 2225920 at the University of Illinois (E.F. and L.N.) and by a postdoctoral fellowship of the Institute for Condensed Matter Theory of the University of Illinois (L.N.). J.M.-M. acknowledges support by ARO MURI grant number W911NF2020166. Research at the University of Maryland was supported by the Department of Energy award number DE-SC-0019154 (sample characterization), the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant number GBMF9071 (materials synthesis), the National Science Foundation under grant number 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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A.A. and V.M. conceived the experiments. The single crystals were provided by S.R., S.R.S., J.P. and N.P.B. M.R. carried out the Laue characterization of the single crystals. A.A. and A.R. obtained the STM data. A.A. and V.M. carried out the analysis and J.M.-M., L.N. and E.F. provided the theoretical input on the interpretation of the data. A.A., V.M., J.M.-M. and E.F. wrote the paper with input from all authors.
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Extended data figures and tables
Extended Data Fig. 1 Laue diffraction from the (011) aligned crystal.
Laue diffraction of a single UTe2 crystal which was used for the STM study is shown. A few specific (hkl) surfaces are marked.
Extended Data Fig. 2 LDOS at 300 mK.
LDOS maps obtained at several energies above and below EF.
Extended Data Fig. 3 FFT of LDOS at 300 mK.
FFTs of LDOS maps obtained at several energies above and below EF.
Extended Data Fig. 4 Inverse FFT of the CDW peaks, FFT showing primary and secondary CDW peaks and low energy dI/dV spectra.
a, Topography obtained on the (011) surface (same area as that shown in Fig. 1c of the manuscript. Inset shows the corresponding FFT with the CDW peaks circled in orange. b, Inverse FFT obtained from the circled CDW peaks (in orange) allowing real space visualization of the CDW modulations. c, FFT at the EF where the primary and secondary CDWs are shown using red circles and blue circles respectively, d, Linecut of the dI/dV spectra (shown in grey) and the average dI/dV spectrum (shown in red) obtained along the Te-chains. Apart from the Fano lineshape associated with the Kondo resonance, the individual spectra and the average dI/dV spectrum show an additional low energy feature (slope change around −1 meV to +2 meV) shown by the blue shaded region.
Extended Data Fig. 5 LDOS in presence of a 10.5 T magnetic field.
LDOS maps obtained at several energies in a perpendicular magnetic field.
Extended Data Fig. 6 FFT of LDOS in presence of a 10.5 T magnetic field.
FFTs of LDOS maps obtained at several energies in a perpendicular magnetic field.
Extended Data Fig. 7 Partial suppression and mirror symmetry breaking of the CDWs in the integrated FFT signal.
a-b, Comparison of FFTs of integrated signal obtained from integrating LDOS maps below EF for a 0 T field and 10.5 T field. The FFT of the integrated signal also shows similar behavior as the FFT of individual energy slices. c–e, Linecuts obtained along 3 different directions for the 3 CDWs illustrating the mirror symmetry breaking. d is clearly more suppressed than c.
Extended Data Fig. 8 Second and third sample-tip combinations for perpendicular magnetic field showing reproducibility of the partial suppression and mirror symmetry breaking of the CDW at 10.5 T.
a–b, Second dataset obtained with a different tip-sample combination showing the partial suppression and mirror symmetry breaking of the CDW in a perpendicular magnetic field. The FFTs shown have the same intensity scale. c–g, Series of FFT of topographies as a function of increasing magnetic field perpendicular to the [011] surface with a third sample-tip combination. (V = 20 mV, I = 100 pA) The intensity scale of all FFTs has been kept constant. The critical field for the mirror-symmetry breaking in \({q}_{1}^{CDW}\) and \({q}_{2}^{CDW}\) is close to 10 T.
Extended Data Fig. 9 FFTs showing the suppression of the CDWs at positive bias in a 11-degree tilted magnetic field.
a–c, Series of FFT of topographies obtained as a function of increasing magnetic field at 11 degrees with respect to the [011] direction with a different tip. (V = 40 mV, I = 120 pA). The intensity scale of all FFTs has been kept constant. The surface tilt is measured using the tilt correction function in the Nanonis module. d–f, Fourier transform linecuts obtained along 3 different directions of the CDWs as a function of magnetic field, showing clear suppression of the peak amplitudes above 9 T.
Extended Data Fig. 10 Additional dataset with a different tip showing reproducibility of the suppression of the CDWs in a 11-degree tilted magnetic field.
a–f, Additional dataset showing a series of FFT of topographies obtained as a function of increasing magnetic field at 11 degrees with respect to the [011] direction with a different tip. (V = 50 mV, I = 150 pA). The intensity scale of all FFTs has been kept constant. The surface tilt is measured using the tilt correction function in the Nanonis module.
Extended Data Fig. 11 Melting of the CDWs as a function of temperature.
a–c, FFTs of LDOS maps obtained as a function of temperature. The CDWs persist till 4 K and have disappeared by 10 K.
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Aishwarya, A., May-Mann, J., Raghavan, A. et al. Magnetic-field-sensitive charge density waves in the superconductor UTe2. Nature 618, 928–933 (2023). https://doi.org/10.1038/s41586-023-06005-8
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DOI: https://doi.org/10.1038/s41586-023-06005-8
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