Abstract
Broken time-reversal symmetry in the absence of spin order indicates the presence of unusual phases such as orbital magnetism and loop currents1,2,3,4. The recently discovered kagome superconductors AV3Sb5 (where A is K, Rb or Cs)5,6 display an exotic charge-density-wave (CDW) state and have emerged as a strong candidate for materials hosting a loop current phase. The idea that the CDW breaks time-reversal symmetry7,8,9,10,11,12,13,14 is, however, being intensely debated due to conflicting experimental data15,16,17. Here we use laser-coupled scanning tunnelling microscopy to study RbV3Sb5. By applying linearly polarized light along high-symmetry directions, we show that the relative intensities of the CDW peaks can be reversibly switched, implying a substantial electro-striction response, indicative of strong nonlinear electron–phonon coupling. A similar CDW intensity switching is observed with perpendicular magnetic fields, which implies an unusual piezo-magnetic response that, in turn, requires time-reversal symmetry breaking. We show that the simplest CDW that satisfies these constraints is an out-of-phase combination of bond charge order and loop currents that we dub a congruent CDW flux phase. Our laser scanning tunnelling microscopy data open the door to the possibility of dynamic optical control of complex quantum phenomenon in correlated materials.
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Data availability
The data for the main figures and the Extended data figures is available at the Illinois Databank (https://doi.org/10.13012/B2IDB-4197245_V1).
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Acknowledgements
This material is based on work supported by the US Department of Energy Office of Science National Quantum Information Science Research Centers as part of the Q-NEXT centre, which supported the laser-STM work of S.B. and provided partial support for laser-STM development. V.M. acknowledges support from the Gordon and Betty Moore Foundation’s EPiQS initiative through grant number GBMF9465 for magnetic-field STM studies and the laser-STM instrument development. Funding for sample growth was provided via the UC Santa Barbara NSF Quantum Foundry funded via the Q-AMASE-i programme under award DMR-1906325. A.N.C.S. acknowledges support from the Eddlemam Center for Quantum Innovation at UC Santa Barbara. E.R., F.Y. and T.B. were supported by NSF CAREER grant DMR-2046020. R.M.F. was supported by the Air Force Office of Scientific Research under award number FA9550-21-1-0423. Z.W. is supported by the US Department of Energy, Basic Energy Sciences (grant number DE-FG02-99ER45747) and by Research Corporation for Science Advancement (Cottrell SEED award number 27856). B.R.O. gratefully acknowledges support from the US Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division.
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Y.X., S.B. and V. M. conceived the project. S.B. constructed the laser-STM set-up and designed the laser experiment. Y.X. and S.B. conducted the laser-STM measurements. Y.X. conducted the STM studies under magnetic field. A.N.C.S., B.R.O. and S.D.W. provided the RbV3Sb5 samples used in this study. E.R., F.Y., T.B., Z.W., and R.M.F. conducted the group theory analysis and theoretical interpretation of the data. Y.X., S.B. and V.M. performed the data analysis and wrote the paper with input from all the authors.
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Extended data figures and tables
Extended Data Fig. 1 Optics layout and experimental procedure of the laser STM.
a, Optics layout of the laser STM. b, Experimental procedure to measure light-induced changes in CDW intensity.
Extended Data Fig. 2 Evolution of the CDW intensity ratio at different sample biases.
For different biases, the sign of \({I}_{r}\) remains the same.
Extended Data Fig. 3 Scanning tunneling spectroscopy (STS) maps and STM topography showing the behavior of the CDW intensity upon illumination of linearly polarized light.
a-b, The two directions of laser polarization with respect to the schematic reciprocal lattice. The red and blue double arrows denote the polarization direction of the laser beam. Upon laser illumination along \({Q}_{1}\) and \({Q}_{3}\) directions, the same switching behaviour of the CDW intensities appears both in the STS map (c-d, \({V}_{{bias}}\) = −200 mV, \({I}_{{set}}\) = 100 pA) and STM topography (e-f).
Extended Data Fig. 4 Agreement between different methods of quantifying the CDW intensity.
a, Typical FT of the Sb surface. The 2 × 2 CDW peaks along the three directions are labelled Q1 to Q3. b-c, Zoomed in FT images showing that the intensities of Q1 and Q3 are mostly localized to a single pixel. d, Light-induced switching of the CDW intensity with an arbitrary illumination sequence with laser polarization along either \({{\boldsymbol{E}}}_{1}\) or \({{\boldsymbol{E}}}_{3}\) (same as Fig. 3a), with the CDW intensities determined by the single pixel method. e, CDW intensity contrast along the same arbitrary illumination sequence with the nearest averaging methods (5 pixels in total). The trends in the intensity contrast remain the same while the absolute value of the intensity contrast is suppressed in most cases suggesting that using the single pixel method provides better signal.
Extended Data Fig. 5 Laser fluence dependence of the CDW intensity contrast.
a, Fig. 3e in main text: \({I}_{r}=({I}_{1}-{I}_{3})/2({I}_{1}+{I}_{3})\) at each illumination with doubling the fluence. Beyond the critical fluence \({F}_{c}\approx \) 8 \({F}_{0}\), the sign of \({I}_{r}\) starts to change depending on the direction of illumination. b, Absolute value of the \({I}_{r}\) (\(\left|{I}_{r}\right|\)) with respect to the fluence on a linear scale. For fluence > \({F}_{c}\), the fluence and \(\left|{I}_{r}\right|\) start to show a proportional relation.
Extended Data Fig. 6 Identification of Bragg peak vector locations.
a, Typical FT of the Sb layer before light illumination. Bragg peaks are clearly observed and highlighted with circles. Zoom-in images of these peaks along \({{\boldsymbol{Q}}}_{B1}\) and \({{\boldsymbol{Q}}}_{B3}\) directions reveal anisotropic intensity distribution in a 5-pixel × 5-pixel size in momentum space, thus enabling us to carry out the effective center of mass to identify the actual peak location (green circles). b, \({{\boldsymbol{Q}}}_{B1}\) and \({{\boldsymbol{Q}}}_{B3}\) peak locations during light illumination along either \({{\boldsymbol{E}}}_{1}\) or \({{\boldsymbol{E}}}_{3}\) directions, showing noticeable extending/shrinking peak location. The red dot in the middle of FT serves as reference for relative peak location change.
Extended Data Fig. 7 Bragg peak ratio (Qr) along the laser polarization sequence with different grid sizes and peak position identification methods.
Different grid sizes (3 × 3 and 5 × 5) and peak position identification methods (center of mass and 2D Gaussian) show similar results for the Bragg peak ratio \({Q}_{r}\). This demonstrates the robustness of the trends in the Bragg peak ratio for the laser/field sequence.
Extended Data Fig. 9 Data on a strained region where the CDW intensity contrast and Bragg vector ratio do not respond to the magnetic field.
a, Large scale topography image (~87 nm × 87 nm) of the post-cleaned region. A wrinkle is clearly observed, indicating the presence of the strong residual in-plane strain in this region. b,d, Zoom-in topography image (30 nm × 30 nm) of the same region under +2 T and −2 T magnetic field perpendicular to the sample surface. c,e, FTs of (b) and (d) show a robust intensity order between \({{\boldsymbol{Q}}}_{1}\) and \({{\boldsymbol{Q}}}_{3}\) with respect to the opposite directions of out-of-plane magnetic field. f, Intensity contrast plot (\({{\boldsymbol{Q}}}_{r}\) in left panel) and Bragg vector ratio (\({{\boldsymbol{Q}}}_{r}\) in right panel) from this region. The intensity contrast does not show a sign change between + 2 and −2 T field. The Bragg vector ratio shows a marginal change (≈0.0005) compared to the case (≈0.01, Fig. 4h) where there is a flip in the sign of the CDW intensity contrast (Fig. 4g).
Extended Data Fig. 10 Vanadium bond order and loop current pattern and their rotation axis for different order parameter configurations.
a, Vanadium bond-order pattern (colored bonds) for the 3Q “real” CDW order parameter configuration \({\bf{L}}=(L,{L}{\prime} ,L)\) on a single kagome layer. The black line denotes the in-plane 2-fold rotation axis. b, Loop-current pattern (green arrows) for the 2Q “imaginary” CDW order parameter configuration \({\boldsymbol{\Phi }}=(\varPhi ,\,0,\,\varPhi )\), whose relative phase between its non-zero components is trivial. The 2-fold rotation axis is denoted as the orange lines. The closed current loops are denoted as red circles. c, Loop-current pattern for the 2Q “imaginary” CDW order parameter configuration \({\boldsymbol{\Phi }}=\left(\varPhi ,\,0,\,-\varPhi \right)\). There exists a relative \(\pi \) phase between the non-zero components, which changes the location of the 2-fold rotation axis. d, An overlay view of the \({L}_{1}={L}_{3}\ne {L}_{2}\) and \({\varPhi }_{1}={\varPhi }_{3}\) orderings. In this case, bond-order and loop-current patterns have different rotation axis so that the 2-fold rotation is broken in the system, which allows a macroscopic out-of-plane magnetic dipole moment. e, An overlay view of the \({L}_{1}={L}_{3}\ne {L}_{2}\) and \({\varPhi }_{1}={-\varPhi }_{3}\) orderings. In this case, both bond-order and loop-current patterns share the same rotation axis, so that the system possesses an in-plane 2-fold rotation axis, which forbids a macroscopic magnetic dipole moment. This configuration allows the system to have piezo-magnetic effect even in the absence of a macroscopic magnetic dipole moment.
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Xing, Y., Bae, S., Ritz, E. et al. Optical manipulation of the charge-density-wave state in RbV3Sb5. Nature 631, 60–66 (2024). https://doi.org/10.1038/s41586-024-07519-5
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DOI: https://doi.org/10.1038/s41586-024-07519-5
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