Anharmonic Strong-Coupling Effects at the Origin of the Charge Density Wave in CsV 3 Sb 5

arXiv:2308.07482 · cond-mat.supr-con · Submitted 2023-08-14 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: We're looking at the paper: "Anharmonic Strong-Coupling Effects at the Origin of the Charge Density Wave in CsV 3 Sb 5".

Mira: Here's the gist of the paper. The gist The formation of charge density waves (CDW) in CsV3Sb5 is driven by strong anharmonic phonon-phonon and electron-phonon coupling, which leads to a large electronic energy gap and an asymmetric amplitude mode.

Kai: Electronic Gap and Charge Density Wave Transition The electronic energy gap 2∆ as derived from the redistribution of the continuum is much larger than expected from mean-field theory and reaches values above 20 for 2∆/kBTCDW.

Mira: The A1g phonon has a discontinuity at TCDW and a precursor starting 20 K above TCDW.

Kai: Density functional theory qualitatively reproduces the redistribution of the electronic continuum at the CDW transition and the phonon energies of the pristine and distorted structures.

Title and authors: Kai: So to summarize the main findings of "Anharmonic Strong-Coupling Effects at the Origin of the Charge Density Wave in CsV3Sb5", they are pointing out that it's not a simple picture.

Mira: They emphasize that this material has a large electronic energy gap, two∆, which is significantly larger than expected from mean-field theory <ref:2308.07482#pg1>.

Lev: That large ratio, two one to two three for the gap to the thermal energy divided by the charge density wave temperature, is a key number they use to back up their argument.

Kai: They also show how this gap comes from the redistribution of a continuum, which they analyze using density functional theory.

Mira: And they link this electronic structure analysis to phonon energies in both pristine and distorted structures, showing how the transition affects them.

Lev: Essentially, they are using DFT to map out the electronic changes alongside the vibrational changes to build a picture of what happens at TCDW.

Kai: They focus on strong coupling involving anharmonic effects between phonons and electrons because that’s what they suspect is causing this behavior in CsV3Sb5.

Mira: Specifically, they highlight the asymmetric A1g amplitude mode exhibiting a Fano-type lineshape as evidence for strong electron-phonon coupling.

Lev: And then they connect this to the phonon renormalization effects across all A1g and E2g modes, showing how they are strongly coupled via phonon-phonon interactions.

Kai: They also detail how lattice distortions, specifically the iSoD distortion, have a reduction in spectral weight below two thousand centimeters per second.

Mira: This structural effect suggests that the iSoD distortion is an important factor in stabilizing this electronic state and influences the observed phonon spectrum below TCDW.

Lev: It’s about using structural information to predict how these coupled modes will behave under different lattice environments, which is a useful predictive tool for any experimentalist.

Kai: So, the paper's summary boils down to strong coupling between phonons and electrons being the likely mechanism for this CDW transition in CsV3Sb5.

Mira: They use the evidence from both the large gap ratio and that specific amplitude mode shape to argue against a weak coupling picture.

Lev: It’s about showing that if you ignore these strong interactions, you don't get the right physical description of what's happening in this material.

The paper's summary: Kai: Now for the suggested improvements, they aren't just saying "this is what we found," but they are suggesting how future work can build on this.

Mira: They suggest that improving materials discovery systems can use the analysis of the electronic energy gap, two∆ as derived from the redistribution of the continuum to predict CDW formation in materials like CsV3Sb5 <ref:2308.07482#pg1>.

Lev: That means an AI system could be trained to look at spectral features and flag a material as potentially having a charge density wave before we even start synthesizing it.

Kai: And they suggest that AI-driven modeling can simulate lattice distortions to predict structural stability, for instance, DFT simulations suggest an iSoD distortion in CsV3Sb5 to have minimum energy.

Mira: So the system could then use that information to guide the selection of stable crystal phases during synthesis.

Lev: That’s a way to use computational modeling not just for post-hoc analysis but as a guiding principle for experimentalists, which is really helpful when you're trying to select a robust starting material.

Kai: They also suggest that predictive models can forecast phonon behavior under charge density wave conditions, like observing the A1g phonon has a discontinuity at TCDW and a precursor starting twenty Kelvin above it.

Mira: This allows us to predict frequency shifts and line width changes in Raman spectra as we cool the material.

Lev: If you can predict those specific temperature dependencies, you save months of experimental tuning because you know exactly what to look for on your data.

Kai: Another point is that the paper suggests using spectral features like the asymmetric Fano-type lineshape in A1g symmetry as a predictor of strong electron-phonon coupling.

Mira: This moves beyond just looking at symmetric Lorentzian line shapes, which are common in other materials where all amplitude modes have a symmetric Lorentzian line-shape.

Lev: That asymmetry is something that would be a strong feature to look for when we're scanning spectroscopic data because it’s not something you can easily ignore.

The paper's improvements: Kai: So, to wrap up, the paper "Anharmonic Strong-Coupling Effects at the Origin of the Charge Density Wave in CsV3Sb5" tells us that strong coupling between phonons and electrons is likely what drives this CDW formation.

Mira: They use the large gap ratio and that specific amplitude mode shape as key evidence against a simple weak coupling picture.

Lev: It’s showing that considering these strong interactions is necessary for a proper physical description of the material's behavior.

Kai: The paper also points toward using AI to predict CDW formation and structural stability by analyzing electronic energy gaps and distortion effects.

Mira: So, the main implication is that we need better predictive models to guide materials discovery and experimental work toward these strongly coupled systems.

Lev: For me, it means when we’re building hardware, we have to account for the complexity of these coupling mechanisms in our design constraints.

Conclusion: Kai: So, we’ve looked at "Anharmonic Strong-Coupling Effects at the Origin of the Charge Density Wave in CsV3Sb5," and really, what this paper is saying is that you can't describe this charge density wave transition with just a simple weak coupling model.

Mira: Exactly. They found a very large electronic energy gap, two∆, which is bigger than mean-field theory even predicted for the CDW temperature divided by the thermal energy divided by Boltzmann constant ratio, two∆ over kBTCDW.

Lev: That large gap number is what you’d have to fight against when building real hardware; it means more energy you need to manage in your cryogenics setup.

Kai: Right, and they show how this gap comes from the redistribution of the electronic continuum, which they look at with density functional theory.

Mira: And that DFT analysis shows how those electronic changes affect the phonon energies for both the pristine and distorted structures.

Lev: So when you’re running error correction codes on real hardware, knowing how a lattice distortion affects those vibrational modes is crucial because it dictates your noise floor.

Kai: The core of their argument is that strong coupling, involving both phonon-phonon and electron-phonon interactions, is the actual driver for this CDW formation in CsV3Sb5.

Mira: They back this up by observing an asymmetric A1g amplitude mode displaying a Fano lineshape, which they say strongly suggests that electron-phonon coupling is actually significant.

Lev: That Fano resonance feature is something we need to look for when designing sensors or detectors; it’s a signature of the interaction you can't easily ignore.

Kai: They also show strong phonon renormalization across all A1g and E2g modes, meaning the coupling between phonons themselves is pretty robust at the transition point.

Mira: The precursor behavior, like that A1g phonon having a discontinuity at TCDW and starting twenty Kelvin above it, gives us a way to predict how those Raman spectra will look as you cool things down.

Lev: Predicting that frequency shift and line width change is what you need when you're trying to calibrate your measurement systems for real-world operation.

Kai: And structurally, the DFT simulations also point toward an iSoD distortion being the lowest energy state for CsV3Sb5, which is a key factor in understanding its stability.

Mira: So they connect the structural detail—the iSoD distortion—to the electronic response, showing how it reduces spectral weight below two thousand centimeters per second.

Lev: That’s useful because it helps us select the right crystal phase to start our experiments with, avoiding unnecessary noise from unstable structures.

Kai: So that’s the summary of "Anharmonic Strong-Coupling Effects at the Origin of the Charge Density Wave in CsV3Sb5," pointing toward strong coupling as the mechanism.

Mira: It suggests that nesting isn't enough; you need to consider these coupled effects between phonons and electrons for a full picture.

Lev: It’s a reminder that when you’re building systems, the interplay between different modes is often where the real complexity lands on hardware overhead.

Kai: Next up, we’re diving into how this same material behaves under extreme non-Hermitian conditions, looking at its spectral functions with tensor networks.

Walther Meissner Institut Bayerische Akademie der Wissenschaften · Department of Materials Science and Engineering Stanford University · Stanford Institute for Materials and Energy Sciences SLAC National Accelerator Laboratory Stanford University · Beijing National Laboratory for Condensed Matter Physics Institute of Physics Chinese Academy of Sciences · Fakultät für Physik E23 Technische Universität München · School of Physical Sciences University of Chinese Academy of Sciences Beijing 7 Geballe Laboratory for Advanced Materials Stanford University 8 Fakult᤟er Physik Technische Universit München Garching 9 IFW Dresden Helmholtzstrasse 20

cond-mat.supr-con

Submitted: 2023-08-14

Updated: 2023-08-14

Comments: 19 pages, 5 figures

Journal ref: Nature Communications 15, 1895(2024)

DOI: 10.1038/s41467-024-45865-0

License: http://creativecommons.org/publicdomain/zero/1.0/

Importance score: 89/100

The gist: The gist The formation of charge density waves (CDW) in CsV3Sb5 is driven by strong anharmonic phonon-phonon and electron-phonon coupling, which leads to a large electronic energy gap and an

Key concepts

Electronic Gap (2∆): This is the energy difference between electronic states caused by the CDW formation. In CsV3Sb5, this gap is very large—around 21-23 times the thermal energy ($k_BT_{CDW}$)—which is much larger than predicted by simple mean-field theories, pointing to strong coupling effects.
Phonon Renormalization: This refers to how the vibrational modes (phonons) change their properties when the CDW forms. The paper shows that both A1g and E2g phonons are significantly altered by this coupling, exhibiting kinks and changes in linewidth as temperature drops below the transition temperature.
Amplitude Mode (AM) / Fano Resonance: These are specific collective oscillations associated with the CDW. The A1g AM displays a unique asymmetric Fano-type lineshape, which is a strong indicator of intense electron-phonon coupling. This specific feature distinguishes CsV3Sb5 from other CDW materials where modes are typically symmetric.

Summary

The gist The formation of charge density waves (CDW) in CsV3Sb5 is driven by strong anharmonic phonon-phonon and electron-phonon coupling, which leads to a large electronic energy gap and an asymmetric amplitude mode.

Electronic Gap and Charge Density Wave Transition

The electronic energy gap 2∆ as derived from the redistribution of the continuum is much larger than expected from mean-field theory and reaches values above 20 for 2∆/kBTCDW. The A1g phonon has a discontinuity at TCDW and a precursor starting 20 K above TCDW. Density functional theory qualitatively reproduces the redistribution of the electronic continuum at the CDW transition and the phonon energies of the pristine and distorted structures. The gap energy is estimated to be close to the intersection points at 87.5 - 96.2 meV yielding a gap ratio of 2∆/kBTCDW ∼ 21−23, similar to the results of IR spectroscopy and recent ARPES measurements. This observation may be attributed to fluctuating short range CDW order [32,page6] or strong anharmonic electron-phonon coupling [2].

Phonon Renormalization and Coupling

The linewidths of all A1g and E2g phonon lines including those emerging below TCDW were analyzed in terms of anharmonic symmetric decay [9] revealing strong phonon-phonon coupling. Both the A1g and the E2g phonons show significant renormalization effects at TCDW. Upon cooling, the A1g phonon has a precursor starting 20 K above TCDW, changes discontinuously at TCDW and saturates below. The line width exhibits a kink at TCDW and decreases faster below TCDW than above. The new lines have similarly large phonon-phonon coupling constants λph−ph as the strong lines appearing above and below TCDW (see Fig. 3 d and f and Tab. I in the Supplementary Materials E), indicating strong phonon-phonon coupling.

Amplitude Modes and Fano Resonance

Two CDW amplitude modes (AMs): one in A1g symmetry and one in E2g symmetry were observed. The A1g AM displays an asymmetric Fano-type lineshape, suggestive of strong electron-phonon coupling. The lines at 105 cm−1 and 208 cm−1 in A1g and E2g symmetry, respectively, have significantly stronger temperature dependences than the other lines appearing below TCDW, and are identified as AMs. The A1g line broadens by approximately an order of magnitude close to TCDW and assumes a rather asymmetric shape in the range 40-80 K. The Fano line of the AM is unique in CsV3Sb5 and has not been observed in other wellknown CDW materials, such as ErTe3 [3].

Lattice Distortion and Structural Effects

The CDW gap is qualitatively reproduced by the DFT simulations as presented in Fig. 2 c. The electronic response of CsV3Sb5 is approximated for pristine-, SoD- and iSoD-distorted-lattices (see the insets of Fig. 2 c) using the joint density of states. A reduction in spectral weight is found in the iSoD distorted lattice below 2000 cm−1, which can barely be seen in the SoD lattice. The new phonon lines below TCDW result from the lowering of the lattice symmetry as spelled out by Wu et al. [23] and Liu et al. [24]. If one considers a SoD or an iSoD distortion (see the insets of Fig. 2 c) that are expected for CsV3Sb5 ([6,17,36]), one expects eight additional Raman active modes (two in A1g, four in E2g and two in E1g). Most of the zone-folded modes quantitatively match the frequencies obtained in the DFT simulations when considering the iSoD distortion [24].

Conclusion on Driving Mechanism

The asymmetric AM, along with the missing soft mode behaviour in the acoustic branches [6,7] and the large 2∆/kBTCDW ratio argue against the weak coupling picture. Thus, strong coupling involving phonon-phonon and electron-phonon interaction is presumably the driving force behind the formation of the CDW in CsV3Sb5. This interpretation is consistent with the large electronic gap and the asymmetric AM. The co-operation of strong electron-phonon and phonon-phonon coupling may be more likely a route to the CDW transition in CsV3Sb5 than, e.g., nesting.

Methods Overview

The inelastic light scattering experiments were preformed in pseudo-backscattering geometry. The electronic response in the main text was approximated using the joint density of states with the following equation. Phonon calculations were performed using the Phonopy code package [44,45]. DFT calculations were performed using VASP [43] with plane wave augmented (PAW) pseudopotentials and a 300 eV energy cutoff. The primary focus here is on the energy of the A1g phonon. Electron phonon coupling to the A1g and E2g was calculated using the frozen phonon method and found to be negligible. The broadening of 0.02 eV was used in the results in the main text.

Sample Preparation

Single crystals of CsV3Sb5 were grown from liquid Cs (purity 99.98 %), V powder (purity 99.9 %) and Sb shot (purity 99.999 %) via a modified self-flux method. The sample used for the Raman experiments has a TCDW of 95 K, characterized by resistivity and in-plane magnetic susceptibility (see Supplementary Materials A for details).

Author Contributions

G.H., L. P., E.C., and R.H. wrote the manuscript with comments from all the authors. G.H., L.P., D. L. and R.S performed the Raman measurements. G.H., L,P., E,C., TPD, and R.H analysed the Raman data. Z.Z., H.-T.Y. and H.-J.G synthesised and characterised the samples. E.C., B.M. and TPD performed DFT calculations. G.H., L,P., E,C. and R.H wrote the manuscript with comments from all the authors. The authors declare no competing interests.

Acknowledgments

We thank R.-Z. Huang for fruitful discussions. This work is supported by the Deutsche Forschungsgemeinschaft (DFG) through the coordinated programme TRR80 (Projekt-ID 107745057) and projects HA2071/12-1 and-3. L.P. and R.H. were partially supported by the Bavaria-California Technology Center (BaCaTeC) under grant number A3 [2022-2]. G.H. would like to thank the Alexander von Humboldt Foundation for a research fellowship. The work in China was supported by grants from the National Key Research and Development Projects of China (2022YFA1204104), the Chinese Academy of Sciences (ZDBS-SSW-WHC001 and XDB33030000),and the National Natural Science Foundation of China (61888102).

Improvements for AI systems

Improved materials discovery systems can predict Charge Density Wave (CDW) formation in Kagome metal compounds like CsV3Sb5 by analyzing the electronic energy gap 2∆ as derived from the redistribution of the continuum, which reaches values above 20 for 2∆/kBTCDW.
The system can identify strong coupling mechanisms by assessing spectral features, specifically detecting a strong Fano resonance between the conduction electrons and the AM in A1g symmetry, moving beyond the weak coupling prediction of 3.53.
AI-driven modeling can simulate lattice distortions to predict structural stability; for instance, DFT simulations suggest an iSoD distortion in CsV3Sb5 to have minimum energy, which informs the selection of stable crystal phases.
The system can characterize collective modes by analyzing temperature dependence, recognizing that the A1g AM displays an asymmetric Fano-type lineshape, suggestive of strong electron-phonon coupling, a feature absent in other materials like ErTe3 or LaTe3 where all AMs have a symmetric Lorentzian line-shape.
Predictive models can forecast phonon behavior under CDW conditions, such as the observation that the A1g phonon has a discontinuity at TCDW and a precursor starting 20 K above TCDW, allowing for the prediction of frequency shifts and line width changes in Raman spectra.

Abstract

The formation of charge density waves (CDW) is a long-standing open problem particularly in dimensions higher than one. Various observations in the vanadium antimonides discovered recently, such as the missing Kohn anomaly in the acoustic phonons or the latent heat at the transition T CDW = 95 K, further underpin this notion. Here, we study the Kagome metal CsV 3 Sb 5 using polarized inelastic light scattering. The electronic energy gap 2Δ as derived from the redistribution of the continuum is much larger than expected from mean-field theory and reaches values above 20 for 2Δ/k BT CDW. The A 1g phonon has a discontinuity at T CDW and a precursor starting 20 K above T CDW. Density functional theory qualitatively reproduces the redistribution of the electronic continuum at the CDW transition and the phonon energies of the pristine and distorted structures. The linewidths of all A 1g and E 2g phonon lines including those emerging below T CDW were analyzed in terms of anharmonic symmetric decay revealing strong phonon-phonon coupling. In addition, we observe two CDW amplitude modes (AMs): one in A 1g symmetry and one in E 2g symmetry. The temperature dependence of both modes deviates from the prediction of mean-field theory. The A 1g AM displays an asymmetric Fano-type lineshape, suggestive of strong electron-phonon coupling. The asymmetric A 1g AM, along with the discontinuity of the A 1g phonon, the large phonon-phonon coupling parameters and the large gap ratio, indicate the importance of anharmonic strong phonon-phonon and electron-phonon coupling for the CDW formation in CsV 3 Sb 5.

Sources

Distinctive momentum dependent charge-density-wave gap observed in CsV$_3$Sb$_5$ superconductor with topological Kagome lattice