Anomalous Thermal Conductivity Reversal Driven by a Fluctuating Charge Density Wave

The gist The thermal transport measurements revealed a striking V-shaped temperature evolution of thermal conductivity featuring three distinct regimes: a pronounced peak near 122 K, a dip around 210 K, and an unexpected upturn at higher temperatures

Thermal Transport as a Probe

Thermal transport provides a sensitive probe of these hidden fluctuations in the layered transition metal dichalcogenide 2H-TaSe2 Because phonons interact with virtually all excitations in a crystal, they are capable of sensing collective modes and hidden dynamics that are elusive conventional probes, thus making thermal conductivity measurement as a comprehensive diagnostic of these elusive degrees of freedom The longitudinal thermal transport possesses a more universal diagnostic reach compared to the thermal Hall conductivity which has recently emerged as a specialized probe of Berry curvature and topological excitations

Anomalous Temperature Dependence

The normal phase (> 122 K) thermal conductivity exhibits a distinctive V-shaped temperature dependence A sharp peak appears at TCDW = 122 K, coinciding with the incommensurate to normal CDW transition This peak originates from a lambda-shaped specific heat peak at critical temperature driven by critical-like fluctuations of the CDW order, a hallmark of continuous phase transitions Upon warming, the thermal conductivity decreases until reaching a minimum around 210K Most remarkably, above 210K, we observe an anomalous increase in thermal conductivity that persists to high temperatures, highly unusual for crystalline materials where thermal conductivity typically decreases with increasing temperature due to enhanced phonon-phonon scattering

Evidence of Persistent Local Order

Selected area electron diffraction (SAED) and X-ray diffraction (XRD) measurements reveal persistent short-range CDW order far above the long-range-order transition and thermal hysteresis in the CDW wavevector Our SAED measurements reveal distinctive residual CDW superlattice peaks persist even at 300K, far above the long-range-order transition temperature of 122 K These surviving satellite peaks demonstrate robust short-range (local) CDW order deep into the nominally disordered phase We also observe a linear increase in SAED peak widths with increasing temperature, as shown in Fig. 4(e), suggesting a decreasing coherence length with 1T−TCDWn scaling behavior, where n ≈ 1 Notably, this scaling is valid not just a few Kelvins near the critical temperature but persists more than 150 K above TCDW

Modeling the Melting Mechanism

The competition between these two effects explains the unusual V-shaped temperature dependence observed in our thermal conductivity measurements, with a minimum around 210K separating the two competing regimes This picture can be formalized by modeling phonon scattering from spatial fluctuations of the CDW order parameter, expressed as ψ(r)a = A(r) exp[i q(z + u(r))] The total thermal conductivity is then obtained from kinetic theory as κ(T) = 1/3 Cv(T)vs2 τtot(T), where the scattering rate is given by a Matthiessen sum τtot−1(T) = AU T exp (−γU T) + Aimp + τCDW−1(T) Fitting to experimental thermal conductivity data results in CDW scattering rates grow with w2A2 at intermediate temperatures (122K 210K), driving a minimum in thermal conductivity, and diminish once the amplitude collapses, allowing κ(T) to recover at elevated temperatures

Conclusion on Transition Nature

The persistence of local CDW order far above TCDW indicates that CDW-related phenomena can remain active well into the nominally normal phase This behavior is fundamentally distinct from both conventional first-order transitions, which exhibit abrupt loss of order with minimal precursor fluctuations, and continuous KTHNY-type melting where topological defect unbinding proceeds without thermodynamic hysteresis The observation of clear thermal hysteresis of the CDW wavevector near the incommensurate transition temperature upon cooling and warming cycles indicates latent energy associated with the transition, a defining feature of first-order transitions This interpretation aligns with contemporary theoretical frameworks for phase transitions in general 2D and quasi-2D systems, which allow for multiple melting scenarios depending on specific material parameters and interaction potentials The results provide a model example of how fluctuating charge order can influence electronic structure and transport without long-range order

Implications for Correlated Matter

The persistence of local CDW order above TCDW suggests that dislocation- and fluctuation-driven melting may represent a unifying description for CDW transitions in low-dimensional layered materials, but the melting in 1T-TaS2 is of KTHNY type involving a hexatic process This behavior is also relevant to other correlated systems, particularly high-temperature superconductors, where short-range charge ordering and fluctuating electronic correlations persist in the pseudogap regime well above the superconducting transition temperature Our results therefore provide a model example of how fluctuating charge order can influence electronic structure and transport without long-range order More broadly, our results highlight how the interplay among lattice distortions, electronic instabilities, and defect-mediated spatial heterogeneity can govern both thermal transport and ordering phenomena in low-dimensional quantum materials This further demonstrates that thermal transport measurements provide a powerful probe of hidden fluctuating order

Experimental Details

2H-TaSe2 has a hexagonal (P63/mmc) structure consisting of two layers of Se–Ta–Se sandwiches stacked along the c-axis Single crystals were synthesized via a two-step solidstate reaction followed by iodine-assisted chemical vapor transport in a temperature gradient of 1050–1000 °C for one week In-plane thermal transport was measured using the transient thermal grating (TTG) technique, a non-contact optical pump–probe method illustrated in Fig. 1(c) Thermal conductivity from 78 K to 350 K was then obtained by combining the diffusivity with the specific heat estimated using the Debye model The peak width is fitted as w(T) = w0 + m(T − 100K), where the fitted w0 ≈ 0.0865 Å−1 and m ≈ 0.00168 Å−1 Fitting to experimental thermal conductivity data results in AU = 1.316 × 105 s−1K−1, Aimp = 4.758 × 106 s−1, aCDW = 5.327 × 108 s−1 Å2, ΘU = 120K, T0 = 196.88K, Δ = 3.95K, and s 0.122 The electron microscopy datasets in this study are available through PARADIM (61) The authors declare no competing interests All other raw data supporting the findings of this study are available upon request

Acknowledgments and Funding

HH, JD, and ZT thank Allan MacDonald for fruitful discussions and suggestions HH, JD, JC, GA, and ZT thank Jacob Ruff for assistance with X-ray diffraction measurements and helpful discussions This research used resources of the Advanced Photon Source Research conducted at the Center for High-Energy X-ray Sciences (CHEXS) was supported by the National Science Foundation under awards DMR-1829070 and DMR-2342336 This research made use of the electron microscopy facility of the Platform for the Accelerated Realization, Analysis, and Discovery of Interface Materials (PARADIM) which is supported by the National Science Foundation under Cooperative Agreement No. DMR-2039380 CS thanks the NSF under 1726077 for the single-crystal X-ray diffraction experiments Funding acquisition was done by CS, DMu, ZT Project administration was done by HH, JD, ZT Supervision was done by ZT

References

J. M. Kosterlitz, D. J. Thouless, Ordering, metastability and phase transitions in twodimensional systems B. I. Halperin, D. R. Nelson, Theory of Two-Dimensional Melting Y. Kato, N. Nagaosa, Monte Carlo simulation of two-dimensional flux-line-lattice melting J. Hu, A. H. MacDonald, Two-dimensional vortex lattice melting J. A. Wilson, F. J. Di Salvo, S. Mahajan, Charge-density waves and superlattices in the metallic layered transition metal dichalcogenides D. E. Moncton, J. D. Axe, F.

1. The AI system can be enhanced to predict material phase stability boundaries by incorporating a phenomenological model linking phonon-CDW scattering, order-parameter fluctuations, and anomalous thermal transport, as described in the text. This allows the system to distinguish between conventional first-order transitions and weak first-order melting by analyzing thermal conductivity anomalies.

2. The AI can develop a diagnostic tool for identifying fluctuating local order in materials using longitudinal thermal transport measurements across temperature ranges up to 300 K. Specifically, it can detect the V-shaped temperature dependence of the thermal conductivity and differentiate it from standard phonon-phonon scattering by analyzing the observed features at temperatures like around 210K.

3. The system can be improved to predict the persistence of short-range order above nominal transition temperatures by modeling how CDW correlations evolve. It can use data showing that persistent local charge-density-wave (CDW) correlations exist far above the long-range-order transition temperature of 122 K to inform predictions about the effective phase diagram stability.

4. The AI can be trained to analyze X-ray and electron diffraction data to quantify lattice dynamics related to CDW fluctuations. It can specifically extract metrics like peak width changes, such as linear increase in SAED peak widths with increasing temperature, which indicates diminishing local CDW order based on the scaling behavior noted.

5. The system can be equipped to analyze thermal hysteresis in structural data to identify latent energy associated with phase transitions. This capability is crucial for distinguishing between transition types, as it can detect clear thermal hysteresis of the CDW wavevector near the incommensurate transition temperature upon cooling and warming cycles, which is a defining feature of first-order transitions.