pith. sign in

arxiv: 2503.03155 · v3 · pith:YP7Q2TI5new · submitted 2025-03-05 · ❄️ cond-mat.mtrl-sci · cond-mat.soft

Glass-like anomalies and unconventional thermoelectric transport in chimney ladder crystals

Pith reviewed 2026-05-25 08:47 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.soft
keywords chimney ladder crystalsglass-like anomaliesboson peakthermoelectric transportphonon hybridizationNowotny compoundslow thermal conductivityoverdamped modes
0
0 comments X

The pith

Chimney ladder crystals show glass-like heat capacity anomalies and linear resistivity due to low-energy phonons from their sublattice structure despite crystalline order.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that Nowotny chimney ladder crystals, which have an ordered structure, display deviations from the Debye model in heat capacity at low temperatures with a boson-peak-like anomaly between 8 and 14 K. This glassy behavior arises from extremely low-energy optical phonons that emerge from the chimney ladder sublattice and hybridize with acoustic phonons. The anomalous thermoelectric properties, such as extended linear temperature dependence in resistivity, are attributed to electrons scattering off overdamped phononic modes. These features make the materials promising for thermoelectric applications with inherently low thermal conductivity.

Core claim

Despite their ordered crystalline structure, the heat capacity of these NCL compounds deviates from the Debye model at low temperatures and exhibits a boson-peak-like glassy anomaly in the range of 8-14 K, attributed to extremely low-energy optical phonons from the chimney ladder sublattice that hybridize with acoustic modes; the anomalous resistivity is explained by electrons scattering with overdamped phononic modes.

What carries the argument

Hybridization of low-energy optical phonons from the chimney ladder sublattice with acoustic phonons, causing avoided crossings and modified acoustic modes.

If this is right

  • The measured thermal conductivity and thermoelectric response show distinct anomalous glass-like features that correlate with the dynamics of the low-lying optical phonons.
  • The electric resistivity displays an extended linear in T behavior and an anomalously large T^2 contribution at low temperature.
  • A simple theoretical framework based on electrons scattering with overdamped phononic modes qualitatively explains the resistivity features.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar glassy anomalies may appear in other materials with complex sublattice structures that support low-energy optical modes.
  • Inelastic scattering experiments could directly confirm the phonon hybridization and avoided crossings predicted by simulations.
  • Engineering the sublattice to tune the phonon energies could optimize thermoelectric performance in related compounds.

Load-bearing premise

The low-energy optical phonons universally emerge from the chimney ladder sublattice structure and their coupling to acoustic phonons directly causes the observed glassy anomaly, based on DFT and AIMD simulations.

What would settle it

An inelastic neutron scattering experiment that fails to detect the predicted low-energy optical phonons or their hybridization with acoustic modes would falsify the proposed microscopic origin.

Figures

Figures reproduced from arXiv: 2503.03155 by Binru Zhao, Chunhao Su, Elen Duverger-Nedellec, F. Malte Grosche, Hui Xing, Jie Ma, Jiong Yang, Junfa Lin, Matteo Baggioli, Srinivas V. Mandyam, Tianlong Xia, Weicen Dong, Xiaoxian Yan, Xi Chen, Yasong Wu, Zhiying Zhao.

Figure 1
Figure 1. Figure 1: ). In contrast, ideal crystalline metals, such as cop￾per and tungsten (displayed for comparison in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (a) proves the validity of these analytical scalings when compared to the numerical solutions of Eq. (5) [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
read the original abstract

Nowotny chimney ladder (NCL) crystals present physical properties in between the contrasting paradigms of ideal crystal and amorphous solid, making them promising candidates for thermoelectric applications due to their inherently low thermal conductivity. In this work, we report an extensive experimental characterization of the thermodynamic and thermoelectric transport properties of a large class of NCL materials, focusing on the intermetallic compound Ru$_2$Sn$_{3}$. We show that, despite their ordered crystalline structure, the heat capacity of these NCL compounds deviates from the Debye model at low temperatures and exhibits a boson-peak-like glassy anomaly in the range of $8$-$14$ K. By combining experimental measurements with density functional theory (DFT) and \emph{ab initio} molecular dynamics (AIMD) simulations, we attribute the microscopic origin of this glassy behavior to extremely low-energy optical phonons that universally emerge from the chimney ladder sublattice structure. Crucially, their coupling to acoustic phonons induces hybridization and avoided crossings, leading to strongly modified acoustic modes that directly contribute to the anomaly as well, similar to the case of other thermoelectric materials such as clathrates. Additionally, the measured thermal conductivity and the thermoelectric response present distinct anomalous glass-like features that strongly correlate with the dynamics of the low-lying optical phonons revealed by simulations. In particular, the electric resistivity displays an extended linear in $T$ behavior and an anomalously large $T^2$ contribution at low temperature. We propose a simple theoretical framework, based on electrons scattering with overdamped phononic modes, that qualitative explains both these features.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript reports experimental measurements of heat capacity, thermal conductivity, and resistivity on Nowotny chimney ladder (NCL) compounds, with focus on Ru2Sn3, showing deviations from Debye behavior and a boson-peak-like anomaly at 8-14 K. These are attributed, via DFT phonon dispersions and AIMD simulations, to low-energy optical phonons emerging from the chimney-ladder sublattice that hybridize with acoustic modes; anomalous resistivity is explained by a qualitative scattering framework involving overdamped phononic modes. The work positions NCLs as intermediate between crystalline and amorphous paradigms for thermoelectric applications.

Significance. If the simulation-to-experiment mapping holds, the results would demonstrate how an ordered sublattice structure can produce glass-like thermodynamic and transport anomalies through specific low-energy phonon hybridization, offering a microscopic route to low thermal conductivity in thermoelectrics. The extensive experimental dataset across multiple NCL compounds and the correlation with AIMD dynamics constitute a clear strength; the paper also supplies a falsifiable qualitative scattering model for the resistivity features.

major comments (1)
  1. [Abstract and simulation sections] Abstract and simulation sections: the central attribution of the 8-14 K heat-capacity anomaly (and the correlated transport anomalies) to chimney-ladder optical phonons and their hybridization with acoustic modes rests on DFT/AIMD inference of mode energies and avoided crossings; no inelastic neutron scattering, X-ray diffuse scattering, or other momentum-resolved phonon data are reported to confirm the mode energies, linewidths, or hybridization gaps in the 1-5 meV window. This mapping is load-bearing for the claim that the anomaly originates from these specific modes rather than alternatives such as disorder-induced two-level systems or anharmonic effects.
minor comments (1)
  1. The resistivity framework is stated to 'qualitatively explain' the linear-T and T^2 terms; a brief expansion on the scattering-rate assumptions or a comparison to a minimal model equation would improve clarity without altering the central narrative.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their detailed review and constructive feedback on our manuscript. The primary concern is the reliance on DFT/AIMD for attributing the low-temperature anomaly without direct momentum-resolved phonon data. We respond point-by-point below and indicate where revisions can strengthen the presentation.

read point-by-point responses
  1. Referee: [Abstract and simulation sections] Abstract and simulation sections: the central attribution of the 8-14 K heat-capacity anomaly (and the correlated transport anomalies) to chimney-ladder optical phonons and their hybridization with acoustic modes rests on DFT/AIMD inference of mode energies and avoided crossings; no inelastic neutron scattering, X-ray diffuse scattering, or other momentum-resolved phonon data are reported to confirm the mode energies, linewidths, or hybridization gaps in the 1-5 meV window. This mapping is load-bearing for the claim that the anomaly originates from these specific modes rather than alternatives such as disorder-induced two-level systems or anharmonic effects.

    Authors: We agree that inelastic neutron scattering or X-ray diffuse scattering would provide valuable direct confirmation of the mode energies, linewidths, and hybridization gaps. Such measurements are not reported because they were outside the scope of the present experimental campaign, which focused on thermodynamic and transport properties across multiple NCL compounds. Our attribution rests on: (i) DFT phonon calculations that consistently predict low-energy optical modes arising from the chimney-ladder sublattice in several compounds, (ii) AIMD simulations that incorporate anharmonicity and demonstrate avoided crossings with acoustic branches, and (iii) the systematic correlation between these simulated features and the experimentally observed boson-peak-like anomaly plus transport anomalies. We explicitly consider alternatives in the manuscript: the ordered crystalline structure and absence of very-low-T glassy thermal conductivity argue against disorder-induced two-level systems, while AIMD already accounts for anharmonic broadening. We will revise the simulation and discussion sections to add a dedicated paragraph explicitly stating the indirect nature of the mapping, the supporting multi-compound correlations, and the limitations relative to direct spectroscopy, thereby making the evidential basis more transparent. revision: partial

Circularity Check

0 steps flagged

No circularity: experimental heat-capacity anomaly is interpreted via independent DFT/AIMD phonon calculations without reduction to fitted inputs or self-citation chains.

full rationale

The paper reports measured C_p(T) deviating from Debye, then performs separate DFT phonon dispersions and AIMD to identify low-energy optical branches and hybridization; the attribution is an interpretive mapping, not a self-definitional or fitted-prediction loop. No equations are shown that force the anomaly from the same parameters used to fit it, and no load-bearing self-citations or ansatzes are invoked in the provided text. The qualitative scattering framework is presented as explanatory rather than predictive by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract; the claim rests on the domain assumption that deviations from the Debye model indicate glassy behavior and on the interpretation of simulation results as causal.

axioms (1)
  • domain assumption Debye model accurately describes low-temperature heat capacity of ideal crystals
    Invoked to identify the observed deviation as an anomaly.

pith-pipeline@v0.9.0 · 5880 in / 1181 out tokens · 34999 ms · 2026-05-25T08:47:33.636098+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. A flat-band perspective on the boson peak in amorphous solids

    cond-mat.soft 2025-09 unverdicted novelty 5.0

    The boson peak arises from accumulation of vibrational spectral weight in a narrow frequency window that is only weakly dependent on wavevector, manifesting as a flat band in the dynamical structure factor rather than...

Reference graph

Works this paper leans on

84 extracted references · 84 canonical work pages · cited by 1 Pith paper

  1. [1]

    Kittel and P

    C. Kittel and P. McEuen, Introduction to solid state physics (John Wiley & Sons, 2018)

  2. [2]

    M. A. Ramos, Low-Temperature Thermal and Vibrational Properties of Disordered Solids (World Scientific (Eu- rope), 2022)

  3. [3]

    D. A. Ackerman, D. Moy, R. C. Potter, A. C. Anderson, and W. N. Lawless, Phys. Rev. B 23, 3886 (1981)

  4. [4]

    Hegenbarth, Ferroelectrics 168, 25 (1995)

    E. Hegenbarth, Ferroelectrics 168, 25 (1995)

  5. [5]

    Ishii, Y

    Y. Ishii, Y. Ouchi, S. Kawaguchi, H. Ishibashi, Y. Kub- ota, and S. Mori, Phys. Rev. Mater. 3, 084414 (2019)

  6. [6]

    Ishii, A

    Y. Ishii, A. Yamamoto, N. Sato, Y. Nambu, S. Ohira- Kawamura, N. Murai, T. Mori, and S. Mori, arXiv e-prints , arXiv:2104.01969 (2021), arXiv:2104.01969 [cond-mat.mtrl-sci]

  7. [7]

    Kobayashi, T

    M. Kobayashi, T. Tomoyose, and M. Aniya, Physica B: Condensed Matter 219-220, 460 (1996), PHONONS 95

  8. [8]

    Etrillard, J

    J. Etrillard, J. C. Lasjaunias, K. Biljakovic, B. Toudic, and G. Coddens, Phys. Rev. Lett. 76, 2334 (1996)

  9. [9]

    Rem´ enyi, S

    G. Rem´ enyi, S. Sahling, K. Biljakovi´ c, D. Stareˇ sini´ c, J.- C. Lasjaunias, J. E. Lorenzo, P. Monceau, and A. Cano, Phys. Rev. Lett. 114, 195502 (2015)

  10. [10]

    Cano and A

    A. Cano and A. P. Levanyuk, Phys. Rev. Lett.93, 245902 (2004)

  11. [11]

    Cano and A

    A. Cano and A. P. Levanyuk, Phys. Rev. B 70, 212301 (2004)

  12. [12]

    Takasu, T

    Y. Takasu, T. Hasegawa, N. Ogita, M. Udagawa, M. A. Avila, K. Suekuni, and T. Takabatake, Phys. Rev. Lett. 100, 165503 (2008)

  13. [13]

    M. A. Avila, K. Suekuni, K. Umeo, H. Fukuoka, S. Ya- manaka, and T. Takabatake, Phys. Rev. B 74, 125109 (2006)

  14. [14]

    Takabatake, K

    T. Takabatake, K. Suekuni, T. Nakayama, and E. Kaneshita, Rev. Mod. Phys. 86, 669 (2014)

  15. [15]

    W. Qiu, L. Xi, P. Wei, X. Ke, J. Yang, and W. Zhang, Proceedings of the National Academy of Sciences 111, 15031 (2014)

  16. [16]

    Akhbarifar, W

    S. Akhbarifar, W. Lutze, N. A. Mecholsky, and I. L. Pegg, Materials Letters 275, 128153 (2020)

  17. [17]

    S. K. Bux, A. Zevalkink, O. Janka, D. Uhl, S. Kauzlarich, J. G. Snyder, and J.-P. Fleurial, J. Mater. Chem. A 2, 215 (2014)

  18. [18]

    Z. Liu, W. Zhang, W. Gao, and T. Mori, Energy Environ. Sci. 14, 3579 (2021)

  19. [19]

    M. A. Avila, K. Suekuni, K. Umeo, H. Fukuoka, S. Ya- manaka, and T. Takabatake, Applied Physics Letters92, 041901 (2008)

  20. [20]

    Bhattacharya, J

    A. Bhattacharya, J. Mater. Chem. C 7, 13986 (2019)

  21. [21]

    Chazallon, H

    B. Chazallon, H. Itoh, M. Koza, W. F. Kuhs, and H. Schober, Phys. Chem. Chem. Phys. 4, 4809 (2002)

  22. [22]

    Christensen, A

    M. Christensen, A. B. Abrahamsen, N. B. Christensen, F. Juranyi, N. H. Andersen, K. Lefmann, J. Andreasson, C. R. H. Bahl, and B. B. Iversen, Nature Materials 7, 811 (2008)

  23. [23]

    Delaire, J

    O. Delaire, J. Ma, K. Marty, A. F. May, M. A. McGuire, M.-H. Du, D. J. Singh, A. Podlesnyak, G. Ehlers, M. D. Lumsden, and B. C. Sales, Nature Materials 10, 614 (2011)

  24. [24]

    Lanigan-Atkins, S

    T. Lanigan-Atkins, S. Yang, J. L. Niedziela, D. Bansal, A. F. May, A. A. Puretzky, J. Y. Y. Lin, D. M. Pa- jerowski, T. Hong, S. Chi, G. Ehlers, and O. Delaire, Nature Communications 11, 4430 (2020)

  25. [25]

    C. W. Li, J. Hong, A. F. May, D. Bansal, S. Chi, T. Hong, G. Ehlers, and O. Delaire, Nature Physics 11, 1063 (2015)

  26. [26]

    J. S. Tse, D. D. Klug, J. Y. Zhao, W. Sturhahn, E. E. Alp, J. Baumert, C. Gutt, M. R. Johnson, and W. Press, Nature Materials 4, 917 (2005)

  27. [27]

    J. Ma, O. Delaire, A. F. May, C. E. Carlton, M. A. McGuire, L. H. VanBebber, D. L. Abernathy, G. Ehlers, T. Hong, A. Huq, W. Tian, V. M. Keppens, Y. Shao- 7 Horn, and B. C. Sales, Nature Nanotechnology 8, 445 (2013)

  28. [28]

    Ren, H.-X

    S. Ren, H.-X. Zong, X.-F. Tao, Y.-H. Sun, B.-A. Sun, D.-Z. Xue, X.-D. Ding, and W.-H. Wang, Nature Com- munications 12, 5755 (2021)

  29. [29]

    Moratalla, J

    M. Moratalla, J. F. Gebbia, M. A. Ramos, L. C. Pardo, S. Mukhopadhyay, S. Rudic, F. Fernandez-Alonso, F. J. Bermejo, and J. L. Tamarit, Phys. Rev. B 99, 024301 (2019)

  30. [30]

    J. Wu, Y. Lin, M. Shu, Y. Liu, Y. Ma, G. Lin, C. Zhang, P. Jiao, F. Zhu, Y. Wu, R. A. Ewings, H. C. Walker, G. Deng, S. Chi, S. Jiang, M. Baggioli, M. Jin, H. Wang, W. Xie, T.-R. Wei, J. Yang, X. Shi, and J. Ma, Nature Communications 15, 6248 (2024)

  31. [31]

    A. I. Krivchikov, A. N. Yushchenko, V. G. Manzhelii, O. A. Korolyuk, F. J. Bermejo, R. Fern´ andez-Perea, C. Cabrillo, and M. A. Gonz´ alez, Phys. Rev. B74, 060201 (2006)

  32. [32]

    M. A. Ramos, S. Vieira, F. J. Bermejo, J. Dawidowski, H. E. Fischer, H. Schober, M. A. Gonz´ alez, C. K. Loong, and D. L. Price, Phys. Rev. Lett. 78, 82 (1997)

  33. [33]

    Tal´ on, M

    C. Tal´ on, M. A. Ramos, S. Vieira, G. J. Cuello, F. J. Bermejo, A. Criado, M. L. Senent, S. M. Bennington, H. E. Fischer, and H. Schober, Phys. Rev. B 58, 745 (1998)

  34. [34]

    Tal´ on, M

    C. Tal´ on, M. A. Ramos, and S. Vieira, Phys. Rev. B66, 012201 (2002)

  35. [35]

    G. A. Vdovichenko, A. I. Krivchikov, O. A. Korolyuk, J. L. Tamarit, L. C. Pardo, M. Rovira-Esteva, F. J. Bermejo, M. Hassaine, and M. A. Ramos, The Journal of Chemical Physics 143, 084510 (2015)

  36. [36]

    Vispa, M

    A. Vispa, M. Romanini, M. A. Ramos, L. C. Pardo, F. J. Bermejo, M. Hassaine, A. I. Krivchikov, J. W. Taylor, and J. L. Tamarit, Phys. Rev. Lett. 118, 105701 (2017)

  37. [37]

    Romanini, P

    M. Romanini, P. Negrier, J. L. Tamarit, S. Capaccioli, M. Barrio, L. C. Pardo, and D. Mondieig, Phys. Rev. B 85, 134201 (2012)

  38. [38]

    Je˙ zowski, M

    A. Je˙ zowski, M. A. Strzhemechny, A. I. Krivchikov, N. A. Davydova, D. Szewczyk, S. G. Stepanian, L. M. Buravt- seva, and O. O. Romantsova, Phys. Rev. B 97, 201201 (2018)

  39. [39]

    Szewczyk, M

    D. Szewczyk, M. Moratalla, G. Chajewski, J. F. Gebbia, A. Je˙ zowski, A. I. Krivchikov, M. Barrio, J. L. Tamarit, and M. A. Ramos, Phys. Rev. B 110, 174204 (2024)

  40. [40]

    Z. Liu, R. Luo, M. Hao, C. Chai, J. Lu, Y. Gao, S. Jin, and X. Chen, Phys. Rev. Lett. 133, 216101 (2024)

  41. [41]

    A. I. Krivchikov, A. Je˙ zowski, D. Szewczyk, O. A. Ko- rolyuk, O. O. Romantsova, L. M. Buravtseva, C. Cazorla, and J. L. Tamarit, The Journal of Physical Chemistry Letters 13, 5061 (2022)

  42. [42]

    Baggioli and A

    M. Baggioli and A. Zaccone, International Journal of Modern Physics B 35, 2130002 (2021)

  43. [43]

    J. M. Schliesser and B. F. Woodfield, Journal of Physics: Condensed Matter 27, 285402 (2015)

  44. [44]

    Baggioli and A

    M. Baggioli and A. Zaccone, Journal of Physics: Materi- als 3, 015004 (2019)

  45. [45]

    Hu and H

    Y.-C. Hu and H. Tanaka, Nature Physics 18, 669 (2022)

  46. [46]

    Hu and H

    Y.-C. Hu and H. Tanaka, Phys. Rev. Res. 5, 023055 (2023)

  47. [47]

    Tømterud, S

    M. Tømterud, S. D. Eder, C. B¨ uchner, L. Wondraczek, I. Simonsen, W. Schirmacher, J. R. Manson, and B. Holst, Nature Physics 19, 1910 (2023)

  48. [48]

    Jiang, Z

    C. Jiang, Z. Zheng, Y. Chen, M. Baggioli, and J. Zhang, Phys. Rev. Lett. 133, 188302 (2024)

  49. [49]

    Jiang and M

    C. Jiang and M. Baggioli, Journal of Physics: Condensed Matter 36, 505101 (2024)

  50. [50]

    Howson and B

    M. Howson and B. Gallagher, Physics Reports 170, 265 (1988)

  51. [51]

    V. V. Pryadun, D. Louzguine-Luzgin, L. V. Shvanskaya, and A. N. Vasiliev, JETP letters 101, 465 (2015)

  52. [52]

    Y. K. Kuo, K. M. Sivakumar, C. A. Su, C. N. Ku, S. T. Lin, A. B. Kaiser, J. B. Qiang, Q. Wang, and C. Dong, Phys. Rev. B 74, 014208 (2006)

  53. [53]

    Schwomma, H

    O. Schwomma, H. Nowotny, and A. Wittmann, Monat- shefte fur Chemie und verwandte Teile anderer Wis- senschaften 94, 681 (1963), publisher: Springer

  54. [54]

    G. Lu, S. Lee, J. Lin, L. You, J. Sun, and J. T. Schmidt, Journal of Solid State Chemistry 164, 210 (2002)

  55. [55]

    H. Han, L. Zhang, X. Zhu, H. Du, M. Ge, L. Ling, L. Pi, C. Zhang, and Y. Zhang, Scientific Reports 6, 39338 (2016)

  56. [56]

    Q. D. Gibson, D. Evtushinsky, A. N. Yaresko, V. B. Zabolotnyy, M. N. Ali, M. K. Fuccillo, J. Van den Brink, B. Buchner, R. J. Cava, and S. V. Borisenko, Scientific Reports 4, 5168 (2014)

  57. [57]

    Kawasoko, T

    H. Kawasoko, T. Takayama, and H. Takagi, Applied Physics Express 7, 115801 (2014)

  58. [58]

    X. Chen, A. Weathers, J. Carrete, S. Mukhopadhyay, O. Delaire, D. A. Stewart, N. Mingo, S. N. Girard, J. Ma, D. L. Abernathy, J. Yan, R. Sheshka, D. P. Sellan, F. Meng, S. Jin, J. Zhou, and L. Shi, Nature Communi- cations 6, 6723 (2015)

  59. [59]

    Buchenau, M

    U. Buchenau, M. Prager, N. N¨ ucker, A. J. Dianoux, N. Ahmad, and W. A. Phillips, Phys. Rev. B 34, 5665 (1986)

  60. [60]

    G. K. White and S. J. Collocott, Journal of Physical and Chemical Reference Data 13, 1251 (1984)

  61. [61]

    Miyazaki, M

    Y. Miyazaki, M. Nakano, A. I. Krivchikov, O. A. Ko- royuk, J. F. Gebbia, C. Cazorla, and J. L. Tamarit, The Journal of Physical Chemistry Letters 12, 2112 (2021)

  62. [62]

    D. J. Poutcharovsky, K. Yvon, and E. Parth´ e, Journal of the Less Common Metals 40, 139 (1975)

  63. [63]

    Zhang, T

    Z. Zhang, T. Wang, H. Jiang, X. Xu, J. Wang, Z. Wang, F. Liu, Y. Yu, Y. Zhang, P. Wang, P. Gao, B. Shen, and X. Wang, Nature Communications 15, 10436 (2024)

  64. [64]

    R. C. Zeller and R. O. Pohl, Phys. Rev. B 4, 2029 (1971)

  65. [65]

    J. F. Gebbia, M. A. Ramos, D. Szewczyk, A. Jezowski, A. I. Krivchikov, Y. V. Horbatenko, T. Guidi, F. J. Bermejo, and J. L. Tamarit, Phys. Rev. Lett.119, 215506 (2017)

  66. [66]

    Krivchikov, G

    A. Krivchikov, G. Vdovichenko, O. Korolyuk, F. Bermejo, L. Pardo, J. Tamarit, A. Jezowski, and D. Szewczyk, Journal of Non-Crystalline Solids 407, 141 (2015), 7th IDMRCS: Relaxation in Complex Systems

  67. [67]

    Peierls, Quantum Theory of Solids , International se- ries of monographs on physics (Clarendon Press, 1955)

    R. Peierls, Quantum Theory of Solids , International se- ries of monographs on physics (Clarendon Press, 1955)

  68. [68]

    D. G. Cahill and R. O. Pohl, Annual Review of Physical Chemistry 39, 93 (1988)

  69. [69]

    Das Sarma and Y.-T

    S. Das Sarma and Y.-T. Tu, Phys. Rev. B 109, 235118 (2024)

  70. [70]

    Ochoa and R

    H. Ochoa and R. M. Fernandes, Phys. Rev. B 108, 075168 (2023)

  71. [71]

    Caprara, C

    S. Caprara, C. D. Castro, G. Mirarchi, G. Seibold, and M. Grilli, Communications Physics 5, 10 (2022)

  72. [72]

    Behnia, Annalen der Physik 534, 2100588 (2022)

    K. Behnia, Annalen der Physik 534, 2100588 (2022)

  73. [73]

    Mizutani, Introduction to the Electron Theory of Met- als (Cambridge University Press, 2001)

    U. Mizutani, Introduction to the Electron Theory of Met- als (Cambridge University Press, 2001). 8

  74. [74]

    J. Zhu, X. Shen, J. Ding, and J. Ma, Revealing the phonon properties for thermoelectric materials by neu- tron scattering (2024)

  75. [75]

    B. Wu, V. Barrena, F. Mompe´ an, M. Garc´ ıa-Hern´ andez, H. Suderow, and I. Guillam´ on, Phys. Rev. B101, 205123 (2020)

  76. [76]

    J. Kim, E. Altman, and S. Chatterjee, Proceedings of the National Academy of Sciences 121, e2405720121 (2024)

  77. [77]

    P. M. Chaikin and T. C. Lubensky, Principles of con- densed matter physics , Vol. 10 (Cambridge university press Cambridge, 1995)

  78. [78]

    Coleman, Introduction to Many-Body Physics (Cam- bridge University Press, 2015)

    P. Coleman, Introduction to Many-Body Physics (Cam- bridge University Press, 2015)

  79. [79]

    Shiomi and E

    Y. Shiomi and E. Saitoh, AIP Advances 7, 035011 (2017)

  80. [80]

    Petˇ r´ ıˇ cek, L

    V. Petˇ r´ ıˇ cek, L. Palatinus, J. Pl´ aˇ sil, and M. Duˇ sek, Zeitschrift fur Kristallographie - Crystalline Materials 238, 271 (2023)

Showing first 80 references.