- Open Access
Lattice thermal transport from phonon spectra beyond perturbation theory
Phys. Rev. B 114, 204303 – Published 9 October, 2026
DOI: https://doi.org/10.1103/bjh1-xb7z
Abstract
We develop a molecular dynamics framework to compute the mode-resolved phonon spectral density from classical correlations of an annihilation-like phonon variable. For harmonic oscillators, classical molecular dynamics exactly reproduces the corresponding quantum Kubo-transformed correlator, providing the basis for extension to anharmonic systems. Using PbTe as a benchmark and as a strongly anharmonic test case, we show that the method captures both quasiparticle and non-Lorentzian spectra beyond perturbative quasiparticle theory, while yielding thermal conductivity in good agreement with experiment. This framework provides a classical molecular dynamics route to mode-resolved phonon spectral densities for spectral Wigner heat transport in strongly anharmonic solids above their Debye temperatures.
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References (62)
- R. Peierls, Zur kinetischen Theorie der Wärmeleitung in Kristallen, Ann. Phys. 395, 1055 (1929).
- R. J. Hardy, Energy-flux operator for a lattice, Phys. Rev. 132, 168 (1963).
- D. A. Broido, M. Malorny, G. Birner, N. Mingo, and D. A. Stewart, Intrinsic lattice thermal conductivity of semiconductors from first principles, Appl. Phys. Lett. 91, 231922 (2007).
- G. Fugallo, M. Lazzeri, L. Paulatto, and F. Mauri, Ab initio variational approach for evaluating lattice thermal conductivity, Phys. Rev. B 88, 045430 (2013).
- G. Barbalinardo, Z. Chen, N. W. Lundgren, and D. Donadio, Efficient anharmonic lattice dynamics calculations of thermal transport in crystalline and disordered solids, J. Appl. Phys. 128, 135104 (2020).
- D. G. Cahill, P. V. Braun, G. Chen, D. R. Clarke, S. Fan, K. E. Goodson, P. Keblinski, W. P. King, G. D. Mahan, A. Majumdar, H. J. Maris, S. R. Phillpot, E. Pop, and L. Shi, Nanoscale thermal transport. II. 2003–2012, Appl. Phys. Rev. 1, 011305 (2014).
- L. Lindsay, C. Hua, X. Ruan, and S. Lee, Survey of ab initio phonon thermal transport, Mater. Today Phys. 7, 106 (2018).
- A. Togo, First-principles phonon calculations with Phonopy and Phono3py, J. Phys. Soc. Jpn. 92, 012001 (2023).
- A. Togo, L. Chaput, T. Tadano, and I. Tanaka, Implementation strategies in Phonopy and Phono3py, J. Phys.: Condens. Matter 35, 353001 (2023).
- M. Simoncelli, N. Marzari, and F. Mauri, Unified theory of thermal transport in crystals and glasses, Nat. Phys. 15, 809 (2019).
- M. Simoncelli, N. Marzari, and F. Mauri, Wigner formulation of thermal transport in solids, Phys. Rev. X 12, 041011 (2022).
- L. Isaeva, G. Barbalinardo, D. Donadio, and S. Baroni, Modeling heat transport in crystals and glasses from a unified lattice-dynamical approach, Nat. Commun. 10, 3853 (2019).
- A. Fiorentino and S. Baroni, From Green-Kubo to the full Boltzmann kinetic approach to heat transport in crystals and glasses, Phys. Rev. B 107, 054311 (2023).
- P. B. Allen and J. L. Feldman, Thermal conductivity of glasses: Theory and application to amorphous Si, Phys. Rev. Lett. 62, 645 (1989).
- Đ. Dangić, O. Hellman, S. Fahy, and I. Savić, The origin of the lattice thermal conductivity enhancement at the ferroelectric phase transition in GeTe, npj Comput. Mater. 7, 57 (2021).
- Y. Wang, M. Zacharias, X. Zhang, N. Pant, J. Even, P. F. P. Poudeu, and E. Kioupakis, Efficient first-principles framework for overdamped phonon dynamics and anharmonic electron-phonon coupling in superionic materials, Phys. Rev. Lett. 135, 056402 (2025).
- Đ. Dangić, G. Caldarelli, R. Bianco, I. Savić, and I. Errea, Lattice thermal conductivity in the anharmonic overdamped regime, Phys. Rev. B 111, 104314 (2025).
- G. Caldarelli, M. Simoncelli, N. Marzari, F. Mauri, and L. Benfatto, Many-body Green's function approach to lattice thermal transport, Phys. Rev. B 106, 024312 (2022).
- L. Paulatto, I. Errea, M. Calandra, and F. Mauri, First-principles calculations of phonon frequencies, lifetimes, and spectral functions from weak to strong anharmonicity: The example of palladium hydrides, Phys. Rev. B 91, 054304 (2015).
- T. Tadano and W. A. Saidi, First-principles phonon quasiparticle theory applied to a strongly anharmonic halide perovskite, Phys. Rev. Lett. 129, 185901 (2022).
- E. Xiao and C. A. Marianetti, Anharmonic phonon behavior via irreducible derivatives: Self-consistent perturbation theory and molecular dynamics, Phys. Rev. B 107, 094303 (2023).
- L. Monacelli, Analyzing the anharmonic phonon spectrum: Self-consistent approximation and temperature-dependent effective potential methods, Phys. Rev. B 112, 014109 (2025).
- Y. Xia, Lattice thermal transport beyond the quasiparticle approximation: Nontrivial spectral competition between three- and four-phonon interactions, Phys. Rev. B 112, L241201 (2025).
- A. J. C. Ladd, B. Moran, and W. G. Hoover, Lattice thermal conductivity: A comparison of molecular dynamics and anharmonic lattice dynamics, Phys. Rev. B 34, 5058 (1986).
- A. J. H. McGaughey and J. M. Larkin, Predicting phonon properties from equilibrium molecular dynamics simulations, Annu. Rev. Heat Transfer 17, 49 (2014).
- R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn. 12, 570 (1957).
- I. R. Craig and D. E. Manolopoulos, Quantum statistics and classical mechanics: Real time correlation functions from ring polymer molecular dynamics, J. Chem. Phys. 121, 3368 (2004).
- T. Sun, X. Shen, and P. B. Allen, Phonon quasiparticles and anharmonic perturbation theory tested by molecular dynamics on a model system, Phys. Rev. B 82, 224304 (2010).
- W. Lv and A. Henry, Direct calculation of modal contributions to thermal conductivity via Green-Kubo modal analysis, New J. Phys. 18, 013028 (2016).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/bjh1-xb7z for derivations, computational details, validation tests, and convergence studies.
- J. Cao and G. A. Voth, The formulation of quantum statistical mechanics based on the Feynman path centroid density. II. Dynamical properties, J. Chem. Phys. 100, 5106 (1994).
- D. Kondratyeva, A study of anharmonic phonons and thermal conductivity, MChem thesis, University of Oxford, 2025.
- A. H. Larsen, J. J. Mortensen, J. Blomqvist, I. E. Castelli, R. Christensen, M. Dułak, J. Friis, M. N. Groves, B. Hammer, C. Hargus, E. D. Hermes, P. C. Jennings, P. Bjerre Jensen, J. Kermode, J. R. Kitchin, E. L. Kolsbjerg, J. Kubal, K. Kaasbjerg, S. Lysgaard, J. Bergmann Maronsson, et al., The atomic simulation environment—A Python library for working with atoms, J. Phys.: Condens. Matter 29, 273002 (2017).
- A. Togo and I. Tanaka, First principles phonon calculations in materials science, Scr. Mater. 108, 1 (2015).
- A. Togo, L. Chaput, and I. Tanaka, Distributions of phonon lifetimes in Brillouin zones, Phys. Rev. B 91, 094306 (2015).
- 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, Giant anharmonic phonon scattering in PbTe, Nat. Mater. 10, 614 (2011).
- G. A. S. Ribeiro, L. Paulatto, R. Bianco, I. Errea, F. Mauri, and M. Calandra, Strong anharmonicity in the phonon spectra of PbTe and SnTe from first principles, Phys. Rev. B 97, 014306 (2018).
- T. Shiga, J. Shiomi, J. Ma, O. Delaire, T. Radzynski, A. Lusakowski, K. Esfarjani, and G. Chen, Microscopic mechanism of low thermal conductivity in lead telluride, Phys. Rev. B 85, 155203 (2012).
- W. Cochran, R. A. Cowley, G. Dolling, and M. M. Elcombe, The crystal dynamics of lead telluride, Proc. R. Soc. London A 293, 433 (1966).
- Y. Xia, Revisiting lattice thermal transport in PbTe: The crucial role of quartic anharmonicity, Appl. Phys. Lett. 113, 073901 (2018).
- V. I. Fedorov and V. I. Machuev, Thermal conductivity of PbTe, SnTe and GeTe in the solid and liquid phases, Sov. Phys. Solid State 11, 1116 (1969).
- Z. Fan, Z. Zeng, C. Zhang, Y. Wang, K. Song, H. Dong, Y. Chen, and T. Ala-Nissila, Neuroevolution machine learning potentials: Combining high accuracy and low cost in atomistic simulations and application to heat transport, Phys. Rev. B 104, 104309 (2021).
- Z. Zeng, Z. Fan, M. Simoncelli, C. Chen, T. Liang, Y. Chen, G. Thornton, and B. Cheng, Lattice distortion leads to glassy thermal transport in crystalline , Proc. Natl. Acad. Sci. USA 122, e2415664122 (2025).
- T. Feng and X. Ruan, Quantum mechanical prediction of four-phonon scattering rates and reduced thermal conductivity of solids, Phys. Rev. B 93, 045202 (2016).
- T. Feng, L. Lindsay, and X. Ruan, Four-phonon scattering significantly reduces intrinsic thermal conductivity of solids, Phys. Rev. B 96, 161201(R) (2017).
- O. Hellman, I. A. Abrikosov, and S. I. Simak, Lattice dynamics of anharmonic solids from first principles, Phys. Rev. B 84, 180301(R) (2011).
- O. Hellman, P. Steneteg, I. A. Abrikosov, and S. I. Simak, Temperature dependent effective potential method for accurate free energy calculations of solids, Phys. Rev. B 87, 104111 (2013).
- A. Castellano, J. P. Alvarinhas Batista, and M. J. Verstraete, Fluctuation-dissipation and virtual processes in interacting phonon systems, arXiv:2502.03362.
- E. Di Lucente, N. Marzari, and M. Simoncelli, Phonon collisional broadening and heat transport beyond the Boltzmann equation, arXiv:2603.16753.
- T. Tadano and S. Tsuneyuki, Self-consistent phonon calculations of lattice dynamical properties in cubic with first-principles anharmonic force constants, Phys. Rev. B 92, 054301 (2015).
- Y. Xia, First-principles theory of five- and six-phonon scattering, Phys. Rev. B 112, 205204 (2025).
- B. L. Huang, A. J. H. McGaughey, and M. Kaviany, Thermal conductivity of metal-organic framework 5 (MOF-5): Part I. Molecular dynamics simulations, Int. J. Heat Mass Transfer 50, 393 (2007).
- Y. Wang, Y. J. Hu, S. A. Firdosy, K. E. Star, J. P. Fleurial, V. A. Ravi, L. Q. Chen, S. L. Shang, and Z. K. Liu, First-principles calculations of lattice dynamics and thermodynamic properties for , J. Appl. Phys. 123, 045102 (2018).
- M. Simoncelli, D. Fournier, M. Marangolo, E. Balan, K. Béneut, B. Baptiste, B. Doisneau, N. Marzari, and F. Mauri, Temperature-invariant crystal–glass heat conduction: From meteorites to refractories, Proc. Natl. Acad. Sci. USA 122, e2422763122 (2025).
- K. Iwanowski, G. Csányi, and M. Simoncelli, Bond-network entropy governs heat transport in coordination-disordered solids, Phys. Rev. X 15, 041041 (2025).
- S. Thébaud, L. Lindsay, and T. Berlijn, Breaking Rayleigh's law with spatially correlated disorder to control phonon transport, Phys. Rev. Lett. 131, 026301 (2023).
- A. Fiorentino, P. Pegolo, S. Baroni, and D. Donadio, Effects of colored disorder on the heat conductivity of SiGe alloys from first principles, Phys. Rev. B 111, 134205 (2025).
- A. Pazhedath, L. Bastonero, N. Marzari, and M. Simoncelli, First-principles characterization of thermal conductivity in -based alloys, Phys. Rev. Appl. 22, 024064 (2024).
- M. Kotiuga, S. Halilov, B. Kozinsky, M. Fornari, N. Marzari, and G. Pizzi, Microscopic picture of paraelectric perovskites from structural prototypes, Phys. Rev. Res. 4, L012042 (2022).
- Z. Fan, Y. Wang, P. Ying, K. Song, J. Wang, Y. Wang, Z. Zeng, K. Xu, E. Lindgren, J. M. Rahm, A. J. Gabourie, J. Liu, H. Dong, J. Wu, Y. Chen, Z. Zhong, J. Sun, P. Erhart, Y. Su, and T. Ala-Nissila, GPUMD: A package for constructing accurate machine-learned potentials and performing highly efficient atomistic simulations, J. Chem. Phys. 157, 114801 (2022).
- Z. Fan, Inputs and outputs of nep in GPUMD [Dataset], Zenodo, 2021, Version v2, https://doi.org/10.5281/zenodo.5519311.
- Z. Zeng, heat conductivity [Dataset], GitHub, 2025, https://github.com/ZengZezhu/Cs3Bi2I6Cl3_heat_conductivity.