Mechanism by which grain boundaries suppress thermal-conductivity divergence in strained two-dimensional momentum-conserving systems, and the asymptotic behavior of the thermal conductivity of strained pristine graphene

In suspended graphene under substantial tensile strain, classical molecular dynamics shows a thermal conductivity that grows without apparent bound with system size and simulation time, a signature of anomalous (non-Fourier) heat transport expected for two-dimensional momentum-conserving systems. Zhou et al. (2025) demonstrated, in million-atom simulations with a near-first-principles neuroevolution potential (NEP, a machine-learned interatomic potential trained on first-principles data), that introducing grain boundaries into graphene restores a finite thermal conductivity even under the same strong tensile strain, but left the microscopic mechanism unexplained and left the asymptotic divergence of strained pristine graphene unconfirmed. The open problem is to identify the dominant scattering processes, length and time scales, and the interplay with asymmetric interatomic interactions and near-integrable dynamics by which grain boundaries suppress the divergence and restore Fourier-like heat conduction in strained two-dimensional momentum-conserving systems, and to definitively establish whether the thermal conductivity of strained pristine graphene diverges in the infinite-size, infinite-time limit.

Background

Whether Fourier's empirical law of heat conduction holds in low-dimensional systems with momentum-conserving dynamics is a long-standing open problem of nonequilibrium statistical physics (A. Dhar, Adv. Phys. 57, 457 (2008); G. Benenti, D. Donadio, S. Lepri, R. Livi, Riv. Nuovo Cimento 46, 105 (2023)). In equilibrium molecular dynamics (MD), thermal conductivity $\kappa$ is computed from the Green-Kubo formula, which integrates the equilibrium heat-current autocorrelation function $C(t)$; the 'running' conductivity $\kappa(t)$ is the integral up to correlation time $t$. In one- and two-dimensional systems whose microscopic dynamics conserve total momentum, hydrodynamic arguments (reasoning from the long-wavelength, fluid-like collective modes) predict a long-time tail $C(t)\sim t^{-d/2}$ in $d$ dimensions, so in 2D the integral grows logarithmically and $\kappa$ is expected to diverge with system size unless some scattering mechanism cuts off the tail. Consistent with this, classical MD of suspended graphene found a finite, size-convergent $\kappa$ without strain but a logarithmically divergent $\kappa$ when uniaxial tensile strain exceeds about 2% (L. F. C. Pereira and D. Donadio, Phys. Rev. B 87, 125424 (2013)); the physical picture is that tensile strain suppresses the out-of-plane flexural (ZA) phonons — the bending modes whose acoustic dispersion is quadratic in unstrained membranes — and thereby weakens the scattering that would otherwise regularize transport. Related first-principles work is contested: M. Xu (Phys. Scr. 98, 115951 (2023)) argued that an anomalous size effect of $\kappa$ is generic in two-dimensional dielectrics, while Z. Han and X. Ruan (Phys. Rev. B 108, L121412 (2023)) found from an exact solution of the phonon Boltzmann transport equation (BTE, the kinetic equation for phonon populations) including four-phonon (higher-order anharmonic) scattering that the room-temperature $\kappa$ of unstrained monolayer graphene converges to about 1300 W/(m K). In one-dimensional momentum-conserving lattices it is known that asymmetric interatomic interactions (potentials that are not even functions of the relative displacement of neighboring atoms) can restore normal heat conduction (Y. Zhong, Y. Zhang, J. Wang, H. Zhao, Phys. Rev. E 85, 060102 (2012)), and nearly integrable dynamics (dynamics close to an integrable one, in which so many quantities are exactly conserved that heat transport cannot fully relax) is also implicated in anomalous crossovers, so both symmetry breaking of the interactions and proximity to integrability are recognized ingredients controlling Fourier behavior. Polycrystalline graphene, as grown by chemical vapor deposition, contains grain boundaries — interfaces between crystalline domains of different lattice orientation — which act as scattering planes for phonons and reduce $\kappa$ in a grain-size-dependent way (Z. Fan et al., Nano Lett. 17, 5919 (2017); the in-plane versus flexural decomposition of $\kappa$ is given in Z. Fan et al., Phys. Rev. B 95, 144309 (2017)). Zhou et al. (J. Appl. Phys. 137, 014305 (2025)) used the neuroevolution potential (NEP, a machine-learned interatomic potential trained on first-principles forces and energies) as implemented in the open-source GPUMD package (a molecular-dynamics code running on graphics processing units) to simulate over 1.4 million atoms. They found that at 300 K under 40 GPa biaxial tensile stress (about 5% strain) the running $\kappa$ of pristine graphene shows no sign of convergence up to a correlation time of 5 ns, consistent with divergence, whereas polycrystalline graphene with a grain size of about 14 nm under the same conditions has a finite, convergent $\kappa$. They state explicitly that these results do not definitely confirm divergence at infinite correlation time, and that further investigations are required to understand the role of grain boundaries and the underlying mechanisms that could lead to Fourier's heat conduction law in low-dimensional momentum-conserving systems.

Problem Statement

Elucidate the microscopic mechanism by which grain boundaries suppress the divergence of the thermal conductivity and restore Fourier-like finite heat conduction in strained, momentum-conserving two-dimensional systems, using polycrystalline graphene under strong tensile strain as the demonstrated instance and stating explicitly whether the mechanism identified for graphene is expected to hold for other strained two-dimensional momentum-conserving systems. The joint target is to identify the dominant scattering processes and the relevant length and time scales through which grain boundaries cut off the long-time hydrodynamic tail of the heat-current autocorrelation; to establish how this suppression interplays with asymmetric interatomic interactions and the near-integrable dynamics of the strained membrane; and, as the complementary half of the same question, to definitively establish the asymptotic (infinite-size, infinite-time) behavior of the thermal conductivity of strained pristine graphene — divergent (with growth law) or convergent — resolving the extrapolation-limited ambiguity left by existing molecular-dynamics data.

References

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