Convergent thermal conductivity in strained monolayer graphene

The strain dependence of thermal conductivity (κ) in monolayer graphene, with reports of enhancement, suppression, or even divergence, has been highly controversial. To address this open question, we have systematically investigated the effects of tensile strain on the κ of graphene using the exact solution of the Peierls-Boltzmann transport equation based on the first-principles interatomic force constants combined with machine learning assisted molecular dynamics simulations. In contrast to previous studies, we find that the κ in the strained graphene is convergent after considering four-phonon scattering, which is dominant for the long-wavelength flexural phonons because of its much weaker frequency dependence (${\tau }_4^{-1}\propto {\omega }^{\beta }$ with β < 2) compared to the three-phonon scattering case (${\tau }_3^{-1}\propto {\omega }^{\beta }$ with β > 2). Furthermore, κ exhibits nonmonotonic variations with increasing strain up to 8% due to the competition between phonon lifetime, group velocity, and heat capacity of acoustic phonons. Our results deepen the fundamental understanding of thermal transport in strained graphene and offer insights for tuning the thermal properties of two-dimensional materials through strain engineering.

Figure 1

Convergence of κ contributed by ZA phonons with respect to the size of q-point mesh ($N$×$N$×1) for graphene with 2% (a), 4% (b), and 6% (c) isotropic tensile strain under RTA at 300 K, respectively. (d), (e), (f) are the same as (a), (b), (c), respectively, but for 1000 K.

Figure 2

Three-phonon and four-phonon RTA scattering rates of ZA phonons in graphene with varying tensile strain (2%, 4%, and 6%) at 300 and 1000 K, respectively.

Figure 3

Convergence of κ of graphene as a function of q-point mesh for 6% isotropic tensile strain under full iterative approach at 1000 K (a), in comparison to that under RTA and 3ph iteration + 4ph RTA. (b) The same as (a), but for the κ normalized by that at $N$ = 80. (c) The total κ and contribution from different acoustic phonon branches as a function of tensile strain under full iterative approach at 1000 K, along with the MD simulation results with a standard deviation. (d) The relative contribution of κ by ZA phonons under full iterative approach at 1000 K.

Figure 4

Strain-dependent group velocity (a), heat capacity (b), phonon lifetime of ZA (c), and that of TA (d) and LA (e) phonons as a function of frequency.

Figure 5

Three-phonon and four-phonon RTA scattering rates of ZA phonons in graphene with a tensile strain ε = 8% at (a) 300 and (b) 1000 K, respectively.

Figure 6

Three-phonon scattering rates of ZA modes contributed by different scattering channels at 1000 K in graphene with ε = 0 (a) and ε = 6% (b), respectively.

Figure 7

Four-phonon scattering rates of ZA modes contributed by different scattering channels at 1000 K in graphene with ε = 0 (a) and ε = 6% (b), respectively.

Figure 8

The calculated acoustic phonon dispersion around Γ point in the direction from Γ to $M$ for graphene with varying tensile strains.

Figure 9

Convergence of κ of unstrained graphene as a function of q-point mesh under full iterative approach at 300 K.

Figure 10

The four-phonon scattering rates contributed by the normal and umklapp processes normalized by the total four-phonon scattering rates. Unstrained graphene and four tensile strains (2%, 4%, 6%, and 8%) are considered here.

Figure 11

Running thermal conductivity as a function of time in the nonequilibrium production stage of the HNEMD simulation for graphene with a tensile strain of 2%, 4%, and 6% at 1000 K, respectively. The thermal conductivity is well converged.