The properties of misoriented bilayer graphene have recently received renewed interest after the discovery of superconductivity at very small rotation angles. Compared to the electronic properties, the effect of misorientation on the phonon and thermal properties has received less attention. For the larger misorientation angles, the in-plane thermal conductivity depends not on the angle, but on the commensurate lattice constant, and the thermal conductivity decreases approximately linearly as the commensurate lattice constant increases . This trend is qualitatively consistent with the hypothesis that the zone folding gives rise to an increase in Umklapp scattering that reduces the low-energy phonon lifetimes and thus the thermal conductivity. However, our recent calculations show that as the misorientation angle falls below 13.2o, this trend reverses itself, and the thermal conductivity starts increasing back towards the value of the unrotated structure. For angles below 13.2o, the thermal conductivity initially increases rapidly as the angle decreases from 13.2o to 7.3o, even though the commensurate lattice constant is monotonically increasing. As the angle continues to decrease down to 1.9o, which is the smallest angle simulated, the thermal conductivity gradually returns to its unrotated value.
For small angles with minimal commensurate unit cells, the commensurate lattice constants monotonically increase as the angles decrease, so that it is not clear what determines the functional dependence of the thermal conductivity in the small angle regime. Is it the misorientation angle or the commensurate lattice constant? To answer this question, we investigated two very different angles, 3.9o and 20.3o. Both of these angles which have exactly the same commensurate lattice constant of 3.6 nm. The thermal conductivities of the two structures are identical indicating that the functional dependence of the thermal conductivity in the low angle regime continues to be on the lattice constant rather than on the misorientation angle.
As the lattice constant increases, the reciprocal lattice constant decreases, so that Umklapp scattering should become more accessible to the low-energy, small-wavevector phonons that determine the thermal conductivity. All else being equal, the increased scattering should decrease the thermal conductivity. While this picture is consistent with the trends in the large angle regime, in the small angle regime (< 13o), this is the opposite of the trend that we observe. However, as the misorientation angle returns to zero degrees, the thermal conductivity must return to that of the AB aligned structure, and this is what we observe. In this talk, we will describe the thermal transport in the low angle regime, and we will present our analysis of the thermal transport that includes the average phonon velocities and density of modes, and we will also present a spectral decomposition of the lattice thermal conductivity determined from the force-velocity cross correlation function.
The investigation uses both nonequilibrium molecular dynamics (NEMD) and ab-initio density functional theory (DFT) combined with the phonon Boltzmann transport equation. For the NEMD direct calculations of the thermal conductivity, the width of the simulated bilayer graphene structures is approximately 10 nm. To ensure that the results do not depend on the sample width, multiple increasing widths are simulated until there is no longer any width dependence. The sample lengths are varied from 20 nm to 426 nm. The largest structure contains 317,600 atoms.
 C. Li, et al., Carbon, 138, 451 (2018).
This work was supported by the National Science Foundation under Award NSF EFRI-1433395. The ab initio simulations used the Extreme Science and Engineering Discovery Environment (XSEDE), supported by National Science Foundation (NSF) grant No. ACI-1548562 and allocation ID TG-DMR130081.