Temperature-dependent resistivity in bilayer graphene due to flexural phonons

We have studied electron scattering by out-of-plane (flexural) phonons in doped suspended bilayer graphene. We have found the bilayer membrane to follow the qualitative behavior of the monolayer cousin. In the bilayer, a different electronic structure combine with a different electron-phonon coupling to give the same parametric dependence in resistivity and, in particular, the same temperature ($T$) behavior. In parallel with the single layer, flexural phonons dominate the phonon contribution to resistivity in the absence of strain, where a density-independent mobility is obtained. This contribution is strongly suppressed by tension, and in-plane phonons become the dominant contribution in strained samples. Among the quantitative differences, an important one has been identified: room-temperature mobility in bilayer graphene is substantially higher than in monolayer graphene. The origin of quantitative differences has been unveiled.

Figure 1

Scattering of electrons in momentum space due to (a) in-plane phonons, (b) nonstrained flexural, and (c) strained flexural phonons.

Figure 2

Resistivity vs $T$ due to scattering by in-plane phonons (dashed thick lines) and flexural phonons (full lines) with and without strain (indicated in percentage) in (a) monolayer and (b) bilayer graphene. We use $n={10}^{12}\hspace{0.5em}{\text{cm}}^{-2}$, $g\approx 3\hspace{0.5em}\text{eV}$, and $\beta \approx 3$.