Temperature-dependent resistivity of suspended graphene

In this paper we investigate the electron-phonon contribution to the resistivity of suspended single-layer graphene. In-plane as well as flexural phonons are addressed in different temperature regimes. We focus on the intrinsic electron-phonon coupling due to the interaction of electrons with elastic deformations in the graphene membrane. The competition between screened deformation potential vs fictitious gauge-field coupling is discussed together with the role of tension in the suspended flake. In the absence of tension, flexural phonons dominate the phonon contribution to the resistivity at any temperature $T$ with a $T^{5/2}$ and $T^2$ dependence at low and high temperatures, respectively. Sample-specific tension suppresses the contribution due to flexural phonons, yielding a linear temperature dependence due to in-plane modes. We compare our results with recent experiments.

Figure 1

The on-shell condition forces the incoming and outgoing electron momenta $\mathbf{k}$ and $\mathbf{k}+\mathbf{Q}$ on the Fermi circle with $\mathbf{Q}$ the phonon-induced scattering wave vector.

Figure 2

The dependence of the resistivity due to scattering off flexural modes on temperature $T$ and electron density $n$. The gray area identifies the region $q_{\ast }>q_T^{\left(h\right)}$ where the relevant flexural phonon dispersion is dominated by tension and ${\omega }_{\mathbf{q}}^{\left(h\right)}\simeq \alpha q$.

Figure 3

(Color online) The combined contributions to the resistivity due to in-plane and flexural-phonons $\Delta \rho$ as a function of the temperature $T$ for three different electron densities $\tilde{n}=0.05,0.15,0.3$ (dashed-dotted, dashed, and continuous line, respectively). Here we assume a tension $\tilde{\gamma }=1$ and a deformation potential coupling ${\tilde{g}}_1=10$. Inset: same plot as in the main figure but for stronger tension $\tilde{\gamma }=20$. Notice the almost perfect linear-$T$ scaling, independent of density.