Chirality-dependent phonon-limited resistivity in multiple layers of graphene

We develop a theory for the temperature and density dependence of phonon-limited resistivity $\rho (T)$ in bilayer and multilayer graphene and compare with the corresponding monolayer result. For the unscreened case, we find $\rho \approx CT$ with $C\propto v_{\mathrm{F}}^{-2}$ in the high-temperature limit, and $\rho \approx A{T}^4$ with $A\propto v_{\mathrm{F}}^{-2}{k}_{\mathrm{F}}^{-3}$ in the low-temperature Bloch-Grüneisen limit, where $v_{\mathrm{F}}$ and $k_{\mathrm{F}}$ are Fermi velocity and Fermi wave vector, respectively. If screening effects are taken into account, $\rho \approx CT$ in the high-temperature limit with a renormalized $C$, which is a function of the screening length, and $\rho \approx A{T}^6$ in the low-temperature limit with $A\propto k_{\mathrm{F}}^{-5}$ but independent of $v_{\mathrm{F}}$. These relations hold in general with $v_{\mathrm{F}}$ and a chiral factor in $C$ determined by the specific chiral band structure for a given density.

Figure 1

Acoustic phonon-limited resistivity of monolayer graphene as a function of temperature for (a) ${\alpha }_{\mathrm{gr}}=0$ with several densities, (b) ${\alpha }_{\mathrm{gr}}=1$ with several densities, (c) $n={10}^{13}$ cm${}^{-2}$ with several ${\alpha }_{\mathrm{gr}}$, and (d) the logarithmic derivatives of (c).

Figure 2

Acoustic phonon-limited resistivity of bilayer graphene as a function of temperature for (a) ${\alpha }_{\mathrm{gr}}=0$ with several densities, (b) ${\alpha }_{\mathrm{gr}}=1$ with several densities, (c) $n={10}^{13}$ cm${}^{-2}$ with several ${\alpha }_{\mathrm{gr}}$, and (d) the logarithmic derivatives of (c).

Figure 3

Density dependence of (a) $A$ for ${\alpha }_{\mathrm{gr}}=0$, (b) $A$ for ${\alpha }_{\mathrm{gr}}=1$, (c) $C$ for ${\alpha }_{\mathrm{gr}}=0$, and (d) $C$ for ${\alpha }_{\mathrm{gr}}=1$ with different stacking sequences.