Effects of optical and surface polar phonons on the optical conductivity of doped graphene

Using the Kubo linear response formalism, we study the effects of intrinsic graphene optical and surface polar phonons (SPPs) on the optical conductivity of doped graphene. We find that inelastic electron-phonon scattering contributes significantly to the phonon-assisted absorption in the optical gap. At room temperature, this midgap absorption can be as large as 20–25$\%$ of the universal ac conductivity for graphene on polar substrates (such as Al${}_2$O${}_3$ or HfO${}_2$) due to strong electron-SPP coupling. The midgap absorption, moreover, strongly depends on the substrates and doping levels used. With increasing temperature, the midgap absorption increases, while the Drude peak, on the other hand, becomes broader as inelastic electron-phonon scattering becomes more probable. Consequently, the Drude weight decreases with increasing temperature.

Figure 1

Calculated frequency dependence of the (real part of the) optical conductivity of suspended graphene and graphene on several different substrates for $n_{\mathrm{i}}=5\times {10}^{11}$ cm${}^{-2}$ and $\mu =0.3$ eV at $T=300$ K and $T=1$ K (inset).

Figure 2

Calculated frequency dependence of the (real part of the) optical conductivity of graphene on a SiO${}_2$ substrate for $n_{\mathrm{i}}=5\times {10}^{11}$ cm${}^{-2}$ and several different chemical potentials at (a) $T=1$ K and (b) $T=300$ K.

Figure 3

Calculated dependence of the midgap absorption (at $\hslash {\omega }_0=\mu$) on the chemical potential for suspended graphene and graphene on several different substrates, $n_{\mathrm{i}}=5\times {10}^{11}$ cm${}^{-2}$, and $T=300$ K.

Figure 4

Calculated frequency dependence of the (real part of the) optical conductivity of suspended graphene and graphene on several different substrates for $n_{\mathrm{i}}=5\times {10}^{11}$ cm${}^{-2}$ and $\mu =0.3$ eV at $T=300$ K and $T=1$ K (inset) if bare Fröhlich couplings are used.

Figure 5

Calculated temperature dependence of the midgap absorption (at $\hslash {\omega }_0=\mu$) for suspended graphene (black) and graphene on several different substrates, $n_{\mathrm{i}}=5\times {10}^{11}$ cm${}^{-2}$, and $\mu =0.3$ eV.

Figure 6

Calculated dependence of the (a) absorption at $\hslash {\omega }_0=\mu$, (b) the Drude weight $D$, and (c) the inverse scattering time $\hslash /\tau$ on the relative strength of the electron-phonon coupling ${\gamma }_{\mathrm{rel}}$ for suspended graphene and graphene on Al${}_2$O${}_3$ and SiO${}_2$, $n_{\mathrm{i}}=5\times {10}^{11}$ cm${}^{-2}$, $T=300$ K, and $\mu =0.3$ eV.