Unconventional optical response in monolayer graphene due to dominant intraband scattering

Scattering dynamics influences the graphene's transport properties and inhibits the charge carrier deterministic behavior. The intra/interband scattering mechanisms are vital for graphene's optical conductivity response under specific considerations of doping. In this study, we systematically explored the impact of scattering on optical conductivity using a semiclassical multiband Boltzmann equation, incorporating both electron-electron and electron-phonon interactions collectively with a single phenomenological relaxation time constant. We found unconventional characteristics of linear optical response with a significant deviation from the universal conductivity $({\mathit{e}}^{\mathit{2}}/4\hslash )$ in doped monolayer graphene. This is explained through phenomenological relaxation rates under low doping regime with dominant intraband scattering. Such novel optical responses vanish at high temperatures or overdoping conditions due to strong Drude behavior. With the aid of approximations around Dirac points we have developed analytical formalism for many-body interactions and are in good agreement with the Kubo approaches.

Figure 1

Incorporation of light-matter interaction energy (${\varepsilon }_{eR}$) into the tight-binding component (${\varepsilon }_o$) with hopping parameter ($\mathit{t}=-2.7$ eV) introduces a more significant band gap expansion, even at relatively low electrical bias (eE).

Figure 2

The solid and dashed lines represent real conductivity of chemical potential values from 0.1–0.6 eV for different scattering rates. (a) Dominant interband scattering induces a narrow width and sharp Drude response [Eq. (13)] near zero frequency. Both solid (${\mathrm{\Gamma }}_{\mathit{i}}=0.5\mathrm{meV}$, ${\mathrm{\Gamma }}_{\mathit{e}}=65\mathrm{meV}$) and dashed lines (${\mathrm{\Gamma }}_{\mathit{i}}=0.414\mathrm{meV}$, ${\mathrm{\Gamma }}_{\mathit{e}}=4.14\mathrm{meV}$) are overlapped in this case. (b) Dominant intraband scattering reduces the Drude response and increases the broadening for solid lines (${\mathrm{\Gamma }}_{\mathit{e}}=0.5\mathrm{meV}$, ${\mathrm{\Gamma }}_{\mathit{i}}=65\mathrm{meV}$) and dashed lines (${\mathrm{\Gamma }}_{\mathit{e}}=0.414\mathrm{meV}$, ${\mathrm{\Gamma }}_{\mathit{i}}=4.14\mathrm{meV}$). ${\mathrm{\Gamma }}_{\mathit{i}}$ and ${\mathrm{\Gamma }}_{\mathit{e}}$ are intraband and interband scattering rates.

Figure 3

Both solid and dashed lines represents varying doping levels ranging from 0.1–0.6 eV. The (a) real and (b) imaginary linear conductivity diagrams induced by dominant interband scattering rate has solid lines corresponding to ${\mathrm{\Gamma }}_{\mathit{e}}=65\mathrm{meV}$ and ${\mathrm{\Gamma }}_{\mathit{i}}=0.5\mathrm{meV}$ with the dashed lines corresponding to ${\mathrm{\Gamma }}_{\mathit{e}}=4.14\mathrm{meV}$ and ${\mathrm{\Gamma }}_{\mathit{i}}=0.414\mathrm{meV}$, whereas the (c) real and (d) imaginary linear conductivity diagrams induced by dominant intraband scattering rate has solid lines corresponding to ${\mathrm{\Gamma }}_{\mathit{e}}=0.5\mathrm{meV}$ and ${\mathrm{\Gamma }}_{\mathit{i}}=65\mathrm{meV}$ with the dashed lines corresponding to ${\mathrm{\Gamma }}_{\mathit{e}}=0.414\mathrm{meV}$ and ${\mathrm{\Gamma }}_{\mathit{i}}=4.14\mathrm{meV}$.