Gate tunable optical absorption and band structure of twisted bilayer graphene

We report the infrared transmission measurement on electrically gated twisted bilayer graphene. The optical absorption spectrum clearly manifests dramatic changes such as the splitting of the interlinear-band absorption step, the shift of the inter-van Hove singularity transition peak, and the emergence of a very strong intravalence (intraconduction) band transition. These anomalous optical behaviors demonstrate consistently a nonrigid band structure modification created by ion-gel gating through layer-dependent Coulomb screening. We propose that this screening-driven band modification is a universal phenomenon that persists to other bilayer crystals in general, establishing electrical gating as a versatile technique to engineer band structures and to create different types of optical absorptions that can be exploited in electro-optical device applications.

Figure 1

Optical absorption of ungated TBG. (a) Optical images of TBG samples with different twisted angles $\theta$. The scale bar is $20\mu \mathrm{m}$. (b) Electronic band diagram of TBG. BE and vHs stand for the band edge of the second band and the saddle-point van Hove singularity, respectively. Two kinds of optical transitions are activated as shown by the red and blue arrows. (c) Optical conductivity ${\sigma }_1\left(\omega \right)$ of the five TBG samples. The peak-$\alpha$ shifts to higher energy as $\theta$ increases. The sharp peak at $E=0.13$ eV is an artifact due to optical phonon absorption of ${\mathrm{SiO}}_2$. The inset compares the measured peak position with the theoretical prediction [25]. (d) The ${\sigma }_1\left(\omega \right)$ can be fit in terms of the LB transition (red curve) and peak-$\alpha$ (blue curve).

Figure 2

Optical absorption of ion-gel gated TBG. (a) Schematic view of the ion-gel gating circuit and the infrared transmission measurement. (b) Optical conductivity of gated TBG $\left(\theta =6.4^{\circ }\right)$ for various gate voltages $V_{\mathrm{G}}$. The gate-driven changes of the LB transition, peak-$\alpha$, and peak-$\beta$ are observed and discussed in detail in the text. (c) The band structure of TBG under gating. The top band and bottom band shift by $E_{\mathrm{T}}$ and $E_{\mathrm{B}}$, respectively. $U$ is their difference, $U=E_{\mathrm{T}}-E_{\mathrm{B}}$. Here, the gap opening is omitted for clarity. (d) Optical transitions change in the gated TBG compared with the ungated one as a result of the band shifts.

Figure 3

Gate-driven evolution of the optical conductivity (left column) and the band structure (right column). (a), (c), (e) Fit of optical conductivity for $V_{\mathrm{G}}=0.84,-1.3$, and $-2.0$ V. (b), (d), (f) Nonrigid band evolution and optical transitions for (a), (c), and (e). As $V_{\mathrm{G}}$ is increased, $U$ becomes stronger, and as a result, peak-$\alpha$ transition energy decreases. In (f), the new $\beta$ transition (sky blue) is activated.

Figure 4

Fitting result of the peak energy and intensity (a) LB-transition energy $E_{\mathrm{T}}$ (and $E^{*})$ for the top graphene, and $E_{\mathrm{B}}$ for bottom graphene. $U$ is calculated from the LB transition and, independently, from the peak-$\alpha$ shift $U=E_{\alpha }\left(0\right)-E_{\alpha }\left(V_{\mathrm{G}}\right)$. (b) Peak energy $E_{\alpha }$ and strength $S_{\alpha }$ of peak-$\alpha$. (c) $E_{\beta }$ and $S_{\beta }$ of peak-$\beta$. The inset shows the band structure along $\overline{M}\to \overline{\mathrm{\Gamma }}$ and $\overline{M}\to \overline{K}$, where the arrows emphasize the optical criticality of peak-$\beta$.