Real-Space Imaging of the Tailored Plasmons in Twisted Bilayer Graphene

We report a systematic plasmonic study of twisted bilayer graphene (TBLG)—two graphene layers stacked with a twist angle. Through real-space nanoimaging of TBLG single crystals with a wide distribution of twist angles, we find that TBLG supports confined infrared plasmons that are sensitively dependent on the twist angle. At small twist angles, TBLG has a plasmon wavelength comparable to that of single-layer graphene. At larger twist angles, the plasmon wavelength of TBLG increases significantly with apparently lower damping. Further analysis and modeling indicate that the observed twist-angle dependence of TBLG plasmons in the Dirac linear regime is mainly due to the Fermi-velocity renormalization, a direct consequence of interlayer electronic coupling. Our work unveils the tailored plasmonic characteristics of TBLG and deepens our understanding of the intriguing nano-optical physics in novel van der Waals coupled two-dimensional materials.

Figure 1

(a) Illustration of the nanoinfrared imaging experiment of a TBLG single crystal. The solid and dashed arrows mark the directions of the incident laser beam and backscattered photons, respectively. (b) Sketch of the crystal structure of TBLG revealing the moiré periodic pattern. The double-sided arrow marks the moiré period. (c) Calculated band structure of TBLG with a twist angle of 5° with the continuum model [25]. Here the momentum unit $\mathrm{\Delta }K$ equals the separation between the two Dirac points ($K_1$ and $K_2$) in the momentum space. (d) Optical image of representative TBLG and SLG single-crystal samples. The scale bar represents $5\mu \mathrm{m}$.

Figure 2

(a) Sketch of the sample geometry indicating two adjacent TBLG grains with different twist angles with respect to SLG. (b),(c) The near-field images plotting the scattering amplitude ($s$) and phase ($\psi$), respectively. In both images, the amplitude or phase signal is normalized to that of SLG. The laser energy is set to be at $E=0.11\mathrm{eV}$. The scale bars represent $3\mu \mathrm{m}$.

Figure 3

(a)–(e) High-resolution near-field amplitude images of the five small regions ($P1–P5$) marked in Fig. S1 (squares), respectively. The white dashed lines in the images mark the SLG edge and the TBLG-SLG boundaries. The scale bars represent 400 nm. (f)–(j) Experimental (gray solid line) and modeled (red dashed line) amplitude profiles taken along the blue dashed lines in the corresponding near-field images above. The blue arrows in (g) and (h) mark the size of ${\lambda }_p^{\mathrm{TBLG}}$ that is twice the fringe period. The vertical dashed lines mark the boundaries between SLG and TBLG.

Figure 4

(a) The ${\lambda }_p^{\mathrm{TBLG}}$ data points extracted by modeling the fringe profiles in Fig. 3. The inset plots the calculated $v_F^{\mathrm{TBLG}}(\theta )$ normalized to $v_F^{\text{S}\mathrm{LG}}(\theta )$ considering different $t$. (b) The ${\gamma }_p^{\mathrm{TBLG}}$ data points extracted by modeling the fringe profiles in Fig. 3. The red curves in (a) and (b) are used for calculations of the amplitude and phase signals in (c) and (d). The blue arrows in (a) and (b) mark the values of ${\lambda }_p^{\mathrm{SLG}}$ and ${\gamma }_p^{\mathrm{SLG}}$, respectively. (c) The $\theta$-dependent near-field amplitude from both experiment (squares) and modeling (red curve). (d) The $\theta$-dependent near-field phase from both experiment (squares) and modeling (red curve). Both the amplitude (c) and phase (d) of TBLG are normalized to those of SLG. The vertical dashed lines in (c) and (d) mark $\theta =3°$.