Electronic structure of $3^{\circ }$-twisted bilayer graphene on 4H-SiC(0001)

The electronic structure of $3^{\circ }$-twisted bilayer graphene (TBG) is studied by angle-resolved photoelectron spectroscopy (ARPES). Sub-mm-sized TBG prepared by direct bonding in a high vacuum enabled us to use conventional ARPES band mapping with synchrotron light. The results indicate that strong interlayer coupling makes a moiré potential for the Dirac electrons and significantly modifies the graphene bands around the $\overline{K}$ points such as the band splitting and electron velocity reduction. The observed electronic structure is consistently reproduced by tight-binding calculations combined with a band unfolding method.

Figure 1

(a) Schematic illustration of $3^{\circ }$ TBG. (b) LEED image of the $3.2^{\circ }$ TBG sample at 58 eV electron energy. The spots from both lower and upper graphene (Gr) layers are separately seen. The light blue line connects the spots from the lower graphene and interface $3\times 3$ superstructure. (c) Magnified graphene LEED image of the same TBG sample indicating satellite spots due to the moiré superstructure. (d) Schematic structure model of the TBG (upper-layer graphene ${\mathrm{Gr}}_u$ and lower ${\mathrm{Gr}}_l$). The purple part between ${\mathrm{Gr}}_l$ and the 4H-SiC substrate represents the interface layer with a $3\times 3$ superstructure.

Figure 2

(a) ARPES constant-energy band image at $E_{\mathrm{F}}$ (upper) and (lower) ARPES band dispersion image along the line through the two $\overline{K}$ points, ${\overline{K}}_u$ (upper layer) and ${\overline{K}}_l$ (lower layer). The data were taken at RT. The logarithmic ARPES intensity is displayed in the upper figure for showing replica bands clearly, and the linear intensity in the lower. Replica ${\overline{K}}_l$ points are shown as ${\overline{k}}_{l1}$ and ${\overline{k}}_{l2}$. (b) ARPES band dispersion image without the division by the Fermi-Dirac distribution curve along the same line as in (a). (c) Calculated band structure of TBG with $\theta =3.{14}^{\circ }$ (upper). The energy difference between the upper and lower graphene layers is set to be 0.05 eV. The band intensity indicates the calculated spectral weight, and the logarithmic intensity is displayed. Calculated constant-energy band image of TBG with $\theta =3.{14}^{\circ }$ at 0.08 eV below $E_{\mathrm{F}}$ (lower). The logarithmic intensity is displayed. The left and right red dots indicate ${\overline{K}}_u$ and ${\overline{K}}_l$, respectively. (d) Graphene BZ and (e) moiré BZ for TBG. ${\overline{k}}_{l1}$ and ${\overline{k}}_{l2}$ are $\overline{K}$ points of the replica lower graphene Dirac bands adjacent to the original upper graphene Dirac band. Definition of the angle $\alpha$ around ${\overline{K}}_u$ is given in (e).

Figure 3

(a)–(c) The calculated band structure of the $3.{14}^{\circ }$ TBG. In each panel, the upper figure indicates the constant-energy map at $E=E_{\mathrm{F}}-0.6$ eV, and the lower one the dispersion along the line though ${\overline{K}}_u$ and ${\overline{K}}_l$. Here, both graphene layers have the same $E_{\mathrm{D}}$, which is equal to $E_{\mathrm{F}}$. The interlayer spacing $\delta$ is 4.5, 3.9, and 3.6 Å. The logarithmic intensity is displayed. Yellow and red dotted ovals indicate the positions of the band splitting, and red dots the positions of ${\overline{K}}_u$ and ${\overline{K}}_l$. (d) Constant-energy maps for $\delta =4.5\AA$ (upper) and 3.6 Å (lower) with the two original Dirac bands (red curves) and replica band (light blue curve). Red dots indicate the positions of ${\overline{K}}_u$ and ${\overline{K}}_l$, and the light-blue dot the position of the replica ${\overline{K}}_l$ point. The black hexagon in the upper panel is the moiré BZ, and the black dotted curves in the lower panel indicate the split bands. (e) Observed constant-energy ARPES intensity map at 0.35 eV below $E_{\mathrm{F}}$. The data were taken at 30 K, and the logarithmic intensity is displayed. The intensity marked as $a$, $b$, $h$, and $j$ originates from the corresponding bands shown in Fig. 2. The red arrow indicates the intensity due to a replica band.

Figure 4

Observed (upper) and calculated (lower) band images in the five planes rotated around ${\overline{K}}_u$. The rotation angle $\alpha$ is defined as an angle from the ${\overline{K}}_u\text{−}{\overline{K}}_l$ line as given in Fig. 2. The spectra were taken at RT and the ARPES intensity was divided by the Fermi-Dirac distribution curve. The data without division by the Fermi-Dirac distribution curve are given in Ref. [28]. Red arrows indicate the positions of the energy gap (a) between ${\overline{K}}_u$ and ${\overline{k}}_{l1}$ and (d) between ${\overline{K}}_u$ and ${\overline{k}}_{l2}$, and blue arrows in (b) and (c) the partial flat bands.