Evidence for Interlayer Coupling and Moiré Periodic Potentials in Twisted Bilayer Graphene

We report a study of the valence band dispersion of twisted bilayer graphene using angle-resolved photoemission spectroscopy and ab initio calculations. We observe two noninteracting cones near the Dirac crossing energy and the emergence of van Hove singularities where the cones overlap for large twist angles ($>5°$). Besides the expected interaction between the Dirac cones, minigaps appeared at the Brillouin zone boundaries of the moiré superlattice formed by the misorientation of the two graphene layers. We attribute the emergence of these minigaps to a periodic potential induced by the moiré. These anticrossing features point to coupling between the two graphene sheets, mediated by moiré periodic potentials.

Figure 1

$k$ space representation of TBG with $\theta =\sim 11.6°$. (a) Photoemission intensity contour of the two Dirac cones at the electron energy $E_F-0.4\mathrm{eV}$, and the primitive BZs of the underlayer and overlayer (red hexagon including the $K$ point and blue one including the $K_{\theta }$ point). Darker shades indicate higher photoemission intensities. The small black hexagon is the moiré superlattice BZ of the $(p,q)=(3,17)$ [15] commensurate TBG. (b) Enlarged image of (a) near the two cones. (c) Photoemission spectra intersecting two cones at $K$ and $K_{\theta }$ points. The red (left) and blue (right) dashed lines illustrate the under- and overlayer cones, respectively, obtained by extrapolating the measured dispersions [62].

Figure 2

Electronic dispersions of the two interacting Dirac cones ($\theta =\sim 11.6°$). (a)–(c) Photoemission intensity contours at $E_F-0.8\mathrm{eV}$ (a), $E_F-1.0\mathrm{eV}$ (b), and $E_F-1.3\mathrm{eV}$ (c). Black hexagons (thick line) indicate the moiré superlattice BZ of the commensurate TBG. ${\Gamma }_s$, $K_s$, and $K^{\prime }{}_s$ are among its high-symmetry points. $K$ and $K_{\theta }$ points are both $K_s$ points in the superlattice BZ. Green hexagons (thin line) are minizones of a continuum model with a Dirac point at its zone center. (d) Photoemission spectra and the DFT states bisecting the two cones and (e) the one orthogonal to (d). Their directions are indicated in (c) by horizontal and vertical black arrows. The schematic to the right of (e) shows the orientations of the photoemission patterns relative to the two primitive Dirac cones without interaction. DFT states are shown as (blue) dots. Calculated states matching the ARPES data are highlighted by blue (thick) and green (thin) circles.

Figure 3

Second derivative of the ARPES intensity with respect to the energy ($\theta =\sim 11.6°$). (a) Contours at $E_F-0.8\mathrm{eV}$. The black hexagons are the superlattice BZ. The red, blue, and black circles with “$U$”, “$O$,” and “$M$” illustrate the locations of underlayer, overlayer, and moiré superlattice Dirac cones, respectively. (b) Processed photoemission pattern along the green arrow in (a) and DFT states (blue dots) connecting $K^{\prime }{}_s$-$K^{\prime }{}_s$-$K^{\prime }{}_s$ points. Circles (green) highlight DFT states matching the ARPES data.

Figure 4

Photoemission intensity patterns (a),(c) and EDCs (b),(d) displaying the minigap as a function of $\theta$. (a),(b) $\theta =\sim 5.6°$, (c),(d) $\theta =\sim 12.0°$. The photoemission pattern bisects the two cones similarly to Fig. 2d. (b) and (d) are EDCs at the black lines in (a) and (c), respectively, fitted to Voigt functions [thin (red) lines].