Direct observation of moiré flat-band breakdown at the edge of magic-angle twisted bilayer graphene

Low-energy moiré flat bands in magic-angle twisted bilayer graphene (tBG) have demonstrated incredible potential to exhibit rich exotic quantum phenomena. Theoretically, the moiré flat bands of tBG are based on the extended structures, i.e., the moiré patterns with periodic boundary conditions. However, a fundamental question of whether the flat bands can exist in the graphene moiré patterns with a reduced structure symmetry, such as sample edges, remains unanswered. Here, via scanning tunneling microscopy and spectroscopy, we study the local electronic properties of magic-angle tBG near the sample terminated edge and report a direct observation of breakdown of the moiré flat bands. We show that the moiré electronic structures, including the low-energy flat bands, can sufficiently exist in a complete moiré spot, i.e., a moiré supercell, right at the edge even if the translational symmetry of the moiré patterns is broken in one direction. However, the flat-band characteristic is obviously absent in the incomplete moiré spots that are partly terminated by the edge. Our results indicate that a whole moiré spot is sufficient and indispensable for the generation of the effective moiré flat bands in tBG.

Figure 1

(a) Top: STM topographic image $(V_b=0.5\mathrm{V},I=0.2\mathrm{nA})$ of $1.{13}^{\circ }$ twisted bilayer graphene (tBG) near a step edge. Inset is the height profile of the step edge. Lower left: Atomic-resolution STM image $\left(V_b=0.3\mathrm{V},I=0.4\mathrm{nA}\right)$ of the graphene layer below the step. Lower right: Magnified STM image $\left(V_b=42\mathrm{mV},I=0.2\mathrm{nA}\right)$ obtained in the tBG region marked by the hexagon in the top panel. (b) Typical $dI/dV-V$ spectrum of $1.{13}^{\circ }$ tBG (AA site). Inset shows the STS spectra recorded in the graphene layer below the step of (a) (blue curve) and in the graphite substate (gray curve). It displays a finite DOS at the Dirac point for the spectrum of graphite and a nearly zero DOS at the Dirac point for the spectrum of the monolayer region (a signature of a massless Dirac fermion), further indicating the decoupling feature of the studied sample. (c) Spatially resolved contour plot of $dI/dV$ spectra measured along the dashed arrow, i.e., the AA-(saddle-point of AB/BA)-AA direction, in the tBG region of (a). (d) $dI/dV$ profile line taken at the energy of 12 meV from (c).

Figure 2

(a) STM topographic image $\left(V_b=0.3\mathrm{V},I=0.1\mathrm{nA}\right)$ of $1.{13}^{\circ }$ tBG around the step edge. (b) STS spectra measured at the bright moiré spots (AA stacking regions) marked by the colored arrows in (a). The curves are offset in the $y$ axis for clarity. (c) Spatially resolved $dI/dV$ spectra obtained along the dashed arrow in the tBG of (a). (d) $dI/dV$ profile line measured at the energy of 12 meV from (c).

Figure 3

Normalized $dI/dV$ spectra recorded in the AA stacking regions, as marked by the polygons in the STM images of the right panels, with and without a complete moiré spot at the step edge. The measurement points are nearly at the same distance, i.e., $\sim 0.4\mathrm{nm}$ for the 0.7–1.0 spots and $\sim 0.3\mathrm{nm}$ for the 0.5 spot (within the AA region), from the edge boundary to avoid edge effects. The curves are offset in the $y$ axis for clarity.