Tunable Lattice Reconstruction, Triangular Network of Chiral One-Dimensional States, and Bandwidth of Flat Bands in Magic Angle Twisted Bilayer Graphene

The interplay between interlayer van der Waals interaction and intralayer lattice distortion can lead to structural reconstruction in slightly twisted bilayer graphene (TBG) with the twist angle being smaller than a characteristic angle ${\theta }_c$. Experimentally, the ${\theta }_c$ is demonstrated to be very close to the magic angle ($\theta \approx 1.08°$). Here we address the transition between reconstructed and unreconstructed structures of the TBG across the magic angle by using scanning tunneling microscopy (STM). Our experiment demonstrates that both structures are stable in the TBG around the magic angle. By using a STM tip, we show that the two structures can be changed to each other and a triangular network of chiral one-dimensional states hosted by domain boundaries can be switched on and off. Consequently, the bandwidth of the flat band, which plays a vital role in the emergent strongly correlated states in the magic angle TBG, is tuned. This provides an extra control knob to manipulate the exotic electronic states of the TBG near the magic angle.

Figure 1

(a)–(d) Typical STM images of four different TBGs ($V_S=400\mathrm{mV}$, $I=0.2\mathrm{nA}$). The $AA$, $AB$, $BA$, and DW regions are marked in (d). (e) Height profiles recorded at TBG along the yellow arrow, as shown in (d). The $x$ axis is normalized by the spacing between two $AA$ regions. (f) Schematic reconstructed and unreconstructed structures of TBG. (g) Left panel: Relative strain and the height ratio of different TBGs. The relative strain is calculated according to the ratio between the lattice constant in the DW region and that in the $AB$ or $BA$ region. The average lattice constant is obtained according to the FFT. Right panel: Representative FFT of the DW and $AB$ and $BA$ regions. The six bright spots are reciprocal lattices of graphene. Scale bar: $2.5{\mathrm{nm}}^{-1}$. Inset: Section views cross the colored circles in the FFT. The dashed lines label the peaks obtained in the $AB$ and $BA$ regions.

Figure 2

(a)–(c) $dI/dV$ maps of three TBGs. The experimental parameters are (a) $Vs=-35\mathrm{mV}$; (b) $V_S=20\mathrm{mV}$; and (c) $V_S=40\mathrm{mV}$. The different stacking regions are marked in the maps.

Figure 3

(a) STM image of a TBG showing both the unreconstructed (region I) and reconstructed structures (region II) ($V_S=30\mathrm{mV}$, $I=0.4\mathrm{nA}$), which are separated by a dashed line. (b) Height profiles along dashed arrows in (a). (c) Typical $dI/dV$ map of TBG at the energy of 30 meV. (d) $dI/dV$ profiles along dashed arrows in (c).

Figure 4

(a) STM image ($V_S=650\mathrm{mV}$ and $I=0.3\mathrm{nA}$) of a 1.13º TBG showing the reconstructed structure. (b) STM image of the same region as (a) after applying a 3-V tip pulse for 0.1 s. (c) Height profiles along dashed lines around the $AA$ region in (a) and (b). The DW and $AB$ and $BA$ regions are marked with different colors. (d),(e) Typical STS spectra taken at the same position marked by solid dots in (a) and (b).