Twisted bilayer graphene with a twist angle of exactly 30° (30°-TBG) is a unique two-dimensional (2D) van der Waals (vdW) system because of its quasicrystalline nature. Here we report, for the first time, scanning tunneling microscopy (STM) measurements of the quasicrystalline 30°-TBG that was obtained in a controllable way by using transfer-assisted fabrication of a pair of graphene sheets. The quasicrystalline order of the 30°-TBG, showing a 12-fold rotational symmetry, was directly visualized in atomic-resolved STM images. In the presence of high magnetic fields, we observed Landau quantization of massless Dirac fermions, demonstrating that the studied 30°-TBG is a relativistic Dirac fermion quasicrystal. Because of a finite interlayer coupling between the adjacent two layers of the 30°-TBG, a suppression of density-of-state (DOS) at the crossing point between the original and mirrored Dirac cones was observed. Moreover, our measurements also observe strong intervalley scattering in the defect-free quasicrystal, indicating that the electronic properties of the 30°-TBG should be quite different from that of its component: the graphene monolayer.

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The interplay between interlayer van der Waals interaction and intralayerlattice distortion can lead to structural reconstruction in slightly twisted bilayer graphene (TBG) with the twist angle being smaller than a characteristic angle θ c . Experimentally, the θ c is demonstrated to be very close to the magic angle (θ ≈ 1.05°). In this work, we address the transition between reconstructed and unreconstructed structures of the TBG across the magic angle by using scanning tunnelling microscopy (STM). Our experiment demonstrates that both the two structures are stable in the TBG around the magic angle. By applying a STM tip pulse, we show that the two structures can be switched to each other and the bandwidth of the flat bands, which plays a vital role in the emergent strongly correlated states in the magic-angle TBG, can be tuned. The observed tunable lattice reconstruction and bandwidth of the flat bands provide an extra control knob to manipulate the exotic electronic states of the TBG near the magic angle.

Ordered atomic-scale superlattices on a surface hold great interest both for basic science and for potential applications in advanced technology. However, controlled fabrication of superlattices down to the atomic scale has proven exceptionally challenging. Here we develop a segregation method to realize self-organization of S superlattices at the interface of graphene and S-rich Cu substrates. Via scanning tunneling microscope measurements, we directly image well-ordered identical nanocluster superlattices and atomic superlattices under the cover of graphene. Scanning tunneling spectra show that the superlattices in turn could modulate the electronic structure of top-layer graphene. Importantly, a special-ordered S monatomic superlattice commensurate with a graphene lattice is found to drive semimetal graphene into a symmetry-broken phasethe electronic Kekulé distortion phasewhich opens a bandgap of ∼245 meV.

Coupled quantum dots (QDs), usually referred to as artificial molecules, are important not only in exploring fundamental physics of coupled quantum objects, but also in realizing advanced QD devices. However, previous studies have been limited to artificial molecules with nonrelativistic fermions. Here, we show that relativistic artificial molecules can be realized when two circular graphene QDs are coupled to each other. Using scanning tunneling microscopy (STM) and spectroscopy (STS), we observe the formation of bonding and antibonding states of the relativistic artificial molecule and directly visualize these states of the two coupled graphene QDs. The formation of the relativistic molecular states strongly alters distributions of massless Dirac fermions confined in the graphene QDs. Because of the relativistic nature of the molecular states, our experiment demonstrates that the degeneracy of different angular-momentum states in the relativistic artificial molecule can be further lifted by external magnetic fields. Then, both the bonding and antibonding states are split into two peaks.