Scanning tunneling microscopy study of the quasicrystalline 30° twisted bilayer graphene

Abstract

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.

High-Angular-Momentum Topological Superconductivity in the Largest-Angle Twisted Homo-bilayer Systems

“…Three examples: The first example is the QC-TBG synthesized recently. Its dodecagonal symmetric QC structure has been verified by various experiments [45][46][47][48][49]. Actually, it has been long to search SC in the graphene.…”

“…two identical n-folded rotation-symmetric monolayers stacked with the largest possible twist angle π n . Synthesized examples of LA-THBs include the 30 • -twisted bilayer graphene (TBG) [45][46][47][48][49] and the 45 • -twisted bilayer cuprates [50,51]. Such materials possess remarkable Moiréless quasi-crystal (QC) structures with doubly enlarged rotation symmetries absent on periodic lattices.…”

Electronic structure of 30∘ twisted double bilayer graphene

“…The 30 • TBG, an incommensurate bilayer configuration, has been grown successfully on H-SiC(0001) [17], Pt(111) [18], Cu-Ni(111) [19], and Cu [20,21] surfaces. As the first two-dimensional quasicrystal based on graphene, 30 • TBG has received increasing attention both experimentally and theoretically [22][23][24][25][26][27][28]. A method to grow high-quality 30 • TBG epitaxially on SiC using borazine as a surfactant has also been proposed [22].…”

“…A method to grow high-quality 30 • TBG epitaxially on SiC using borazine as a surfactant has also been proposed [22]. The 12-fold rotation symmetry and quasiperiodicity of 30 • TBG have been demonstrated by various measurements, such as the Raman spectroscopy, lowenergy electron microscopy/diffraction, transmission electron microscopy, and scanning tunneling microscopy measurements [17][18][19]22,27]. A number of Dirac cones, especially the mirror-symmetric ones, have been observed by the angle-resolved photoemission spectroscopy (ARPES) measurements [17,18].…”

Emergence of quasiperiodic Bloch wave functions in quasicrystals

“…Rather than proposing alternative forms for the electronic eigenfunctions in quasicrystals [4,5], or suggesting a generalized formulation for the Bloch theorem [6], we examine here whether Bloch wave functions may still appear naturally in quasicrystals despite the failure of Bloch's theorem. This may have immediate practical implications, as the study of correlated electrons in quasicrystals [7,8] is regaining interest [9][10][11], amid the experimental observation of Dirac electrons in dodecagonal bilayer graphene quasicrystals [12,13], and the reformulation of the early spectral theories of electrons, phonons, and photons in quasicrystals [14,15] using modern topological classifications [16][17][18][19][20]. It may also have experimental significance with the increasing ability, at least in metamaterials, to observe and manipulate the actual wave functions [21] and their topological nature [22][23][24], while inducing topological defects [25], phason excitations [26], and static disorder [27] in the otherwise perfectly ordered quasicrystalline potential.…”