Dirac electrons in a dodecagonal graphene quasicrystal

Abstract

Quantum states of quasiparticles in solids are dictated by symmetry. We have experimentally demonstrated quantum states of Dirac electrons in a two-dimensional quasicrystal without translational symmetry. A dodecagonal quasicrystalline order was realized by epitaxial growth of twisted bilayer graphene rotated exactly 30°. We grew the graphene quasicrystal up to a millimeter scale on a silicon carbide surface while maintaining the single rotation angle over an entire sample and successfully isolated the quasicrystal from a substrate, demonstrating its structural and chemical stability under ambient conditions. Multiple Dirac cones replicated with the 12-fold rotational symmetry were observed in angle-resolved photoemission spectra, which revealed anomalous strong interlayer coupling with quasi-periodicity. Our study provides a way to explore physical properties of relativistic fermions with controllable quasicrystalline orders.

Interlayer Decoupling in 30° Twisted Bilayer Graphene Quasicrystal

“…47 ARPES measurements of exactly 30º -tBLG indicated the strong scattering of the electron waves between the layers . 15,16 Our results provide the direct local DOS measurement and especially their response to external gating, which add to the understanding of the electronic structure in 30°-tBLG.…”

“…For the first type, the bilayer region exhibits only a set of 6 diffraction spots 6 that is identical to the monolayer region ( Figure 1b), confirming the AB stacking order. In contrast, for the second type, the diffraction pattern of the bilayer region has 12 spots, 15 which can be regarded as a combination of two sets of 6-fold patterns that is rotated by 30° ( Figure 1c). The up and bottom layers of the 30°-tBLG can be distinguished from the -LEED pattern because the intensity of the upper layer (blue circles in Figure 1c) is larger than the bottom layer (pink circles in Figure 1c).…”

“…18,19 We note that the electronic structures of the 30°-tBLG are acquired directly on the growth substrates by ARPES in these pioneer works. 15,16 This cannot avoid the influence of the substrates, which could have strong interaction with the 30°-tBLG overlayer.…”

Dodecagonal bilayer graphene quasicrystal and its approximants

“…Previous ARPES measurements 29,30 and theoretical studies 29 show that the band structures around these six kpoints (K, K, K 1 , K 1 , K 2 and K 2 ) are Dirac cones. The Fermi velocities for K, K, K 1 and K 1 Dirac cones are 9.3, 9.2, 8.9 and 9.1 ×10 5 m/s, respectively 29 .…”

“…dodecagonal graphene quasicrystal, which will be referred as graphene quasicrystal for simplicity in the rest of the paper, has been grown successfully on different substrates, including 4H-SiC(0001) 29 , Pt(111) 30 and Cu-Ni(111) 31 surfaces. The interplay between the quasiperiodicity and interlayer interaction results in the emergence of extra Dirac points 29 and critical eigenstates 32 . These novel properties are very different from those of graphene, although the twist angle is even more than 15 • .…”