Graphene quasicrystal

Quasicrystals have been used to study quantum states between the limits of periodic order and disorder. Recently, we reported that quasicrystals can be realized by stacking atomic layers at a specific configuration [1]. And, as a specific example of such designer quasicrystals, we reported a graphene quasicrystal composed of two graphene layers stacked at a rotation angle of 30°.
In this talk, I will discuss the theory of Dirac electrons in a graphene quasicrystal and show the characteristic features of this structure [2]. I will first report a rigorous effective model of the electronic structures of graphene quasicrystal. Then, I will show the emergence of the critical states, which are neither perfectly localized nor fully extended, and reveal the origin of these states as well as the minimum wave functions for describing the electronic structures. In addition, I will show that the wave functions show 12-fold rotational symmetry and report the band dispersion of graphene quasicrystal.
[1] S. J. Ahn,* P. Moon,* T.-H. Kim* et al., Science 361, 782 (2018).
[2] P. Moon, M. Koshino, and Y.-W. Son (in preparation).