1. physics of incommensurately stacked two-dimensional atomic layers

  2. - from moire superlattices to quasicrystals -

Pilkyung Moon

New York University, Shanghai & New York

9 March 2021 Tue 4 pm

                                      IBS Center for Theoretical Physics of Complex Systems (PCS), Administrative Office (B349), Theory Wing, 3rd floor

                                      Expo-ro 55, Yuseong-gu, Daejeon, South Korea, 34126 Tel: +82-42-878-8633                     

When two-dimensional atomic layers are stacked incommensurately, the moire interference between the lattices makes a new kind of superlattices where the interlayer interaction is crucial to determine its electronic structures [1, 2]. In this talk, I will first discuss the electronic structures of moiré superlattices with a long superlattice period, and show that their physical properties are significantly altered if compared with those of the pristine graphene [1, 3]. I will also show that the moire superlattice affords a unique opportunity to study the fundamental problems, such as Hofstadter’s butterfly [4] and incommensurate double-walled nanotubes [5].

Then, I will introduce a graphene quasicrystal. When two hexagonal lattices are overlapped at a twist angle of 30°, the atomic arrangement is mapped on to a quasicrystalline lattice, which is ordered but not periodic [6]. I will introduce a momentum-space tight-binding model which can reveal the electronic structures of general incommensurately stacked atomic layers, and reveal the electronic structures of graphene quasicrystal by fully respecting both the dodecagonal rotational symmetry and the massless Dirac nature [7]. The resulting quasi-band structure is composed of the nearly flat bands with spiky peaks in the density of states, where the wave functions exhibit characteristic patterns which fit to the fractal inflations of the quasicrystal tiling. I also demonstrate that the 12-fold resonant states appear as spatially-localized states in a finite-size geometry, which is another hallmark of quasicrystal.


[1] P. Moon and M. Koshino, Phys. Rev. B 87, 205404 (2013).

[2] M. Koshino, P. Moon, and Y.-W. Son, Phys. Rev. B 91, 035405 (2015).

[3] P. Moon and M. Koshino, Phys. Rev. B 90, 155406 (2014).

[4] P. Moon and M. Koshino, Phys. Rev. B 85, 195458 (2012); C. R. Dean et al., Nature 497, 598 (2013); B. Hunt et al., Science 340, 1427 (2013); P. Moon and M. Koshino, Phys. Rev. B 88, 241412(R) (2013).

[5] M. Koshino,* P. Moon,* and Y.-W. Son,* Phys. Rev. B 91, 035405 (2015).

[6] S. Ahn,* P. Moon,* T.-H. Kim* et al., Science 361, 782 (2018).

[7] P. Moon,*,† M. Koshino,* Y.-W. Son, Phys. Rev. B 99, 165430 (2019); J. A. Crosse and P. Moon, Phys. Rev. B 103, 045408 (2021).