Title: Quasicrystalline resonant states and nonlinear Landau fan diagram in van der Waals superlattices
Abstract: When two atomic lattices are superimposed in an incommensurate configuration, the interlayer interaction generates an extra order along the in-plane direction in the form of a moiré interference pattern. In this talk we discuss two unique states of the electrons subjected to the potentials of such an extra order.
We first show the emergence of quasicrystalline resonant states in dodecagonal and octagonal van der Waals quasicrystals as long as all dominant interlayer interactions occur between atomic orbitals having the same magnetic quantum number [1]. We present a theoretical model that can accurately calculate the electronic structures of such non-periodic systems without introducing any non-physical assumptions [2]. In addition, we discuss the geometry of van der Waals quasicrystals and show that the existence of the "precise center", which exhibits the highest rotational symmetry, is not guaranteed in these systems due to the difference in cardinality between the sets of integers and real numbers [3].
We then report conductance oscillations in graphene electrons exposed to moiré potentials that deviate from the linear Landau fan diagram [4]. And we explain that such anomalous behavior is due to the coexistence of multiple orbits resulting from the simultaneous occupation of multiple minibands and magnetic breakdown. We then propose a novel method to extract the spectral gaps without measuring the activation energy or carrying out tunneling spectroscopy, by using the density of states of the open orbits as a measure. This method is quite general, so it can be applied to any multiband system.
[1] J. A. Crosse and P. Moon†, Phys. Rev. B 103, 045408 (2021).
[2] P. Moon†, M. Koshino, Y.-W. Son, Phys. Rev. B 99, 165430 (2019).
[3] P. Moon, Phys. Rev. B 104, 115407 (2021).
[4] P. Moon†, Y. Kim, M. Koshino†, T. Taniguchi, K. Watanabe, J. H. Smet†, Nano Lett. 24, 3339 (2024).