Moiré patterns, appeared on solid surfaces or at heterojuctions of atomic layers, have recently been reported to show dramatic properties, such as superconductivity and manipulations of Dirac electrons. Here, we organize the special issue on “Moiré pattern and surface science”, to introduce hot topics in the frontier researches and to make readers aware existence of the deep science hidden in the patterns that we see in our surroundings every day.

We present an overview of recent studies on the moiré superlattices in Van der Waals atomic layer materials. We first introduce typical moiré superlattices such as twisted bilayer graphene and graphene h-BN superlattice. We also argue about the Hofstadter fractal energy spectrum in magnetic fields, the strain effect and domain formation, and the graphene quasicrystals.

We provide a simple theoretical study on the Dirac cone existing in the monolayer χ₃ borophene. Owing to the lattice mismatch with the substrate, the borophene is known to be subject to a long-range perturbation. The Dirac cone of the free-standing borophene is thereby expected to be preserved or lost depending on the degree of the lattice mismatch. We explain their relation using a minimal tight-binding model.

Strain-induced modulation of electronic states in a Moiré pattern on a hexagonal-type FeN monoatomic layer has been studied using scanning tunneling microscopy and spectroscopy. The hexagonal FeN film is stabilized by a strong Fe-N bond even on the square Cu(001) substrate and shows a strip structure comprising regular and deformed hexagonal lattices. By analyzing the atomically resolved images, we have found that the lattice is periodically deformed along a hypothetical Moiré pattern between a perfect hexagonal lattice and the square Cu(001) lattice. Moreover, dI/dV spectra exhibit spatial change of the unoccupied local density of states, which is attributed to an energy shift of the antibonding states due to the periodic compressive lattice strain.

Moire fringes are observed when two (or more) crystal lattices are interfered in transmission electron microscopy (TEM). Typical application is the evaluation of epitaxial films grown on a substrate, in where their crystallographic orientation relationship could be investigated. Visualization of defects distribution using Moire fringes are also useful. Sometimes Moire fringes between crystal and digital pixel lattices are intentionally formed to visualize a strain map. In the present paper, some of those applications are introduced.

Improving spatial resolution in imaging techniques has been great challenges in human history. The use of moiré provides a solution to obtain structural information in a scale less than the spatial resolution that can be achieved by an imaging technique. In this review, several examples of the use of moiré, such as super-resolution imaging and large-field-of-view imaging with unresolvable-pitch spatial carrier fringes, are shown.