Related papers: Moir\'e, Euler, and self-similarity -- the lattice…
Crystal structures are characterized by atomic bases within a primitive unit cell that repeats along a regular lattice throughout 3D space. The periodic and infinite nature of crystals poses unique challenges for geometric graph…
The unique properties of two-dimensional moire systems have been widely studied from many perspectives. However, relatively little work has explored how the real space structure of the moire systems can directly engender novel properties…
In multilayer moir\'e heterostructures, the interference of multiple twist angles ubiquitously leads to tunable ultra-long-wavelength patterns known as supermoir\'e lattices. However, their impact on the system's many-body electronic phase…
Lattice constants such as unit cell edge lengths and plane angles are important parameters of the periodic structures of crystal materials. Predicting crystal lattice constants has wide applications in crystal structure prediction and…
Moir\'e patterns have recently become a very active field in nanophotonics. Those structures exhibit novel photonic properties unattainable with traditional photonic crystals. Especially, moir\'e magic configurations have been shown to…
A real-space method using generating integers is used to classify the possible moire patterns for two equal hexagonal lattices. The result is that the rotations that take (n,m) to (m,n) with n,m relatively prime form the fundamental moire…
We propose a scheme to achieve breathing kagome moir\'e superlattices using three twisted layers of transition metal dichalcogenides. In this scheme, the top and bottom layers are twisted relative to the middle layer by small angles…
We investigate the connections between some simple Maier-Saupe lattice models, with a discrete choice of orientations of the microscopic directors, and a recent proposal of a two-tensor formalism to describe the phase diagrams of nematic…
Changes in lattice structure across sub-regions of protein crystals are challenging to assess when relying on whole crystal measurements. Because of this difficulty, macromolecular structure determination from protein micro and nano…
Moir\'e magnetism, parallel with moir\'e electronics that has led to novel correlated and topological electronic states, emerges as a new venue to design and control exotic magnetic phases in twisted magnetic two-dimensional(2D) crystals.…
Symmetry considerations suggest that moire superlattices formed by twisted two-dimensional materials should preserve overall inversion symmetry. However, experiments consistently report robust ferroelectricity in systems such as twisted…
In the tight-binding approximation the Harper like equation describing an electron in 3D crystal subject to a uniform magnetic field is obtained. It is supposed that the vector H can be oriented along several directions in the lattice. The…
In this article, the solidification phase transition between isotropic liquids and icosahedral quasicrystalline structures is classified by the application of a quaternion orientational order parameter. We suggest that the formation of the…
Geometrical moir\'e patterns, generic for almost aligned bilayers of two-dimensional (2D) crystals with similar lattice structure but slightly different lattice constants, lead to zone folding and miniband formation for electronic states.…
Forming long wavelength moir\'e superlattices (MSL) at small-angle twist van der Waals (vdW) bilayers has been a key approach to creating moir\'e flat bands. The small-angle twist, however, leads to strong lattice reconstruction, causing…
Anisotropies of Young's modulus E, the shear modulus G, and Poisson's ratio of all 2D symmetry systems are studied. Simple necessary and sufficient conditions on their elastic compliances are derived to identify if any of these crystals are…
Van der Waals (vdW) heterostructures formed by 2D atomic crystals provide a powerful approach towards designer condensed matter systems. Incommensurate heterobilayers with small twisting and/or lattice mismatch lead to the interesting…
Heterostructures made from 2D transition-metal dichalcogenides are known as ideal platforms to explore excitonic phenomena ranging from correlated moir\'e excitons to degenerate interlayer exciton ensembles. So far, it is assumed that the…
Two-dimensional Rydberg atoms are modeled at low temperatures by means of the classical Monte Carlo method. The Coulomb repulsion of charged ions competing with the repulsive van der Waals long-range tail is modeled by a number of…
We report experimental and theoretical studies of MoTe$_2$-MoSe$_2$ heterobilayers with rigid moir\'e superlattices controlled by the twist angle. Using an effective continuum model that combines resonant interlayer electron tunneling with…