Related papers: An Existence Criterion for Low-Dimensional Materia…
Two-dimensional (2D) metallic lattices with kagome topology provide a unique platform for exploring the interplay between geometric frustration, reduced coordination, and lattice stability in elemental systems. Motivated by the recent…
Nanopores in two-dimensional (2D) materials, including graphene, can be used for a variety of applications, such as gas separations, water desalination, and DNA sequencing. So far, however, all plausible isomeric shapes of graphene…
We establish various qualitative properties of liquid Lane-Emden stars in $\mathbb{R}^d$, including bounds for its density profile $\rho$ and radius $R$. Using them we prove that against radial perturbations, the liquid Lane-Emden stars are…
In this note, we show that the solution to the Dirichlet problem for the minimal surface system in any codimension is unique in the space of distance-decreasing maps. This follows as a corollary of the following stability theorem: if a…
Silicene, a monolayer of silicon atoms tightly packed into a two-dimensional honeycomb lattice, is the challenging hypothetical reflection in the silicon realm of graphene, a one-atom thick graphite sheet, presently the hottest material in…
Since its discovery in 2004, graphene has attracted the interest of the scientific community due to its excellent properties of high carrier mobility, flexibility, strong light-matter interaction and broadband absorption. Despite of its…
We review the state of the art and recently obtained theoretical and experimental results for two- and three-dimensional (2D and 3D) solitons and related states, such as quantum droplets, in optical systems, atomic Bose-Einstein condensates…
We calculate mean square deviations for crystals in one and two dimensions. For the two dimensional lattices, we consider several distinct geometries (i.e. square, triangular, and honeycomb), and we find the same essential phenomena for…
Graphene, one of the strongest materials ever discovered, triggered the exploration of many 2D materials in the last decade. However, the successful synthesis of a stable nanomaterial requires a rudimentary understanding of the relationship…
Carbon-based materials have attracted great attention due to their exceptional structural diversity and wide-ranging applications. Recently, a new two-dimensional carbon allotrope, named pentagraphene (PG), was proposed. In this study, we…
Designing new 2D systems with tunable properties is an important subject for science and technology. Starting from graphene, we developed an algorithm to systematically generate 2D carbon crystals belonging to the family of graphdiynes…
Single-atom-thick two-dimensional materials such as graphene usually have a hexagonal lattice while the square-planar lattice is uncommon in the family of two-dimensional materials. Here, we demonstrate that single-atom-thick transition…
Two-dimensional (2D) materials exhibit a number of improved mechanical, optical, electronic properties compared to their bulk counterparts. The absence of dangling bonds in the cleaved surfaces of these materials allows combining different…
Graphene is a 2-dimensional (2D) carbon allotrope with the atoms arranged in a honeycomb lattice. The low-energy electronic excitations in this 2D crystal are described by massless Dirac fermions that have a linear dispersion relation…
We lay down a nonlinear elastic constitutive framework for the modeling of some 2D crystals of current interest. The 2D crystals we treat are graphene, hexagonal boron nitride and some metal dichalcogenides: molybdenium disulfide (MoS$_2$),…
Fundamental research on two-dimensional (2D) magnetic systems based on van der Waals materials has been gaining traction rapidly since their recent discovery. With the increase of recent knowledge, it has become clear that such materials…
Graphene and graphene-based materials exhibit exceptional optical and electrical properties with great promise for novel applications in light detection. However, several challenges prevent the full exploitation of these properties in…
Trapped substances between a 2D crystal, such as graphene, and an atomically flat substrate, for example, hexagonal boron nitride, give rise to the formation of bubbles. We show that the size, shape and internal pressure inside these…
Two-dimensional (2D) materials display nanoscale dynamic ripples that significantly impact their properties. Defects within the crystal lattice are the elementary building blocks to tailor the material's morphology. While some studies have…
Unlike conventional two-dimensional (2D) semiconductor superlattices, moir\'{e} patterns in 2D materials are flexible and their electronic, magnetic, optical, and mechanical properties depend on their topography. Within a…