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Biological cells in soft materials can be modeled as anisotropic force contraction dipoles. The corresponding elastic interaction potentials are long-ranged ($\sim 1/r^3$ with distance $r$) and depend sensitively on elastic constants,…
Using density functional theory (DFT), we investigate mechanical properties of a few 2D metal-organic frameworks (MOFs) and covalent-organic frameworks (COFs) having Dirac and flat bands. These porous materials have become a subject of…
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…
A controllable soft solid is realised in vortex matter in a type II superconductor. The two-dimensional unit cell area can be varied by a factor of $10^4$ in the solid phase, without a change of crystal symmetry offering easy exploration of…
Moire superlattices in twisted bilayer graphene (TBG) and its derived structures can host exotic correlated quantum phenomena because the narrow moire flat minibands in those systems effectively enhance the electron-electron interaction.…
Two dimensional (2D) layered materials have recently gained renewed interest due to their exotic electronic properties along with high specific surface area. The prospects of exploiting these properties in sensing, catalysis, energy…
Mechanical metamaterials are periodic lattice structures with complex unit cell architectures that can achieve extraordinary mechanical properties beyond the capability of bulk materials. A new class of metamaterials is proposed, whose…
The Luttinger liquid (LL) model of one-dimensional (1D) electronic systems provides a powerful tool for understanding strongly correlated physics including phenomena such as spin-charge separation. Substantial theoretical efforts have…
Patterning and defect engineering are key methods to tune 2D materials' properties. However, generating 2D periodic patterns of point defects in 2D materials has been elusive until now, despite the well-established methods for creating…
We have studied theoretically, using density functional theory, several materials properties when going from one C layer in graphene to two and three g raphene layers and on to graphite. The properties we have focused on are the elastic…
Twisted 2D bilayer materials are created by artificial stacking of two monolayer crystal networks of 2D materials with a desired twisting angle $\theta$. The material forms a moir\'e superlattice due to the periodicity of both top and…
Homogenization in linear elliptic problems usually assumes coercivity of the accompanying Dirichlet form. In linear elasticity, coercivity is not ensured through mere (strong) ellipticity so that the usual estimates that render…
Semiconducting transition metal dichalcogenides (TMDs), such as MoSe$_2$ and WSe$_2$, exhibit unique optical and electronic properties. Vertical stacking of layers of one or more TMDs, to create heterostructures, has expanded the fields of…
The trade-off between strength and ductility has plagued the design of macroscopic assemblies of two-dimensional materials for a long time. In order to break the strength-ductility paradox, the design of self-folded two-dimensional…
Two-dimensional multi-layer materials with an induced moir\'e pattern, either due to strain or relative twist between layers, provide a versatile platform for exploring strongly correlated and topological electronic phenomena. While these…
Quantum confinement endows two-dimensional (2D) layered materials with exceptional physics and novel properties compared to their bulk counterparts. Although certain two- and few-layer configurations of graphene have been realized and…
The electronic band structure of crystals is generally influenced by the periodic arrangement of their constituent atoms. Specifically, the emerging two-dimensional (2D) layered structures have shown different band structures with respect…
Elastic wave manipulation is important in a wide variety of scales in applications including information processing in tiny elastic devices and noise control in big solid structures. The recent emergence of topological materials opens a new…
We present an analytical model to investigate the mechanics of 2-dimensional lattices composed of elastic beams of non-uniform cross-section. Our approach is based on reducing a lattice to a single beam subject to the action of a set of…
The rapidly growing class of atomically thin and tunable van der Waals materials is intensely investigated both in the context of fundamental science and for new technologies. There is in this connection a widespread need for new ways to…