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The electronic structure and thermodynamic stability of tetragonal $\rm{BiFeO_3}$(001) surfaces have been investigated using density functional theory. In this work, four different structures having different lattice constants with two…
Electronic properties of bilayer and multilayer graphene have generally been interpreted in terms of AB or Bernal stacking. However, it is known that many types of stacking defects can occur in natural and synthetic graphite; rotation of…
We study the semilinear wave equation \[ \partial_t^2 \psi-\Delta \psi=|\psi|^{p-1}\psi \] for $p > 3$ with radial data in three spatial dimensions. There exists an explicit solution which blows up at $t=T>0$ given by \[ \psi^T(t,x)=c_p…
This paper contributes in the first part to the correct understanding of the linear limit in the Schamel equation (S-equation) from the perspective of structure formation in collisionless plasmas. The corresponding modes near equilibrium…
The elastic energy of mixing for multi-component solid solutions is derived by generalizing Eshelby's sphere-in-hole model for binary alloys. By surveying the dependence of the elastic energy on chemical composition and lattice misfit, we…
Silicene is an intriguing silicon allotrope with a honeycomb lattice structure similar to graphene with slightly buckled geometry. Molybdenum disulfide (MoS2), on the other hand, is a significant 2D transition metal dichalcogenide that has…
Using the renormalized-ring-diagram approximation, we study the compressibility of the interacting electrons in bilayer graphene. The compressibility is equivalent to the spin susceptibility apart from a constant factor. The chemical…
We consider magnetic breakdown in twisted bilayer graphene where electrons may hop between semiclassical $k$-space trajectories in different layers. These trajectories within a doubled Brillouin zone constitute a network in which an…
Using first principles calculations, the energetic stability of two-dimensional (2D) binary compounds $XY$ is investigated, where $X$ and $Y$ indicate the metallic element from Li to Pb in the periodic table. Here, 1081 compounds in the…
The structure and dynamics of a range of polystyrene sulphonate comb polyelectrolytes with well defined chain architectures were examined with static light scattering, dynamic light scattering, small angle neutron/X-ray scattering, particle…
The so-called ``symplectic method'' is used for studying the linear stability of a self-gravitating collisionless stellar system, in which the particles are also submitted to an external potential. The system is steady and spherically…
We construct an analytic continuum model to describe the electronic structure and the electron-phonon interaction in twisted bilayer graphenes with arbitrary lattice deformation. Starting from the tight-binding model, we derive the…
We propose a new allotrope of graphane, named as tricycle graphane,with a 4up/2down UUUDUD hydrogenation in each hexagonal carbon ring,which is different from previously proposed allotropes with UUDUUD(boat-1) and UUUUDD (boat-2) types of…
Both even- and odd-numbered neutral carbon clusters Cn (n = 2-10) are systematically studied using the energy minimization method and the modified Brenner potential for the carbon-carbon interactions. Many stable configurations were found…
We present a simple discrete formula for the elastic energy of a bilayer. The formula is convenient for rapidly computing equilibrium configurations of actuated bilayers of general initial shapes. We use maps of principal curvatures and…
There has been considerable controversy regarding the structure of TiBe$_{12}$, which is variously reported as hexagonal and tetragonal. Lattice dynamics simulations based on density functional theory show the tetragonal phase space group…
One novel family of two-dimensional IV-V compounds have been proposed, whose dynamical stabilities and electronic properties have been systematically investigated using the density functional theory. Extending from our previous work, two…
The dynamics of a soft sphere model glass, studied by molecular dynamics, is investigated. The vibrational density of states divided by $\omega^2$ shows a pronounced boson peak. Its shape is in agreement with the universal form derived for…
We explore elemental Si, Ge and Sn free-standing slabs in diamond, clathrate and other competing structures and evaluate their stability by comparing Kohn-Sham total energies at the same atoms/area coverage $\rho$. We find that within 3-6…
The structures, stability, mechanical and electronic properties of a-boron and its twined brother a*-boron have been studied by first-principles calculations. Both a-boron and a*-boron consist of equivalent icosahedra B12 clusters in…