Carrier Plasmon Induced Nonlinear Band Gap Renormalization in Two-Dimensional Semiconductors

In reduced-dimensional semiconductors, doping-induced carrier plasmons can strongly couple with quasiparticle excitations, leading to a significant band gap renormalization. We develop a new plasmon-pole theory that efficiently and accurately capture this coupling. Using monolayer molybdenum disulfide (MoS2) as a prototype two-dimensional (2D) semiconductor, we reveal an enhanced band gap renormalization around 400 meV and an unusual nonlinear evolution of its band gap with doping. This 2D prediction significantly differs from the linear behaviors that are common to one-dimensional structures. Our developed approach allows for a quantitative understanding of many-body interactions in general doped 2D semiconductors and paves the way for novel band gap engineering techniques

Multidimensional BSDEs with uniformly continuous coefficients: the general result

In this paper, by introducing a new notion of envelope of the stochastic process, we construct a family of random differential equations whose solutions can be viewed as solutions of a family of ordinary differential equations and prove that the multidimensional backward stochastic differential equations (BSDEs for short) with the general uniformly continuous coefficients are uniquely solvable. As a result, we solve the open problem of multidimensional BSDEs with uniformly continuous coefficients.Comment: 20 page

Superconvergence of Numerical Gradient for Weak Galerkin Finite Element Methods on Nonuniform Cartesian Partitions in Three Dimensions

A superconvergence error estimate for the gradient approximation of the second order elliptic problem in three dimensions is analyzed by using weak Galerkin finite element scheme on the uniform and non-uniform cubic partitions. Due to the loss of the symmetric property from two dimensions to three dimensions, this superconvergence result in three dimensions is not a trivial extension of the recent superconvergence result in two dimensions \cite{sup_LWW2018} from rectangular partitions to cubic partitions. The error estimate for the numerical gradient in the $L^{2}$-norm arrives at a superconvergence order of ${\cal O}(h^r) (1.5 \leq r\leq 2)$ when the lowest order weak Galerkin finite elements consisting of piecewise linear polynomials in the interior of the elements and piecewise constants on the faces of the elements are employed. A series of numerical experiments are illustrated to confirm the established superconvergence theory in three dimensions.Comment: 31 pages, 24 table

Exciton Energy Spectra in Two-Dimensional Graphene Derivatives

The energy spectra and wavefunctions of bound excitons in important two-dimensional (2D) graphene derivatives, i.e., graphyne and graphane, are found to be strongly modified by quantum confinement, making them qualitatively different from the usual Rydberg series. However, their parity and optical selection rules are preserved. Thus a one-parameter modified hydrogenic model is applied to quantitatively explain the ab initio exciton spectra, and allows one to extrapolate the electron-hole binding energy from optical spectroscopies of 2D semiconductors without costly simulations. Meanwhile, our calculated optical absorption spectrum and enhanced spin singlet-triplet splitting project graphyne, an allotrope of graphene, as a candidate for intriguing energy and biomedical applications

ϕϵ\phi_\epsilon-coordinated modules for vertex algebras

We study $\phi_\epsilon$-coordinated modules for vertex algebras, where $\phi_\epsilon$ with $\epsilon$ an integer parameter is a family of associates of the one-dimensional additive formal group. As the main results, we obtain a Jacobi type identity and a commutator formula for $\phi_\epsilon$-coordinated modules. We then use these results to study $\phi_\epsilon$-coordinated modules for vertex algebras associated to Novikov algebras by Primc.Comment: late

Constraining cosmological parameters in FLRW metric with lensed GW+EM signals

We proposed a model-independent method to constrain the cosmological parameters using the Distance Sum Rule of the FLRW metric by combining the time delay distances and the comoving distances through a multi-messenger approach. The time delay distances are measured from lensed gravitational wave~(GW) signals together with their corresponding electromagnetic wave~(EM) counterpart, while the comoving distances are obtained from a parametrized fitting approach with independent supernova observations. With a series of simulations based on Einstein Telescope, Large Synoptic Survey Telescope and The Dark Energy Survey, we find that only 10 lensed GW+EM systems can achieve the constraining power comparable to and even stronger than 300 lensed quasar systems due to more precise time delay from lensed GW signals. Specifically, the cosmological parameters can be constrained to ~$k=0.01_{-0.05}^{+0.05}$ and ~$H_0=69.7_{-0.35}^{+0.35}$ (1$\sigma$). Our results show that more precise time delay measurements could provide more stringent cosmological parameter values, and lensed GW+EM systems therefore can be applied as a powerful tool in the future precision cosmology.Comment: Accepted for publication in The Astrophysical Journa

Effective numerical treatment of sub-diffusion equation with non-smooth solution

In this paper we investigate a sub-diffusion equation for simulating the anomalous diffusion phenomenon in real physical environment. Based on an equivalent transformation of the original sub-diffusion equation followed by the use of a smooth operator, we devise a high-order numerical scheme by combining the Nystrom method in temporal direction with the compact finite difference method and the spectral method in spatial direction. The distinct advantage of this approach in comparison with most current methods is its high convergence rate even though the solution of the anomalous sub-diffusion equation usually has lower regularity on the starting point. The effectiveness and efficiency of our proposed method are verified by several numerical experiments.Comment: 15 pages, 6 figure

Quasiparticle band-edge energy and band offsets of monolayer of molybdenum and tungsten chalcogenide

We report the quasiparticle energy of monolayer of molybdenum and tungsten dichalcogenides, MX2 (M=Mo, W; X=S, Se, Te). Beyond calculating bandgaps, we have achieved converged absolute band energies relative to the vacuum level. Compared with the results from other approaches, the GW calculation reveals substantially larger bandgaps and different absolute band energies because of enhanced many-electron effects. Interestingly, our fully-converged quasiparticle energies ratify the band-gap-center approximation, making it a convenient way to estimate quasiparticle energy. The absolute quasiparticle energies and band offsets obtained in this work are important for designing heterojunction devices and chemical catalysts based on monolayer dichalcogenides

Pressure Tuned Enhancement of Superconductivity and Change of Ground State Properties in LaO0.5F0.5BiSe2 Single Crystals

By using a hydrostatic pressure, we have successfully tuned the ground state and superconductivity in LaO0.5F0.5BiSe2 single crystals. It is found that, with the increase of pressure, the original superconducting phase with Tc about 3.5 K can be tuned to a state with lower Tc, and then a new superconducting phase with Tc about 6.5 K emerges. Accompanied by this crossover, the ground state is switched from a semiconducting state to a metallic one. Accordingly, the normal state resistivity also shows a nonmonotonic change with the external pressure. Furthermore, by applying a magnetic field, the new superconducting state under pressure with Tc about 6.5 K is suppressed, and the normal state reveals a weak semiconducting feature again. These results illustrate a non-trivial relationship between the normal state property and superconductivity in this newly discovered superconducting system.Comment: 6 pages, 4 figure

Provably size-guaranteed mesh generation with superconvergence

The properties and applications of superconvergence on size-guaranteed Delaunay triangulation generated by bubble placement method (BPM), are studied in this paper. First, we derive a mesh condition that the difference between the actual side length and the desired length $h$ is as small as ${\cal O}(h^{1+{\alpha}})$ $({\alpha}>0)$. Second, the superconvergence estimations are analyzed on linear and quadratic finite element for elliptic boundary value problem based on the above mesh condition. In particular, the mesh condition is suitable for many known superconvergence estimations of different equations. Numerical tests are provided to verify the theoretical findings and to exhibit the superconvergence property on BPM-based grids