Graphene Versus MoS2: a Short Review

Graphene and MoS2 are two well-known quasi two-dimensional materials. This review is a comparative survey of the complementary lattice dynamical and mechanical properties of graphene and MoS2. This comparison facilitates the study of graphene/MoS2 heterostructures, which is expected to mitigate the negative properties of each individual constituent.Comment: Frontiers of Physics, published, Focus Revie

Monomial ideals under ideal operations

In this paper, we show for a monomial ideal $I$ of $K[x_1,x_2,\ldots,x_n]$ that the integral closure \ol{I} is a monomial ideal of Borel type (Borel-fixed, strongly stable, lexsegment, or universal lexsegment respectively), if $I$ has the same property. We also show that the $k^{th}$ symbolic power $I^{(k)}$ of $I$ preserves the properties of Borel type, Borel-fixed and strongly stable, and $I^{(k)}$ is lexsegment if $I$ is stably lexsegment. For a monomial ideal $I$ and a monomial prime ideal $P$, a new ideal $J(I, P)$ is studied, which also gives a clear description of the primary decomposition of $I^{(k)}$. Then a new simplicial complex $_J\bigtriangleup$ of a monomial ideal $J$ is defined, and it is shown that $I_{_J\bigtriangleup^{\vee}} = \sqrt{J}$. Finally, we show under an additional weak assumption that a monomial ideal is universal lexsegment if and only if its polarization is a squarefree strongly stable ideal.Comment: 18 page

A tight-binding model for the excitonic band structure of a one-dimensional molecular chain: UV-Vis spectra, Zak phase and topological properties

Recently organic optics becomes a hot topic due to the rapid development of organic light-emitting diodes, organic solar cells, and organic photon detectors. The optical spectra of the molecular semiconductors are difficult to solve an model from first-principles because (i) the very large number of atoms in a unit cell and (ii) the accurate theoretical excited state is still under development. Here we present a tight-binding model of an exciton band structure in a molecular chain. We take into account the intra-molecule and charge-transfer excitation within a molecular dimer in a unit cell, then we apply the tight-binding model by including the coupling between two types of excitations. We not only found that our calculations can explain a body of UV-Vis optical spectra of transition-metal phthalocyanines, but also a one-dimensional excitonic topological band structure if we fine-tune the couplings in a dimerized molecular chain. We have found a large space to obtain the topological Zak phase in the parameter space, in which there is a simple linear relationship between the hopping integrals between cells and within cell.Comment: 5 pages, 5 figure