Large bulk band gap is critical for application of the quantum spin Hall (QSH) insulator or two dimensional (2D) topological insulator (TI) in spintronic device operating at room temperature (RT). Based on the first-principles calculations, here we predict a group of 2D topological insulators BiX/SbX (X = H, F, Cl, and Br) monolayers with extraordinarily large bulk gaps from 0.32 to a record value of 1.08 eV. These giant-gaps are entirely due to the result of strong spin-orbit interaction related to px and py orbitals of Bi/Sb atoms around the two valley K and K of honeycomb lattice, which is different significantly from the one consisted of pz orbital just like in graphene/silicene. The topological characteristic of BiX/SbX monolayers is confirmed by the calculated nontrivial Z2 index and an explicit construction of the low energy effective Hamiltonian in these systems. We show that the honeycomb structures of BiX monolayers remain stable even at a temperature of 600 K. These features make the giant-gap TIs BiX/SbX monolayers an ideal platform to realize many exotic phenomena and fabricate new quantum devices operating at RT. Furthermore, biased BiX/SbX monolayers become a quantum valley Hall insulator, showing valley-selective circular dichroism.
We explore the cosmological implications of five modified gravity (MG) models by using the recent cosmological observational data, including the recently released SNLS3 type Ia supernovae sample, the cosmic microwave background anisotropy data from the Wilkinson Microwave Anisotropy Probe 7-yr observations, the baryon acoustic oscillation results from the Sloan Digital Sky Survey data release 7, and the latest Hubble constant measurement utilizing the Wide Field Camera 3 on the Hubble Space Telescope. The MG models considered include the Dvali-Gabadadze-Porrati(DGP) model, two $f(R)$ models, and two $f(T)$ models. We find that compared with the $Lambda$CDM model, MG models can not lead to a appreciable reduction of the $chi^2_{min}$. The analysis of AIC and BIC shows that the simplest cosmological constant model($Lambda$CDM) is still most preferred by the current data, and the DGP model is strongly disfavored. In addition, from the observational constraints, we also reconstruct the evolutions of the growth factor in these models. We find that the current available growth factor data are not enough to distinguish these MG models from the $Lambda$CDM model.
In this two-part paper, we consider SDL constructions of optical queues with a limited number of recirculations through the optical switches and the fiber delay lines. We show that the constructions of certain types of optical queues, including linear compressors, linear decompressors, and 2-to-1 FIFO multiplexers, under a simple packet routing scheme and under the constraint of a limited number of recirculations can be transformed into equivalent integer representation problems under a corresponding constraint. Given $M$ and $k$, the problem of finding an emph{optimal} construction, in the sense of maximizing the maximum delay (resp., buffer size), among our constructions of linear compressors/decompressors (resp., 2-to-1 FIFO multiplexers) is equivalent to the problem of finding an optimal sequence ${dbf^*}_1^M$ in $Acal_M$ (resp., $Bcal_M$) such that $B({dbf^*}_1^M;k)=max_{dbf_1^Min Acal_M}B(dbf_1^M;k)$ (resp., $B({dbf^*}_1^M;k)=max_{dbf_1^Min Bcal_M}B(dbf_1^M;k)$), where $Acal_M$ (resp., $Bcal_M$) is the set of all sequences of fiber delays allowed in our constructions of linear compressors/decompressors (resp., 2-to-1 FIFO multiplexers). In Part I, we propose a class of emph{greedy} constructions of linear compressors/decompressors and 2-to-1 FIFO multiplexers by specifying a class $Gcal_{M,k}$ of sequences such that $Gcal_{M,k}subseteq Bcal_Msubseteq Acal_M$ and each sequence in $Gcal_{M,k}$ is obtained recursively in a greedy manner. We then show that every optimal construction must be a greedy construction. In Part II, we further show that there are at most two optimal constructions and give a simple algorithm to obtain the optimal construction(s).
