Retrieval of material properties of monolayer transition-metal dichalcogenides from magnetoexciton energy spectra

Reduced exciton mass, polarizability, and dielectric constant of the surrounding medium are essential properties for semiconduction materials, and they can be extracted recently from the magnetoexciton energies. However, the acceptable accuracy of the previously suggested method requires very high magnetic intensity. Therefore, in the present paper, we propose an alternative method of extracting these material properties from recently available experimental magnetoexciton s-state energies in monolayer transition-metal dichalcogenides (TMDCs). The method is based on the high sensitivity of exciton energies to the material parameters in the Rytova-Keldysh model. It allows us to vary the considered material parameters to get the best fit of the theoretical calculation to the experimental exciton energies for the $1s$, $2s$, and $3s$ states. This procedure gives values of the exciton reduced mass and 2D polarizability. Then, the experimental magnetoexciton spectra compared to the theoretical calculation gives also the average dielectric constant. Concrete applications are presented only for monolayers WSe$_2$ and WS$_2$ from the recently available experimental data. However, the presented approach is universal and can be applied to other monolayer TMDCs. The mentioned fitting procedure requires a fast and effective method of solving the Schr\"{o}dinger of an exciton in monolayer TMDCs with a magnetic field. Therefore, we also develop such a method in this study for highly accurate magnetoexciton energies.Comment: 8 pages, 4 figures, 4 table

On approximating the rank of graph divisors

Baker and Norine initiated the study of graph divisors as a graph-theoretic analogue of the Riemann-Roch theory for Riemann surfaces. One of the key concepts of graph divisor theory is the rank of a divisor on a graph. The importance of the rank is well illustrated by Baker’s Specialization lemma, stating that the dimension of a linear system can only go up under specialization from curves to graphs, leading to a fruitful interaction between divisors on graphs and curves. Due to its decisive role, determining the rank is a central problem in graph divisor theory. Kiss and T´othm´eresz reformulated the problem using chip-firing games, and showed that computing the rank of a divisor on a graph is NP-hard via reduction from the Minimum Feedback Arc Set problem. In this paper, we strengthen their result by establishing a connection between chip-firing games and the Minimum Target Set Selection problem. As a corollary, we show that the rank is difficult to approximate to within a factor of O(2log1−ε n) for any ε > 0 unless P = N P . Furthermore, assuming the Planted Dense Subgraph Conjecture, the rank is difficult to approximate to within a factor of O(n1/4−ε) for any ε > 0

Combinatorial generation via permutation languages. I. Fundamentals

In this work we present a general and versatile algorithmic framework for exhaustively generating a large variety of different combinatorial objects, based on encoding them as permutations. This approach provides a unified view on many known results and allows us to prove many new ones. In particular, we obtain the following four classical Gray codes as special cases: the Steinhaus-Johnson-Trotter algorithm to generate all permutations of an $n$-element set by adjacent transpositions; the binary reflected Gray code to generate all $n$-bit strings by flipping a single bit in each step; the Gray code for generating all $n$-vertex binary trees by rotations due to Lucas, van Baronaigien, and Ruskey; the Gray code for generating all partitions of an $n$-element ground set by element exchanges due to Kaye. We present two distinct applications for our new framework: The first main application is the generation of pattern-avoiding permutations, yielding new Gray codes for different families of permutations that are characterized by the avoidance of certain classical patterns, (bi)vincular patterns, barred patterns, boxed patterns, Bruhat-restricted patterns, mesh patterns, monotone and geometric grid classes, and many others. We also obtain new Gray codes for all the combinatorial objects that are in bijection to these permutations, in particular for five different types of geometric rectangulations, also known as floorplans, which are divisions of a square into $n$ rectangles subject to certain restrictions. The second main application of our framework are lattice congruences of the weak order on the symmetric group~$S_n$. Recently, Pilaud and Santos realized all those lattice congruences as $(n-1)$-dimensional polytopes, called quotientopes, which generalize hypercubes, associahedra, permutahedra etc. Our algorithm generates the equivalence classes of each of those lattice congruences, by producing a Hamilton path on the skeleton of the corresponding quotientope, yielding a constructive proof that each of these highly symmetric graphs is Hamiltonian. We thus also obtain a provable notion of optimality for the Gray codes obtained from our framework: They translate into walks along the edges of a polytope

Drawings of Complete Multipartite Graphs up to Triangle Flips

For a drawing of a labeled graph, the rotation of a vertex or crossing is the cyclic order of its incident edges, represented by the labels of their other endpoints. The extended rotation system (ERS) of the drawing is the collection of the rotations of all vertices and crossings. A drawing is simple if each pair of edges has at most one common point. Gioan's Theorem states that for any two simple drawings of the complete graph Kn with the same crossing edge pairs, one drawing can be transformed into the other by a sequence of triangle flips (a.k.a. Reidemeister moves of Type 3). This operation refers to the act of moving one edge of a triangular cell formed by three pairwise crossing edges over the opposite crossing of the cell, via a local transformation. We investigate to what extent Gioan-type theorems can be obtained for wider classes of graphs. A necessary (but in general not sufficient) condition for two drawings of a graph to be transformable into each other by a sequence of triangle flips is that they have the same ERS. As our main result, we show that for the large class of complete multipartite graphs, this necessary condition is in fact also sufficient. We present two different proofs of this result, one of which is shorter, while the other one yields a polynomial time algorithm for which the number of needed triangle flips for graphs on n vertices is bounded by O(n16). The latter proof uses a Carathéodory-type theorem for simple drawings of complete multipartite graphs, which we believe to be of independent interest. Moreover, we show that our Gioan-type theorem for complete multipartite graphs is essentially tight in the following sense: For the complete bipartite graph Km, n minus two edges and Km, n plus one edge for any m, n ≥ 4, as well as Kn minus a 4-cycle for any n ≥ 5, there exist two simple drawings with the same ERS that cannot be transformed into each other using triangle flips. So having the same ERS does not remain sufficient when removing or adding very few edges

Characterization of Single-Shot Attosecond Pulses with Angular Streaking Photoelectron Spectra

Most of the traditional attosecond pulse retrieval algorithms are based on a so-called attosecond streak camera technique, in which the momentum of the electron is shifted by an amount depending on the relative time delay between the attosecond pulse and the streaking infrared pulse. Thus, temporal information of the attosecond pulse is encoded in the amount of momentum shift in the streaked photoelectron momentum spectrogram S(p, τ), where p is the momentum of the electron along the polarization direction and τ is the time delay. An iterative algorithm is then employed to reconstruct the attosecond pulse from the streaking spectrogram. This method, however, cannot be applied to attosecond pulses generated from free-electron x-ray lasers where each single shot is different and stochastic in time. However, using a circularly polarized infrared laser as the streaking field, a two (or three)-dimensional angular streaking electron spectrum can be used to retrieve attosecond pulses for each shot, as well as the time delay with respect to the circularly polarized IR field. Here we show that a retrieval algorithm previously developed for the traditional streaking spectrogram can be modified to efficiently characterize single-shot attosecond pulses. The methods have been applied to retrieve 188 single shots from recent experiments. We analyze the statistical behavior of these 188 pulses in terms of pulse duration, bandwidth, pulse peak energy, and time delay with respect to the IR field. The retrieval algorithm is efficient and can be easily used to characterize a large number of shots in future experiments for attosecond pulses at free-electron x-ray laser facilities

Resist materials for 157-nm microlithography: an update

Fluorocarbon polymers and siloxane-based polymers have been identified as promising resist candidates for 157 nm material design because of their relatively high transparency at this wavelength. This paper reports our recent progress toward developing 157 nm resist materials based on the first of these two polymer systems. In addition to the 2-hydroxyhexafluoropropyl group, (alpha) -trifluoromethyl carboxylic acids have been identified as surprisingly transparent acidic functional groups. Polymers based on these groups have been prepared and preliminary imaging studies at 157 nm are described. 2-Trifluoromethyl-bicyclo[2,2,1] heptane-2-carboxylic acid methyl ester derived from methyl 2-(trifluoromethyl)acrylate was also prepared and gas-phase VUV measurements showed substantially improved transparency over norbornane. This appears to be a general characteristic of norbornane-bearing geminal electron-withdrawing substituents on the 2 carbon bridge. Unfortunately, neither the NiII nor PdII catalysts polymerize these transparent norbornene monomers by vinyl addition. However, several new approaches to incorporating these transparent monomers into functional polymers have been investigated. The first involved the synthesis of tricyclononene (TCN) monomers that move the bulky electron withdrawing groups further away from the site of addition. The hydrogenated geminally substituted TCN monomer still has far better transparency at 157 nm than norbornane. The second approach involved copolymerizing the norbornene monomers with carbon monoxide. The third approach involved free-radical polymerization of norbornene monomers with tetrafluoroethylene and/or other electron-deficient comonomers. All these approaches provided new materials with encouraging absorbance at 157 nm. The lithographic performance of some of these polymers is discussed

Enzyme-linked immunoassay for dengue virus IgM and IgG antibodies in serum and filter paper blood

BACKGROUND: The reproducibilty of dengue IgM and IgG ELISA was studied in serum and filter paper blood spots from Vietnamese febrile patients. METHODS: 781 pairs of acute (t0) and convalescent sera, obtained after three weeks (t3) and 161 corresponding pairs of filter paper blood spots were tested with ELISA for dengue IgG and IgM. 74 serum pairs were tested again in another laboratory with similar methods, after a mean of 252 days. RESULTS: Cases were classified as no dengue (10 %), past dengue (55%) acute primary (7%) or secondary (28%) dengue. Significant differences between the two laboratories' results were found leading to different diagnostic classification (kappa 0.46, p < 0.001). Filter paper results correlated poorly to serum values, being more variable and lower with a mean (95% CI) difference of 0.82 (0.36 to 1.28) for IgMt3, 0.94 (0.51 to 1.37) for IgGt0 and 0.26 (-0.20 to 0.71) for IgGt3. This also led to differences in diagnostic classification (kappa value 0.44, p < 0.001) The duration of storage of frozen serum and dried filter papers, sealed in nylon bags in an air-conditioned room, had no significant effect on the ELISA results. CONCLUSION: Dengue virus IgG antibodies in serum and filter papers was not affected by duration of storage, but was subject to inter-laboratory variability. Dengue virus IgM antibodies measured in serum reconstituted from blood spots on filter papers were lower than in serum, in particular in the acute phase of disease. Therefore this method limits its value for diagnostic confirmation of individual patients with dengue virus infections. However the detection of dengue virus IgG antibodies eluted from filter paper can be used for sero-prevalence cross sectional studies