Optical Absorption by Indirect Excitons in a Transition Metal Dichalcogenide Double Layer

We calculate the binding energy, transition energies, oscillator strength, and absorption coefficient of indirect excitons in transition metal dichalcogenide (TMDC) double layers separated by an integer number of hexagonal boron nitride (h-BN) monolayers. The absorption factor, a dimensionless quantity which gives the fraction of incoming photons absorbed by the indirect excitons in the double layer, is evaluated. The aforementioned optical quantities are obtained for transitions from the ground state to the first two excited states. All quantities are studied as a function of the interlayer separation, which may be experimentally controlled by varying the number of h-BN monolayers between the TMDC layers. Calculations are performed by using the exciton wave function and eigenenergies obtained for the Keldysh potential. For each material, we choose a combination of the exciton reduced mass and the dielectric screening length from the existing literature which give the largest and the smallest indirect exciton binding energy. These combinations of material parameters provide upper and lower bounds on all quantities presented. Our findings can be examined experimentally via two-photon spectroscopy.Comment: 13 pages, 3 figure

Number of surveys required to determine species presence at occupied sites.

<p>Data provided at three levels of certainty, with 95% confidence intervals in parentheses.</p

Naïve occupancy plus estimated occupancy () and detection probabilities () for each data set.

<p> is the probability of detecting a species at an occupied site on at least one of the six survey visits carried out.</p

Number of sites to detect an occupancy decline with a given power.

<p>Number of sites to detect an occupancy decline with a given power.</p

Mean square error (MSE) for the occupancy estimator in the hierarchical/naïve models, and their ratio, obtained from simulations of three “abundance” scenarios: (a) Scenario B1 from [14], (b) Scenario B2 and (c) Scenario B3.

<p>Simulations were run for a range of sample sizes, with <i>S</i> sites and <i>K</i> replicate surveys per site (5000 simulations per case). When , the naïve model was fitted to the data resulting from collapsing the detection/non-detection history into a single record per site (1 if species detected at least once, 0 otherwise). The hierarchical model outperforms the naïve model, being clearly superior in the third example.</p

Ignoring Imperfect Detection in Biological Surveys Is Dangerous: A Response to ‘Fitting and Interpreting Occupancy Models'

<div><p>In a recent paper, Welsh, Lindenmayer and Donnelly (WLD) question the usefulness of models that estimate species occupancy while accounting for detectability. WLD claim that these models are difficult to fit and argue that disregarding detectability can be better than trying to adjust for it. We think that this conclusion and subsequent recommendations are not well founded and may negatively impact the quality of statistical inference in ecology and related management decisions. Here we respond to WLD's claims, evaluating in detail their arguments, using simulations and/or theory to support our points. In particular, WLD argue that both disregarding and accounting for imperfect detection lead to the same estimator performance regardless of sample size when detectability is a function of abundance. We show that this, the key result of their paper, only holds for cases of extreme heterogeneity like the single scenario they considered. Our results illustrate the dangers of disregarding imperfect detection. When ignored, occupancy and detection are confounded: the same naïve occupancy estimates can be obtained for very different true levels of occupancy so the size of the bias is unknowable. Hierarchical occupancy models separate occupancy and detection, and imprecise estimates simply indicate that more data are required for robust inference about the system in question. As for any statistical method, when underlying assumptions of simple hierarchical models are violated, their reliability is reduced. Resorting in those instances where hierarchical occupancy models do no perform well to the naïve occupancy estimator does not provide a satisfactory solution. The aim should instead be to achieve better estimation, by minimizing the effect of these issues during design, data collection and analysis, ensuring that the right amount of data is collected and model assumptions are met, considering model extensions where appropriate.</p></div

Simulated scenarios (marked with asterisk * those also tested by WLD).

<p>For all scenarios we tested all the combinations of the following sampling sizes: sites and replicate surveys per site. The beta distributions below are plotted in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0099571#pone-0099571-g004" target="_blank">Figure 4</a>.</p

RRT_Ngalvez_JAPP

RRT data. First line are the headings. Second column are the RRT results (0 no; 1 yes). Following columns are the identification of the covariables

Mean square error (MSE) for the occupancy estimator in the hierarchical/naïve models, and their ratio, obtained from simulations of (a) Scenario A1 and (b) Scenario A2 (see Table 1 for details).

<p>Simulations were run for a range of sample sizes, with <i>S</i> sites and <i>K</i> replicate surveys per site (5000 simulations per case). When , the naïve model was fitted to the data resulting from collapsing the detection/non-detection history into a single record per site (1 if species detected at least once, 0 otherwise). In the majority of these cases the performance of the hierarchical model was either comparable or considerably superior to that of the naïve model. A ratio <1 indicates that the MSE of the hierarchical model is smaller than in the naïve model.</p

Beta distributions used to generate detectability in the “abundance” scenarios for the different covariate categories.

<p>Lines correspond to (solid), (dashed) and (dotted). Panel (a) displays the probability density functions (pdf) for the distributions used by WLD (Scenario B1) and panel (b) for the distributions used in our Scenarios B2 and B3. The distribution that WLD used for has considerable mass for detectability very close to zero: . Panels (c-d) display the pdf of the probability of detecting the species in at least one of <i>K</i> surveys () at sites (from darker to lighter, lines correspond to ).</p