Exciton ionization in multilayer transition-metal dichalcogenides

Abstract

Photodetectors and solar cells based on materials with strongly bound excitons rely crucially on field-assisted exciton ionization. We study the ionization process in multilayer transition-metal dichalcogenides (TMDs) within the Mott-Wannier model incorporating fully the pronounced anisotropy of these materials. Using complex scaling, we show that the field-dependence of the ionization process is strongly dependent on orientation. Also, we find that direct and indirect excitons behave qualitatively differently as a result of opposite effective anisotropy of these states. Based on first-principles material parameters, an analysis of several important TMDs reveals WSe 2 and MoSe 2 to be superior for applications relying on ionization of direct and indirect excitons, respectively.

Fast summation of divergent series and resurgent transseries from Meijer- G approximants

“…We will then briefly review alternatives to Padé and Borel-Padé that make use of analytic continuation functions with a built-in branch cut, in particular the hypergeometric resummation method we introduced in Refs. [5][6][7]. After reviewing these other approaches we finally introduce the algorithm to calculate Meijer-G approximants and highlight various properties that make this method well suited to yield inexpensive-and yet accurate-low order approximations to the sum of a divergent series.…”

“…Recently we have introduced hypergeometric resummation-a technique that enables summation on the cut using only a small number of expansion coefficients [5][6][7]46,47]. Various flavors of this technique were applied to a variety of problems with good results: in particular, it was shown how one could use low order data to derive accurate approximations to the decay rate in Stark-type problems [5][6][7].…”

“…Various flavors of this technique were applied to a variety of problems with good results: in particular, it was shown how one could use low order data to derive accurate approximations to the decay rate in Stark-type problems [5][6][7]. Typically the idea is to use hypergeometric functions to analytically continue divergent series.…”

“…The hypergeometric approximants we introduced in Refs. [5][6][7]46] have a number of clear limitations, which we overcome in this work and which we enumerate below:…”

“…This is exemplified by the asymptotic series for the LoSurdo-Stark effect of atoms and molecules where first-and second-order terms match measurements well, but only for very weak electric fields [3], or by high precision calculations of multiloop Feynman diagrams in quantum electrodynamics [4]where the fine-structure constant is small. On the other hand, extracting physically relevant information from the asymptotic series at larger coupling constants calls, almost invariably, for resummation techniques as exemplified by the LoSurdo-Stark effect [5,6] and field assisted excitonic ionization in layered materials [7], anharmonic oscillators in quantum mechanics [8,9], ϕ 4 theory in QFT [10], quantum chromodynamics [11], string perturbation theory [12,13], and diagrammatic Monte Carlo techniques in condensed matter physics [14]. Given the ubiquity of divergent series in physics, research on summation techniques remains an active research area [15,16].…”