The influence of Coulomb interaction screening on the excitons in disordered two-dimensional insulators

Abstract

We study the joint effect of disorder and Coulomb interaction screening on the exciton spectra in two-dimensional (2D) structures. These can be van der Waals structures or heterostructures of organic (polymeric) semiconductors as well as inorganic substances like transition metal dichalcogenides. We consider 2D screened hydrogenic problem with Rytova–Keldysh interaction by means of so-called fractional Scrödinger equation. Our main finding is that above synergy between screening and disorder either destroys the exciton (strong screening) or promote the creation of a bound state, leading to its collapse in the extreme case. Our second finding is energy levels crossing, i.e. the degeneracy (with respect to index $$\mu $$ μ ) of the exciton eigenenergies at certain discrete value of screening radius. Latter effects may also be related to the quantum manifestations of chaotic exciton behavior in above 2D semiconductor structures. Hence, they should be considered in device applications, where the interplay between dielectric screening and disorder is important.

Stabilization of 1D Solitons By Fractional Derivatives In Systems With Quintic Nonlinearity

“…where we have already substituted y 0 (9). The properties of operator L in (21) are already known, see, e.g. [27].…”

“…[27]. This means that we can look for solution of the equations for perturbative corrections (21) in the form of expansion over the eigenfunctions of operator L. But as this operator has also continuous spectrum, latter approach becomes much less profitable than simple method of variations of parameters, known from classical theory of linear differential equations, see, e.g. [28].…”

“…In other words, at α = α cr = 2/3 we have "fractionality collapse" of the soliton. We may speculate here, that as Lévy index α can be viewed as a measure of disorder in a system (see [3,19,20,21] and references therein; the more α deviates from 2, the stronger is the disorder), the value α cr = 2/3 may be regarded as some threshold disorder strength, at which the solitons cease to exist in a system. Really, at α < α cr , our iterative process of the numerical solution diverges so that no localized solutions of the equation ( 7) could be found.…”

“…In the linear regime, the 1D problems of fractional quantum well [17] and quantum oscillator [18] had been solved. Possible physical realizations of 2D [19] and 3D hydrogen atom [20] as well as 2D hydrogen atom with Rytova-Keldysh (screened) interaction [21] had been pointed out along with solutions of corresponding problems. It has been speculated there (see Ref.…”

“…It has been speculated there (see Ref. [21]) that as strong (like substance amorphization) disorder is usually associated with non-Gaussian probability distributions, the fractional Schrödinger equation gives the simple phenomenological description of corresponding strongly disordered quantum system. In this case, as Lévy index α is responsible for the deviation of the underlying system trajectories from Gaussian ones, this quantity plays a role of a phenomenological descriptor of the degree of disorder.…”