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 ) 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.
Highlights
We study the joint effect of disorder and Coulomb interaction screening on the exciton spectra in two-dimensional (2D) structures
The message of the present paper is that the synergy between the nonlocal screening of 2D Coulomb interaction and disorder in semiconducting surfaces, interfaces, thin films, and multilayers has novel properties, which do not occur either in 2D unscreened ordered case or in 3D one
Our main supposition here is that Laskin’s construction of path integrals with Lévy measure[26] is equivalent to “extraction” of probability density function from fractional Langevin equation and, in turn, to the assumptions made in seminal Andeson paper[32]
Summary
It can be shown that this feature occurs for E2,±2 , E3,±3 and possibly higher excited states This shows that the synergy between disorder and (nonlocal27) screening in two dimensions minimizes the energy (as compared to the ordered unscreened case) for some values of orbital quantum number m. The synergy between screening and strong disorder (like substance amorphization, which is common for semiconductor interfaces, where high mechanical stresses occur) may destroy (either ionize or collapse them, depending on the relation between screening radius ξ , Lévy index μ and orbital quantum number m, see above) the excitons, which may preclude the functionality of the devices like solar cells and/or light emitting diodes. This for sure will have a detrimental effect on the optoelectronic and/or spintronic device functionalities
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