Chaotization of internal motion of excitons in ultrathin layers by spin-orbit coupling

Spin-orbit-coupled fractional oscillators and trapped Bose-Einstein condensates

We study the ensemble of pseudo-spin 1/2 ultracold bosons, performing Lévy flights, confined in a parabolic potential. The (pseudo-) spin-orbit coupling (SOC) is additionally imposed on these particles. We consider the structure and dynamics of macroscopic pseudospin qubits based on Bose-Einstein condensates, obtained from the above "fractional" bosons. Under "fractional" we understand the substitution of the ordinary second derivative (kinetic energy term) in the Gross-Pitaevskii equation by a so-called fractional Laplacian, characterized by the Lévy index μ. We show that the joint action of interparticle interaction, SOC, and Zeeman splitting in a synthetic magnetic field makes the dynamics of corresponding qubit highly nontrivial with evident chaotic features at both strong interactions and Lévy indices μ→1 when the Lévy trajectories of bosons with long jumps dominated over those derived from ordinary Gaussian distribution, corresponding to μ=2. Using analytical and numerical arguments, we discuss the possibilities to control the above qubit using the synergy of SOC, interaction strength, and "fractionality," characterized by the Lévy index μ.

Screened Coulomb interaction in insulators with strong disorder

We study the effect of disorder on the excitons in a semiconductor with screened Coulomb interaction. Examples are polymeric semiconductors and/or van der Waals structures. In the screened hydrogenic problem, we consider the disorder phenomenologically using the so-called fractional Scrödinger equation. Our main finding is that joint action of screening and disorder either destroys the exciton (strong screening) or enhances the bounding of electron and hole in an exciton, leading to its collapse in the extreme case. Latter effects may also be related to the quantum manifestations of chaotic exciton behavior in the above semiconductor structures. Hence, they should be considered in device applications, where the interplay between dielectric screening and disorder is important. Our theoretical results permit one to predict the various excitonic properties in semiconductor samples with different degrees of disorder and Coulomb interaction screenings.

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

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 [Formula: see text]) 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.

Lévy distributions and disorder in excitonic spectra

We study analytically the spectrum of excitons in disordered semiconductors like transition metal dichalcogenides, which are important for photovoltaic and spintronic applications. We show that ambient disorder exerts a strong influence on the exciton spectra. For example, in such a case, the well-known degeneracy of the hydrogenic problem (related to Runge-Lenz vector conservation) is lifted so that the exciton energy starts to depend on both the principal quantum number n and orbital l. We model the disorder phenomenologically substituting the ordinary Laplacian in the corresponding Schrödinger equation by the fractional one with Lévy index μ, characterizing the degree of disorder. Our variational treatment (corroborated by numerical results) shows that an exciton exists for 1 < μ≤ 2. The case μ = 2 corresponds to the "ordered" hydrogenic problem, while in the opposite case μ = 1 the exciton collapses. The exciton spectrum is dominated by the sample areas with moderate disorder. Our theory permits controlled predictions to be made of the excitonic properties in semiconductor samples with different degrees of disorder.

The influence of disorder on the exciton spectra in two-dimensional structures

We study the role of disorder in the exciton spectra in two-dimensional (2D) semiconductors. These can be heterostructures, thin films and multilayers (so-called van der Waals structures) of organometallic perovskites, transition metal dichalcogenides and other semiconductors for optoelectronic applications. We model the disorder by introduction of a fractional Laplacian (with Lévy index μ, defining the degree of disorder) to the Scrödinger equation with 2D Coulomb potential. Combining analytical and numerical methods, we observe that the exciton exists only for μ > 1, while the point μ = 1 (strongest disorder) corresponds to the exciton collapse. We show also that in the fractional (disordered, corresponding to 1 < μ < 2; μ = 2 corresponds to the ordered case) 2D hydrogenic problem, the orbital momentum degeneracy is lifted so that its energy starts to depend not only on principal quantum number n but also on orbital m. These features can have a profound influence on the lifetime of optically generated excitons in the above 2D semiconductor structures. They should be taken into account while designing the photovoltaic cells, nanolasers and optical spintronics devices, where 2D excitons play a significant role.

Fractional Laplacians in bounded domains: Killed, reflected, censored, and taboo Lévy flights

The fractional Laplacian (-Δ)^{α/2}, α∈(0,2), has many equivalent (albeit formally different) realizations as a nonlocal generator of a family of α-stable stochastic processes in R^{n}. On the other hand, if the process is to be restricted to a bounded domain, there are many inequivalent proposals for what a boundary-data-respecting fractional Laplacian should actually be. This ambiguity not only holds true for each specific choice of the process behavior at the boundary (e.g., absorbtion, reflection, conditioning, or boundary taboos), but extends as well to its particular technical implementation (Dirichlet, Neumann, etc., problems). The inferred jump-type processes are inequivalent as well, differing in their spectral and statistical characteristics, which may strongly influence the ability of the formalism (if uncritically adopted) to provide an unambiguous description of real geometrically confined physical systems with disorder. Specifically that refers to their relaxation properties and the near-equilibrium asymptotic behavior. In the present paper we focus on Lévy flight-induced jump-type processes which are constrained to stay forever inside a finite domain. This refers to a concept of taboo processes (imported from Brownian to Lévy-stable contexts), to so-called censored processes, and to reflected Lévy flights whose status still remains to be unequivocally settled. As a by-product of our fractional spectral analysis, with reference to Neumann boundary conditions, we discuss disordered semiconducting heterojunctions as the bounded domain problem.