Energy-level repulsion by spin-orbit coupling in two-dimensional Rydberg excitons

Stephanovich, V. A.; Sherman, E. Ya.; Zinner, N. T.; Marchukov, Oleksandr V.

doi:10.1103/physrevb.97.205407

Cited by 22 publications

(17 citation statements)

References 29 publications

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“…This might point to the possible chaotic features of exciton motion in the above 2D dielectric structures, especially in the presence of spin-orbit interaction 63 . The point is that recently such chaotic features have been found in the excitonic spectra of 2D structures with unscreened Coulomb interaction, but with the inclusion of Rashba spin–orbit interaction 64 , 65 . In context of free electrons and holes, the role of latter interaction in 2D electron gas confined in GaAS quantum well had been studied in 66 .…”

Section: Discussionmentioning

confidence: 93%

“…Namely, the spin–orbit interaction term can be added to the corresponding fractional Schrödinger equation. In this case, the solution will be more sophisticated as the wave function will be spinor now 65 although the problem can possibly be solved in the momentum space similar to the present consideration. Such a problem turns out to be extremely important for the above classes of substances 67 where chaos can even disrupt the functionality of corresponding optoelectronic and/or photovoltaic devices.…”

Section: Discussionmentioning

confidence: 99%

“…Such a problem turns out to be extremely important for the above classes of substances 67 where chaos can even disrupt the functionality of corresponding optoelectronic and/or photovoltaic devices. It has been shown 65 that the description utilizing the “ordinary” (i.e. that both with conventional Laplacian and unscreened Coulomb interaction) hydrogenic problem does not show strong quantum chaotic features like non-Poissonian energy level statistics, see, e.g., 68 .…”

Section: Discussionmentioning

confidence: 99%

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

Кириченко

Stephanovich

2021

Sci Rep

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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.

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Section: Discussionmentioning

confidence: 93%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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

Кириченко

Stephanovich

2021

Sci Rep

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“…Namely, the chaotic behavior has been obtained explicitly in the form of "messy" electronic trajectories [105]. At the same time, in the quantized version only weak effects like energy levels repulsion have been revealed [106]. It is tempting to expose the quantum chaotic features (along with direct quantum trajectories simulations) of this problem by substitution of the ordinary 2D Laplacian by the fractional one in the Schrödinder equation (78).…”

Section: A General Considerationsmentioning

confidence: 99%

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

Garbaczewski

Stephanovich

2019

Phys. Rev. E

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The fractional Laplacian (−∆) 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 holds true not only for each specific choice of the process behavior at the boundary (like e.g. absorbtion, reflection, conditioning or boundary taboos), but extends as well to its particular technical implementation (Dirchlet, 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 unambigous 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. That 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 byproduct of our fractional spectral analysis, with reference to Neumann boundary conditions, we discuss disordered semiconducting heterojunctions as the bounded domain problem. I. MOTIVATIONBrownian motion in a bounded domain is a classic problem with an ample coverage in the literature, specifically concerning the absorbing (Dirichlet) and reflecting (Neumann) boundary data (for the present purpose we disregard other boundary data choices). A coverage concerning their physical relevance is enormous as well [1,2].Anticipating further discussion, we quite inentionally point out source papers dealing with reflected Brownian motion, [3] and exposing at some length the method of eigenfuction expansions for the reflected and other boundarydata problems, [4]- [8], c.f. also [9]. The latter method is as well an indispensable tool in the analysis of spectral properties of fractional Laplacians and related jump-type processes in bounded domains. Its direct link with well developed theory of heat semigroups for jump-type processes (mostly these with absorpion/killing) allows to address the statistics of exits from the domain, like e.g. the first and mean first exit times, large time behavior, stationarity issues, probability of survival and its asymptotic decay, c.f.[10]- [15]. Compare e.g. also [16,17] (Brownian case) and [19][20][21] (Lévy-stable case), where the role of lowest eigenstates and eigenvalues (thence eigenvalue gaps) of the motion generator has appeared to be vital for the description of decay rates of killed stochastic processes. The spectral data of motion generators are relevant for quantifying long-living processes in a spatial...

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“…where k is now the 3D vector and parameter k 0 is again related to eigenenergy by Eq. (11). The solution of 3D problem can be sought of in the form of a decomposition by radial R nlµ (k) and angular parts…”

Section: Discussionmentioning

confidence: 99%

On the discreet spectrum of fractional quantum hydrogen atom in two dimensions

Stephanovich¹

2019

Phys. Scr.

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We consider a fractional generalization of two-dimensional (2D) quantum-mechanical Kepler problem corresponding to 2D hydrogen atom. Our main finding is that the solution for discreet spectrum exists only for µ > 1 (more specifically 1 < µ ≤ 2, where µ = 2 corresponds to "ordinary" 2D hydrogenic problem), where µ is the Lévy index. We show also that in fractional 2D hydrogen atom, 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. To solve the spectral problem, we pass to the momentum representation, where we apply the variational method. This permits to obtain approximate analytical expressions for eigenvalues and eigenfunctions with very good accuracy. Latter fact has been checked by numerical solution of the problem. We also found the new integral representation (in terms of complete elliptic integrals) of Schrödinger equation for fractional hydrogen atom in momentum space. We point to the realistic physical systems like bulk semiconductors as well as their heterostructures, where obtained results can be used.

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Energy-level repulsion by spin-orbit coupling in two-dimensional Rydberg excitons

Cited by 22 publications

References 29 publications

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

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

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

On the discreet spectrum of fractional quantum hydrogen atom in two dimensions

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