Two-dimensional electron gas at the LaAlO3/SrTiO3 inteface with a potential barrier

A spin-orbit coupling-induced two-dimensional electron gas in BiAlO3/SrTiO3 heterostructures

Both LaAlO₃ and BiAlO₃ are isostructural, isoelectronic and band insulators. Therefore, in analogy to the LaAlO₃/SrTiO₃ heterostructure, a quasi two dimensional electron gas (q-2DEG) could be anticipated in BiAlO₃/SrTiO₃ heterostructures. Our density functional theory based scalar relativistic calculations show that BiAlO₃/SrTiO₃ heterostructures remain insulating for a BiAlO₃ film thickness up to 5 unit cells. However, with spin orbit coupling included in the crystal Hamiltonian, we find a thickness dependent insulator to metal transition for BiAlO₃/SrTiO₃ heterostructures. However, unlike the Ti³⁺/Ti⁴⁺ electronic reconstruction in LaAlO₃/SrTiO₃, the conductivity in BiAlO₃/SrTiO₃ is found to originate from the subsurface Bi 6p states. The results suggest that the properties of q-2DEG in BiAlO₃/SrTiO₃ can be controlled using an external electric field, leading to a wide range of solid state applications.

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.

CADEM: calculate X-ray diffraction of epitaxial multilayers

Epitaxial multilayers and superlattice (SL) structures are gaining increasing importance as they offer the opportunity to create artificial crystals with new functionalities. These crystals deviate from the parent bulk compounds not only in terms of the lattice constants but also in the symmetry classification, which renders calculation of their X-ray diffraction (XRD) patterns tedious. Nevertheless, XRD is essential to get information on the multilayer/SL structure such as, for example, out-of-plane lattice constants, strain relaxation and period length of the crystalline SL. This article presents a powerful yet simple program, based on the general one-dimensional kinematic X-ray diffraction theory, which calculates the XRD patterns of tailor-made multilayers and thus enables quantitative comparison of measured and calculated XRD data. As the multilayers are constructed layer by layer, the final material stack can be entirely arbitrary. Moreover, CADEM is very flexible and can be straightforwardly adapted to any material system. The source code of CADEM is available as supporting material for this article.

Lévy flights in an infinite potential well as a hypersingular Fredholm problem

We study Lévy flights with arbitrary index 0<μ≤2 inside a potential well of infinite depth. Such a problem appears in many physical systems ranging from stochastic interfaces to fracture dynamics and multifractality in disordered quantum systems. The major technical tool is a transformation of the eigenvalue problem for initial fractional Schrödinger equation into that for Fredholm integral equation with hypersingular kernel. The latter equation is then solved by means of expansion over the complete set of orthogonal functions in the domain D, reducing the problem to the spectrum of a matrix of infinite dimensions. The eigenvalues and eigenfunctions are then obtained numerically with some analytical results regarding the structure of the spectrum.