Two-dimensional electron gas at the LaAlO<sub>3</sub>/SrTiO<sub>3</sub> inteface with a potential barrier

Stephanovich, V. A.; Dugaev, V. K.; Barnaś, J.

doi:10.1039/c5cp06627a

Cited by 9 publications

(12 citation statements)

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“…Despite intense experimental and theoretical studies, the statistics of tunneling electrons through barriers in such structures remains unclear due to disorder which is inevitably present in such structures [52,53]. The above barriers are technologically realized in inversion semiconductor layers, heterostructures (like perovskite interface LaAlO 3 -SrTiO 3 [54][55][56]), quantum wells or in graphene [52,53,57]. The common formalism for description of electronic states in the above structures is different variations of particle in a potential well prob-lem (see, e.g.…”

Section: Discussionmentioning

confidence: 99%

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

et al. 2016

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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.

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Section: Discussionmentioning

confidence: 99%

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

et al. 2016

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“…One class of such systems is an electronic ensemble, which tunnels through potential barriers in so-called spintronic devices (see [96][97][98] and references therein). One of the realistic examples here is heterostructures like the LaAlO 3 /SrTiO 3 interface [99][100][101]. To describe the experimental data related to above tunneling statistics, fractional derivatives should be introduced in the conventional quantum-mechanical problem of a tunneling particle.…”

Section: A General Considerationsmentioning

confidence: 99%

“…The influence of technologically unavoidable disorder is modeled by the introduction of fractional derivative (−∆) 1/2 instead of ordinary gradient d/dz. Our further notations are as follows [100] s c (z) = s c1 [1 − θ(z)] + s c2 θ(z),…”

Section: A General Considerationsmentioning

confidence: 99%

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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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“…Well-known examples are the interfaces between perovskite oxides [1,2], which may have all the above properties [1,3,4] along with metallic interfacial conductivity [5][6][7][8]. Here we report the first time observation of local superconductivity in the magnetoelectric Pb(Fe 1/2 Sb 1/2 )O 3 (PFS).…”

Section: Introductionmentioning

confidence: 80%

Cluster Superconductivity in the Magnetoelectric Pb(Fe_1/2Sb_1/2)O₃ Ceramics

et al. 2017

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We report the observation of cluster (local) superconductivity in the magnetoelectric Pb(Fe 1/2 Sb 1/2 )O3 ceramics prepared at a hydrostatic pressure of 6 GPa and temperatures 1200-1800 K to stabilize the perovskite phase. The superconductivity is manifested by an abrupt drop of the magnetic susceptibility at the critical temperature Tc ≈ 7 K. Both the magnitude of this drop and Tc decrease with magnetic field increase. Similarly, the low-field paramagnetic absorption measured by EPR spectrometer drops significantly below Tc as well. The observed effects and their critical magnetic field dependence are interpreted as manifestation of the superconductivity and the Meissner effect in metallic Pb nanoclusters existing in the ceramics. Their volume fraction and average size were estimated as 0.1-0.2% and 140-150 nm, respectively. The superconductivity related effects disappear after oxidizing annealing of the ceramics.

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

Cited by 9 publications

References 37 publications

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

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

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

Cluster Superconductivity in the Magnetoelectric Pb(Fe_1/2Sb_1/2)O₃ Ceramics

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

Cited by 9 publications

References 37 publications

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

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

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

Cluster Superconductivity in the Magnetoelectric Pb(Fe1/2Sb1/2)O3 Ceramics

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

Cluster Superconductivity in the Magnetoelectric Pb(Fe_1/2Sb_1/2)O₃ Ceramics