On the determinant formula in the inverse scattering procedure with a partially known steplike potential

We are concerned with the inverse scattering problem for the full line Schr\"odinger operator $-\partial_x^2+q(x)$ with a steplike potential $q$ a priori known on $\Reals_+=(0,\infty)$. Assuming $q|_{\Reals_+}$ is known and short range, we show that the unknown part $q|_{\Reals_-}$ of $q$ can be recovered by {equation*} q|_{\Reals_-}(x)=-2\partial_x^2\log\det(1+(1+\mathbb{M}_x^+)^{-1}\mathbb{G}_x), {equation*} where $\mathbb{M}_x^+$ is the classical Marchenko operator associated to $q|_{\Reals_+}$ and $\mathbb{G}_x$ is a trace class integral Hankel operator. The kernel of $\mathbb{G}_x$ is explicitly constructed in term of the difference of two suitably defined reflection coefficients. Since $q|_{\Reals_-}$ is not assumed to have any pattern of behavior at $-\infty$, defining and analyzing scattering quantities becomes a serious issue. Our analysis is based upon some subtle properties of the Titchmarsh-Weyl $m$-function associated with $\Reals_-$

Phenomenological three-cluster model of 6^{6}He

By using the method of hyperspherical functions within the appropriate for this method K_{\min} approximation, the simple three-cluster model for description of the ground state and the continuous spectrum states of \6He is developed. It is shown that many properties of \6He (its large rms radius and large values of the matrix elements of electromagnetic transitions from the ground state into the continuous spectrum) follow from the fact that the potential energy of \6He system decreases very slowly (as \rho^{-3}) and the binding energy is small

Variation of the character of spin-orbit interaction by Pt intercalation underneath graphene on Ir(111)

Under the terms of the Creative Commons Attribution License 3.0 (CC-BY).-- et al.The modification of the graphene spin structure is of interest for novel possibilities of application of graphene in spintronics. The most exciting of them demand not only high value of spin-orbit splitting of the graphene states, but non-Rashba behavior of the splitting and spatial modulation of the spin-orbit interaction. In this work we study the spin and electronic structure of graphene on Ir(111) with intercalated Pt monolayer. Pt interlayer does not change the 9.3×9.3 superlattice of graphene, while the spin structure of the Dirac cone becomes modified. It is shown that the Rashba splitting of the π state is reduced, while hybridization of the graphene and substrate states leads to a spin-dependent avoided-crossing effect near the Fermi level. Such a variation of spin-orbit interaction combined with the superlattice effects can induce a topological phase in graphene.The work was partially supported by grants of Saint Petersburg State University for scientific investigations (Grants No. 11.38.271.2014, No. 15.61.202.2015 and No. 11.37.634.2013) and Russian Foundation for Basic Research (RFBR) projects (No. 13-02-91327). We acknowledge the financial support of the University of Basque Country UPV/EHU (Grant No. GIC07-IT-756-13), the Departamento de Educacion del Gobierno Vasco, and the Spanish Ministerio de Ciencia e Innovacion (Grant No. FIS2010-19609-C02-01), the Spanish Ministry of Economy and Competitiveness MINECO (Grant No. FIS2013-48286-C2-1-P), and the Tomsk State University Competitiveness Improvement Program.Peer Reviewe

Variation of the character of spin-orbit interaction by Pt intercalation underneath graphene on Ir(111)

The modification of the graphene spin structure is of interest for novel possibilities of application of graphene in spintronics. The most exciting of them demand not only high value of spin-orbit splitting of the graphene states, but non-Rashba behavior of the splitting and spatial modulation of the spin-orbit interaction. In this work we study the spin and electronic structure of graphene on Ir(111) with intercalated Pt monolayer. Pt interlayer does not change the 9.3×9.3 superlattice of graphene, while the spin structure of the Dirac cone becomes modified. It is shown that the Rashba splitting of the π state is reduced, while hybridization of the graphene and substrate states leads to a spin-dependent avoided-crossing effect near the Fermi level. Such a variation of spin-orbit interaction combined with the superlattice effects can induce a topological phase in graphene