Pairing state in multicomponent superconductors

We use the microscopic weak coupling theory to predict the pairing state in superconductors of cubic, hexagonal, or tetragonal symmetry, where the order parameter is multicomponent, i.e., transforms according to either a 2-dimensional or a 3-dimensional representation of the crystal point group. We show that the superconducting phase usually breaks the time-reversal symmetry for singlet multicomponent superconductors. The superconducting order parameter for triplet superconductors in most cases turns out to be non-magnetic.Comment: 7 page

On the Construction and the Structure of Off-Shell Supermultiplet Quotients

Recent efforts to classify representations of supersymmetry with no central charge have focused on supermultiplets that are aptly depicted by Adinkras, wherein every supersymmetry generator transforms each component field into precisely one other component field or its derivative. Herein, we study gauge-quotients of direct sums of Adinkras by a supersymmetric image of another Adinkra and thus solve a puzzle from Ref.[2]: The so-defined supermultiplets do not produce Adinkras but more general types of supermultiplets, each depicted as a connected network of Adinkras. Iterating this gauge-quotient construction then yields an indefinite sequence of ever larger supermultiplets, reminiscent of Weyl's construction that is known to produce all finite-dimensional unitary representations in Lie algebras.Comment: 20 pages, revised to clarify the problem addressed and solve

D-module Representations of N=2,4,8 Superconformal Algebras and Their Superconformal Mechanics

The linear (homogeneous and inhomogeneous) (k, N, N-k) supermultiplets of the N-extended one-dimensional Supersymmetry Algebra induce D-module representations for the N=2,4,8 superconformal algebras. For N=2, the D-module representations of the A(1,0) superalgebra are obtained. For N=4 and scaling dimension \lambda=0, the D-module representations of the A(1,1) superalgebra are obtained. For $\lambda\neq 0$, the D-module representations of the D(2,1;\alpha) superalgebras are obtained, with $\alpha$ determined in terms of the scaling dimension $\lambda$ according to: $\alpha=-2\lambda$ for k=4, i.e. the (4,4) supermultiplet, $\alpha=-\lambda$ for k=3, i.e. (3,4,1), and $\alpha=\lambda$ for k=1, i.e. (1,4,3). For $\lambda\neq 0$ the (2,4,2) supermultiplet induces a D-module representation for the centrally extended sl(2|2) superalgebra. For N=8, the (8,8) root supermultiplet induces a D-module representation of the D(4,1) superalgebra at the fixed value $\lambda=1/4$. A Lagrangian framework to construct one-dimensional, off-shell, superconformal invariant actions from single-particle and multi-particles D-module representations is discussed. It is applied to explicitly construct invariant actions for the homogeneous and inhomogeneous N=4 (1,4,3) D-module representations (in the last case for several interacting supermultiplets of different chirality).Comment: 22 page

On Supergroups with Odd Clifford Parameters and Supersymmetry with Modified Leibniz Rule

We investigate supergroups with Grassmann parameters replaced by odd Clifford parameters. The connection with non-anticommutative supersymmetry is discussed. A Berezin-like calculus for odd Clifford variables is introduced. Fermionic covariant derivatives for supergroups with odd Clifford variables are derived. Applications to supersymmetric quantum mechanics are made. Deformations of the original supersymmetric theories are encountered when the fermionic covariant derivatives do not obey the graded Leibniz property. The simplest non-trivial example is given by the N=2 SQM with a real $(1,2,1)$ multiplet and a cubic potential. The action is real. Depending on the overall sign ("Euclidean" or "Lorentzian") of the deformation, a Bender-Boettcher pseudo-hermitian hamiltonian is encountered when solving the equation of motion of the auxiliary field. A possible connection of our framework with the Drinfeld twist deformation of supersymmetry is pointed out.Comment: Final version to be published in Int. J. Mod. Phys. A; 20 page

Twist Deformation of Rotationally Invariant Quantum Mechanics

Non-commutative Quantum Mechanics in 3D is investigated in the framework of the abelian Drinfeld twist which deforms a given Hopf algebra while preserving its Hopf algebra structure. Composite operators (of coordinates and momenta) entering the Hamiltonian have to be reinterpreted as primitive elements of a dynamical Lie algebra which could be either finite (for the harmonic oscillator) or infinite (in the general case). The deformed brackets of the deformed angular momenta close the so(3) algebra. On the other hand, undeformed rotationally invariant operators can become, under deformation, anomalous (the anomaly vanishes when the deformation parameter goes to zero). The deformed operators, Taylor-expanded in the deformation parameter, can be selected to minimize the anomaly. We present the deformations (and their anomalies) of undeformed rotationally-invariant operators corresponding to the harmonic oscillator (quadratic potential), the anharmonic oscillator (quartic potential) and the Coulomb potential.Comment: 20 page

Comparative Analysis of the Electronic Energy Structure of Nanocrystalline Polymorphs of Y2O3 Thin Layers: Theory and Experiments

The results of fabrication and characterization of atomic structure of nanocrystalline thin layers of Y2O3 in cubic and monoclinic phases is reported. Experimental data demonstrate crystalline ordering in nanocrystalline films with average grain size of ~10-14 nm both for cubic and monoclinic studied structures. Density Functional Theory (DFT) based simulations demonstrate insignificant differences of electronic structure of these phases in the bulk and on the surfaces. Theoretical modeling also pointed out the significant broadening of valence and conductive bands caused by means of energy levels splitting in agreement with experimental data (X-ray photoelectron and photoluminescence spectra). The presence of various intrinsic and extrinsic defects (including surface adsorption of carbon mono- and dioxide) does not promote visible changes in electronic structure of Y2O3 surface for both studied phases. Optical absorption and luminescence measurements indicate insignificant bandgap reduction of Y2O3 nanocrystalline layers and the very little contribution from defect states. Simulation of extrinsic compression and expanding demonstrate stability of the electronic structure of nanocrystalline Y2O3 even under significant strain. Results of comprehensive studies demonstrate that yttrium oxide based nanocrystalline layers are prospective for various optical applications as a stable material.Comment: 24 pages, 13 figures, accepted to Applied Surface Scienc

Uncommon 2D Diamond-like Carbon Nanodots Derived from Nanotubes: Atomic Structure, Electronic States and Photonic Properties

In this article, we report the results of relatively facile fabrication of carbon nanodots from single-walled and multi-walled carbon nanotubes (SWCNT and MWCNT). The results of X-ray photoelectron spectroscopy (XPS) and Raman measurements show that the obtained carbon nanodots are quasi-two-dimensional objects with a diamond-like structure. Based on the characterization results, a theoretical model of synthesized carbon nanodots was developed. The measured absorption spectra demonstrate the similarity of the local atomic structure of carbon nanodots synthesized from single-walled and multi-walled carbon nanotubes. However, the photoluminescence (PL) spectra of nanodots synthesized from both sources turned out to be completely different. Carbon dots fabricated from MWCNTs exhibit PL spectra similar to nanoscale carbon systems with sp3 hybridization and a valuable edge contribution. At the same time nanodots synthesized from SWCNTs exhibit PL spectra which are typical for quantum dots with an estimated size of ~0.6-1.3 nm.Comment: 22 pages, 9 figures, to appear in PCC

The ways to improve the energy conversion efficiency in erbium-doped Gd 2 O 3 nanoparticles

The basic requirements for the crystal lattice and defectiveness of Gd 2 O 3 matrix as well as for the concentration of Er 3+ dopants to achieve the enhanced parameters of energy conversion in Gd 2 O 3 :Er nanoparticles are summarized. The obtained data allow to optimize and improve the functional characteristics of Gd 2 O 3 :Er-based down-conversion layers applying in solar cells. © 2018 Institute of Physics Publishing. All rights reserved.The work has been funded by the Ministry of Education and Science of the Russian Federation (Government task №3.1485.2017/4.6)