Effect of the type I to type II Weyl semimetal topological transition on superconductivity

The influence of recently discovered topological transition between type I and type II Weyl semi-metals on superconductivity is considered. A set of Gorkov equations for weak superconductivity in Weyl semi-metal under topological phase transition is derived and solved. The critical temperature and superconducting gap both have spike in the point the transition point as function of the tilt parameter of the Dirac cone determined in turn by the material parameters like pressure. The spectrum of superconducting excitations is different in two phases: the sharp cone pinnacle is characteristic for a type I, while two parallel almost flat bands, are formed in type II. Spectral density is calculated on both sides of transition demonstrate different weight of the bands. The superconductivity thus can be used as a clear indicator for the topological transformation. Results are discussed in the light of recent experiments.Comment: 13 pages, 5 figure

Chiral universality class of the normal-superconducting and the exciton condensation transition on the surface of topological insulator

New two dimensional systems like surface of topological insulator and graphene offer a possibility to experimentally investigate situations considered "exotic" just a decade ago. One of those is the quantum phase transition of the "chiral" type in electronic systems with relativistic spectrum. Phonon mediated ("conventional") pairing in the Dirac semimetal appearing on the surface of topological insulator leads to transition into a chiral superconducting state, while exciton condensation in these gapless systems has been envisioned long time ago in the physics of the narrow band semiconductors. Starting from the microscopic Dirac Hamiltonian with local attraction or repulsion, the BCS type gaussian approximation is developed in the framework of functional integrals. It is shown that due to an "ultra-relativistic" dispersion relation there is a quantum critical point governing the zero temperature transition to a superconducting or the exciton condensed state. The quantum transitions that have critical exponents very different from the conventional ones. They belong to the chiral universality class. We discuss the application of these results to recent experiments in which surface superconductivity was found in topological insulators and estimate feasibility of the phonon pairing.Comment: 19pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1405.594

Superconductivity in 2D electron gas induced by high energy optical phonon mode and large polarization of the STO substrate

Theory of superconductivity generated in one atomic layer thick two dimensional electron gas by a single flat band of high energy longitudinal optical phonons is considered. The polar dielectric $SrTiO_{3}$ (STO) exhibits such an energetic phonon mode and the 2DEG is created both when one unit cell $FeSe$ layer is grown on its $\left( 100\right)$ surface and on the interface with another dielectric like $LaAlO_{3}$ (LAO). We obtain a quantitative description of both systems solving the gap equation for $T_{c}$ without making use of approximations like the Kirzhnits Ansatz for arbitrary chemical potential $\mu$, electron-phonon coupling $\lambda$ and the phonon frequency $\Omega$, and direct (RPA) electron-electron repulsion strength $\alpha$. The high temperature superconductivity in 1UC$FeSe$/STO is possible due to a combination of three factors: high LO phonon frequency, large electron-phonon coupling $\lambda \sim 0.5$ and huge dielectric constant of the substrate suppression the Coulomb repulsion. It is shown that very low density electron gas in the interfaces is still capable of generating superconductivity of the order of $0.1$ K in LAO/STO. Superconductivity persists even on the band edge $\mu =0$.Comment: 19 pages, 7 figure

Magnetic impurities make superconductivity in 3D Dirac semi-metal triplet

Conventional electron-phonon coupling induces either odd (triplet) or even (singlet) pairing states in a time reversal and inversion invariant Dirac semi - metal. In certain range of the chemical potential $\mu$ and parameters characterizing the pairing attraction (effective electron-electron coupling constant $\lambda$ and the Debye energy $T_{D}$) the energy of the singlet although always lower, prevails by a very slim margin over the triplet. This means that interactions that are small but discriminate between the spin singlet and the spin triplet determine the nature of the superconducting order there. It shown that in materials close enough to the Dirac point ($\mu \lesssim T_{D}$) magnetic impurities stabilize the odd pairing superconducting state.Comment: 5 pages, 4 figures.Supplemenatry materials, 5 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1407.077

Singular solutions of the L^2-supercritical biharmonic Nonlinear Schrodinger equation

We use asymptotic analysis and numerical simulations to study peak-type singular solutions of the supercritical biharmonic NLS. These solutions have a quartic-root blowup rate, and collapse with a quasi self-similar universal profile, which is a zero-Hamiltonian solution of a fourth-order nonlinear eigenvalue problem

Harnessing emotions to deliberative argumentation in classroom discussions on historical issues in multi-cultural contexts

AbstractThis theoretical paper is about the role of emotions in historical reasoning in the context of classroom discussions. Peer deliberations around texts have become important practices in history education according to progressive pedagogies. However, in the context of issues involving emotions, such approaches may result in an obstacle for historical clairvoyance. The expression of strong emotions may bias the use of sources, compromise historical reasoning, and impede argumentative dialogue. Coping with emotions in the history classrooms is a new challenge in history education. In this paper, we suggest that rather than attempting to foster positive emotion only or to avoid emotions all together, we should look at ways of engaging with emotion in history teaching. We present examples of peer deliberations on charged historical topics according to three pedagogical approaches that address emotions in different ways. The protocols we present open numerous questions: (a) whether facilitating engagement with own and the other's emotions may lead to better processing of information and better deliberation of a historical question; (b) whether promoting national pride boosts reliance on collective narratives; and (c) whether adopting a critical teaching approach eliminates emotions and biases. Based on these examples and findings in social psychology, we bring forward working hypotheses according to which we suggest that instead of dodging emotional issues, teachers should harness emotions – not only positive but also negative ones, to critical and productive engagement in classroom activities.