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