Two step I to II type transitions in layered Weyl semi-metals and their impact on superconductivity.

Novel "quasi two dimensional" typically layered (semi) metals offer a unique opportunity to control the density and even the topology of the electronic matter. Along with doping and gate voltage, a robust tuning is achieved by application of the hydrostatic pressure. In Weyl semi-metals the tilt of the dispersion relation cones, [Formula: see text] increases with pressure, so that one is able to reach type II ([Formula: see text]starting from the more conventional type I Weyl semi-metals [Formula: see text]. The microscopic theory of such a transition is constructed. It is found that upon increasing pressure the I to II transition occurs in two continuous steps. In the first step the cones of opposite chirality coalesce so that the chiral symmetry is restored, while the second transition to the Fermi surface extending throughout the Brillouin zone occurs at higher pressures. Flattening of the band leads to profound changes in Coulomb screening. Superconductivity observed recently in wide range of pressure and chemical composition in Weyl semi-metals of both types. The phonon theory of pairing including the Coulomb repulsion for a layered material is constructed and applied to recent extensive experiments on [Formula: see text].

Type I superconductivity in Dirac materials.

Superconductivity of the second kind was observed in many 3D Weyl and Dirac semi-metals while in the PdTe2, superconductivity is clearly of the first kind. This is very rare in Dirac semi-metals, but is expected in clean conventional metallic superconductors with 3D parabolic dispersion relation. The conduction bands in this material exhibit the linear (Dirac) dispersion only along two directions, while in the third direction the dispersion is parabolic. Therefore the 'hybrid' Dirac-parabolic material is intermediate between the two extremes. A microscopic pairing theory is derived for arbitrary tilt parameter of the 2D cone and used to determine anisotropic coherence lengths, the penetration depths and applied to recent extensive experiments. Magnetic properties of these superconductors are then studied in the parallel to the layers magnetic field on the basis of microscopically derived Ginzburg-Landau effective theory for the order parameter.

Triplet superconductivity in 3D Dirac semi-metal due to exchange interaction.

Conventional phonon-electron interaction induces either triplet or one of two (degenerate) singlet pairing states in time reversal and inversion invariant 3D Dirac semi-metal. Investigation of the order parameters and energies of these states at zero temperature in a wide range of values of chemical potential µ, the effective electron-electron coupling constant λ and Debye energy TD demonstrates that when the exchange interaction is neglected the singlet always prevails, however, in significant portions of the (µ, λ, TD) parameter space the energy difference is very small. This means that interactions that are small, but discriminate between the spin singlet and the spin triplet, are important in order to determine the nature of the superconducting order there. The best candidate for such an interaction in the materials under consideration is the exchange (the Stoner term) characterized by constant λex. We show that at values of λex, much smaller than ones creating Stoner instability to ferromagnetism λex âˆ¼ 1, the triplet pairing becomes energetically favored over the singlet ones. The 3D quantum critical point at µ = 0 is considered in detail. This can be realized experimentally in optically trapped cold atom systems.

Effect of nanoholes on the vortex core fermion spectrum and heat transport in p-wave superconductors.

The spectrum of core excitations of the Abrikosov vortex pinned by a nanohole of the size of the coherence length is considered. While the neutral zero energy Majorana core state remains intact due to its topological origin, the energy of charged excitations is significantly enhanced compared to that in the unpinned vortex. As a consequence of the pinning the minigap separating the Majorana state from the charged levels increases from Δ(2)/E(F) (E(F) is the Fermi energy and Δ is the bulk p-wave superconducting gap) to a significant fraction of Δ. Suppression of the thermodynamic and kinetic effects of the charged excitations allows us to isolate the Majorana state so it can be used for quantum computation. It is proposed that thermal conductivity along the vortex cores is a sensitive method to demonstrate the minigap. Using the Butticker-Landauer-Kopnin formula, we calculate the thermal conductance beyond the linear response as a function of the hole radius.

Spatiotemporal vortex matter oscillations in Bi2Sr2CaCu2O8+delta crystals.

We observed an oscillatory behavior, both in space and time, of the induction in Bi2Sr2CaCu2O8+delta crystals exposed to a steady magnetic field. This new "flux waves" phenomenon appears near the order-disorder vortex phase transition, under specific conditions of temperature and induction gradient. A theoretical description of this effect is based on two coupled equations: the Landau-Khalatnikov dynamic equation for the order parameter of the vortex phase transition and the diffusion equation for the time evolution of the magnetic induction. A linear stability analysis of these equations predicts an oscillatory instability characterized by a period and wavelength in accordance with the experimental results.

Ring-shaped vortex domain in type-II superconductors.

We present results of experiments in superconducting niobium and numerical simulations showing the creation of a metastable ring-shaped vortex domain by heating. Such vortex rings, if pinned by structural defects, can exist forever.