Emergence of flat bands and their impact on superconductivity of Mo5_5Si3−x_{3-x}Px_x

The first-principles calculations and measurements of the magnetic penetration depths, the upper critical field, and the specific heat were performed for a family of Mo$_5$Si$_{3-x}$P$_x$ superconducotrs. First-principles calculations suggest the presence of a flat band dispersion, which gradually shifts to the Fermi level as a function of phosphorus doping $x$. The flat band approaches the Fermi level at $x\simeq 1.3$, thus separating Mo$_5$Si$_{3-x}$P$_x$ between the purely steep band and the steep band/flat band superconducting regimes. The emergence of flat bands lead to an abrupt change of nearly all the superconducting quantities. In particular, a strong reduction of the coherence length $\xi$ and enhancement of the penetration depth $\lambda$ result in nearly factor of three increase of the Ginzburg-Landau parameter $\kappa=\lambda/\xi$ (from $\kappa\simeq 25$ for $x\lesssim 1.2$ to $\kappa\simeq 70$ for $x\gtrsim 1.4$) thus initiating the transition of Mo$_5$Si$_{3-x}$P$_x$ from a moderate to an extreme type-II superconductivity.Comment: 6 pages, 4 figure

An implementation of nDGP gravity in Pinocchio

In this paper we investigate dark matter structure formation in the normal branch of the Dvali-Gabadadze-Porrati (nDGP) model using the PINOCCHIO algorithm. We first present 2nd order Lagrangian perturbation theory for the nDGP model, which shows that the 1st- and 2nd-order growth functions in nDGP are larger than those in {\Lambda}CDM. We then examine the dynamics of ellipsoidal collapse in nDGP, which is accelerated compared to {\Lambda}CDM due to enhanced gravitational interactions. Running the nDGP-PINOCCHIO code with a box size of 512 Mpc/h and 1024*1024*1024 particles, we analyze the statistical properties of the output halo catalogs, including the halo power spectrum and halo mass function. The calibrated PINOCCHIO halo power spectrum agrees with N-body simulations within 5% in the comoving wavenumber range k < 0.3 (h/Mpc) at redshift z = 0. The agreement is extended to smaller scales for higher redshifts. For the cumulative halo mass function, the agreement between N-body and PINOCCHIO is also within the simulation scatter.Comment: 18 pages, 3 figure