Charge density waves are a common occurrence in all families of high critical temperature superconducting cuprates. Although consistently observed in the underdoped region of the phase diagram and at relatively low temperatures, it is still unclear to what extent they influence the unusual properties of these systems. Using resonant x-ray scattering we carefully determined the temperature dependence of charge density modulations in (Y,Nd)Ba2Cu3O7-δ for three doping levels. We discovered short-range dynamical charge density fluctuations besides the previously known quasi-critical charge density waves. They persist up to well above the pseudogap temperature T*, are characterized by energies of few meV and pervade a large area of the phase diagram, so that they can play a key role in shaping the peculiar normal-state properties of cuprates.Main text: High-Tc superconductors (HTS) are doped Mott insulators, where the quasi-twodimensionality of the layered structure and the large electron-electron repulsion (responsible, e.g., for the robust short-range antiferromagnetic correlations) make them deviating from the Landau Fermi liquid paradigm. The doping-temperature (p-T) phase diagram encompasses, at low T, the antiferromagnetic and the superconducting orders and, at higher T, the pseudogap region, which marks, below the cross-over temperature T*, a reduction of the quasiparticle density of states in some sections of the Fermi surface. In the pseudogap state and up to optimal doping p0.17, short/medium range incommensurate charge density waves (CDW) emerge as an order weakly competing with superconductivity.CDW were proposed theoretically since the early times of the high temperature superconductivity age (1,2,3); experimental evidence by surface and bulk sensitive techniques came initially in selected materials (4,5,6,7), and later in all cuprate families (8,9,10,11,12). Moreover long-range tridimensional CDW (3D-CDW) order has been observed inside the superconductive dome (for p0.08-0.17) in special circumstances, e.g. in high magnetic fields that weaken superconductivity or in epitaxially grown samples (13,14,15). Finally, it has come as a surprise the recent observation of CDW modulations in overdoped (Bi,Pb)2.12Sr1.88CuO6+δ outside the pseudogap regime too (16), hinting at a wider than expected occurrence of this phenomenon.

In superconductor-topological insulator-superconductor hybrid junctions, the barrier edge states are expected to be protected against backscattering, to generate unconventional proximity effects, and, possibly, to signal the presence of Majorana fermions. The standards of proximity modes for these types of structures have to be settled for a neat identification of possible new entities. Through a systematic and complete set of measurements of the Josephson properties we find evidence of ballistic transport in coplanar Al-Bi2Se3-Al junctions that we attribute to a coherent transport through the topological edge state. The shunting effect of the bulk only influences the normal transport. This behavior, which can be considered to some extent universal, is fairly independent of the specific features of superconducting electrodes. A comparative study of Shubnikov -de Haas oscillations and Scanning Tunneling Spectroscopy gave an experimental signature compatible with a two dimensional electron transport channel with a Dirac dispersion relation. A reduction of the size of the Bi2Se3 flakes to the nanoscale is an unavoidable step to drive Josephson junctions in the proper regime to detect possible distinctive features of Majorana fermions.