Using the anisotropic electron transport and susceptibility measurements we demonstrate the appearance of inhomogeneous gossamer superconductivity in FeSe single crystals at ambient pressure and at temperature five times higher than its zero resistance $T_c$. We also find and quantitatively describe a general property: If inhomogeneous superconductivity in a anisotropic conductor first appears in the form of isolated superconducting islands, it reduces electric resistivity anisotropically with maximal effect along the least conducting axis. This gives a simple tool to study inhomogeneous superconductivity in various anisotropic compounds, which helps to investigate the onset of high-temperature superconductivity.

A theoretical model has been proposed to describe the conductivity of a layered anisotropic normal metal containing small superconducting inclusions at an arbitrary eccentricity of spheroidal superconducting islands. The electron transport and magnetic properties of FeSe single crystals have been measured. The results indicate the existence of superconductivity at temperatures much higher than the critical superconducting transition temperature corresponding to vanishing electrical resistance. Within the proposed model, quantitative agreement has been achieved between the volume fraction of superconducting inclusions and its temperature dependence determined from the transport and magnetic measurements.

The dependence of the electric resistance R of nanoperforated graphene samples on the position of the Fermi level EF, which is varied by the gate voltage Vg, has been studied. Nanoperforation has...