The cuprates and iron-based high-temperature superconductors share many common features: layered strongly anisotropic crystal structure, strong electronic correlations, interplay between different types of electronic ordering, the intrinsic spatial inhomogeneity due to doping. The understanding of complex interplay between these factors is crucial for a directed search of new high-temperature superconductors. Here we show the appearance of inhomogeneous gossamer superconductivity in bulk FeSe compound at ambient pressure and at temperature 5 times higher than its zero-resistance T c . This discovery helps to understand numerous remarkable superconducting properties of FeSe. We also find and prove 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 and very general tool to detect inhomogeneous superconductivity in anisotropic compounds, which is critically important to study the onset of high-temperature superconductivity.

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We report on direct observation of microscopic solitons in single electronic processes of the coherent interlayer tunneling in charge density waves. Special nanoscale devices were fabricated from the chain compound using focused ion beams. The spectra were drastically refined by working at high (up to 27 T) magnetic fields. Internal quantum tunneling of electrons can go through solitons that are energetically more favorable quantum particles than electrons. In addition to the interband tunneling across the gap 2Delta, we observe a clear peak at the intermediate voltage approximately 2Delta/3, which we associate with the creation of microscopic solitons, the energy of which must be 2Delta/pi. These solitons might correspond to the long sought special quasiparticle--the spinon.

Tunneling spectra of chain materials NbSe3 and TaS3 were studied in nanoscale mesa devices. Current-voltage I-V characteristics related to all charge density waves (CDWs) reveal universal spectra within the normally forbidden region of low V, below the electronic CDW gap 2Delta. The tunneling always demonstrates a threshold Vt approximately 0.2Delta, followed, for both CDWs in NbSe3, by a staircase fine structure. T dependencies of Vt(T) and Delta(T) scale together for each CDW, while the low T values Vt(0) correlate with the CDWs' transition temperatures Tp. Fine structures of CDWs perfectly coincide when scaled along V/Delta. The results evidence the sequential entering of CDW vortices (dislocations) in the junction area with the tunneling current concentrated in their cores. The subgap tunneling proceeds via the phase channel: coherent phase slips at neighboring chains.

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