We study the coexistence of superconductivity (SC) and density-wave state and reconcile various puzzling experimental data in organic superconductors ${\left(\mathrm{TMTSF}\right)}_2{\mathrm{PF}}_6$ and ${\left(\mathrm{TMTSF}\right)}_2{\mathrm{ClO}}_4$. The anisotropic resistance drop above $T_c$ is qualitatively described by nascent isolated SC islands within a bulk analytical model. However, the observed anisotropic SC onset is explained only when the finite size and flat needle shape of samples is considered. Our results pave a way to estimate the volume fraction and the typical size of SC islands far from the sample surface and apply to many inhomogeneous superconductors, including high-$T_c$ cuprate or Fe-based ones.

In highly anisotropic organic superconductor (TMTSF)${}_2$ClO${}_4$, superconducting (SC) phase coexists with metallic and spin-density wave phases in the form of domains. Using the Maxwell-Garnett approximation (MGA), we calculate the volume ratio and estimate the shape of these embedded SC domains from resistivity data at various temperature and anion disorder, controlled by the cooling rate or annealing time of (TMTSF)${}_2$ClO${}_4$ samples. We found that the variation of cooling rate and of annealing time affect differently the shape of SC domains. In all cases the SC domains have oblate shape, being the shortest along the interlayer z-axis. This contradicts the widely assumed filamentary superconductivity along the z-axis, used to explain the anisotropic superconductivity onset. We show that anisotropic resistivity drop at the SC onset can be described by the analytical MGA theory with anisotropic background resistance, while the anisotropic $T_c$ can be explained by considering a finite size and flat shape of the samples. Due to a flat/needle sample shape, the probability of percolation via SC domains is the highest along the shortest sample dimension (z-axis), and the lowest along the sample length (x-axis). Our theory can be applied to other heterogeneous superconductors, where the size d of SC domains is much larger than the SC coherence length $\xi$, e.g., cuprates, iron-based or organic superconductors. It is also applicable when the spin/charge-density wave domains are embedded inside a metallic background, or vice versa.

Heterogeneous superconductivity onset is a common phenomenon in high-T${}_c$ superconductors of both the cuprate and iron-based families. It is manifested by a fairly wide transition from the metallic to zero-resistance states. Usually, in these strongly anisotropic materials, superconductivity (SC) first appears as isolated domains. This leads to anisotropic excess conductivity above T${}_c$, and the transport measurements provide valuable information about the SC domain structure deep within the sample. In bulk samples, this anisotropic SC onset gives an approximate average shape of SC grains, while in thin samples, it also indicates the average size of SC grains. In this work, both interlayer and intralayer resistivity were measured as a function of temperature in FeSe samples of various thicknesses. To measure the interlayer resistivity, FeSe mesa structures oriented across the layers were fabricated using FIB. As the sample thickness decreases, a significant increase in superconducting transition temperature T${}_c$ is observed: T${}_c$ raises from 8 K in bulk material to 12 K in microbridges of thickness ∼40 nm. We applied analytical and numerical calculations to analyze these and earlier data and find the aspect ratio and size of the SC domains in FeSe consistent with our resistivity and diamagnetic response measurements. We propose a simple and fairly accurate method for estimating the aspect ratio of SC domains from T${}_c$ anisotropy in samples of various small thicknesses. The relationship between nematic and superconducting domains in FeSe is discussed. We also generalize the analytical formulas for conductivity in heterogeneous anisotropic superconductors to the case of elongated SC domains of two perpendicular orientations with equal volume fractions, corresponding to the nematic domain structure in various Fe-based superconductors.

Most high-$T_c$ superconductors are spatially inhomogeneous. Usually, this heterogeneity originates from the interplay of various types of electronic ordering. It affects various superconducting properties, such as the transition temperature, the magnetic upper critical field, the critical current, etc. In this paper, we analyze the parameters of spatial phase segregation during the first-order transition between superconductivity (SC) and a charge- or spin-density wave state in quasi-one-dimensional metals with imperfect nesting, typical of organic superconductors. An external pressure or another driving parameter increases the transfer integrals in electron dispersion, which only slightly affects SC but violates the Fermi surface nesting and suppresses the density wave (DW). At a critical pressure $P_c$, the transition from a DW to SC occurs. We estimate the characteristic size of superconducting islands during this phase transition in organic metals in two ways. Using the Ginzburg–Landau expansion, we analytically obtain a lower bound for the size of SC domains. To estimate a more specific interval of the possible size of the superconducting islands in (TMTSF)${}_2$PF${}_6$ samples, we perform numerical calculations of the percolation probability via SC domains and compare the results with experimental resistivity data. This helps to develop a consistent microscopic description of SC spatial heterogeneity in various organic superconductors.

To increase the storage time of ultracold neutrons (UCNs) inside the material traps it is promising to cover the trap walls by liquid ${}^4\mathrm{He}$, a material which does not absorb neutrons at all. The rough side wall of UCN trap holds the required amount of ${}^4\mathrm{He}$ by the capillary effects, but the edges of the wall roughness remain insufficiently coated. Here we propose to apply an electric voltage to these rough side walls of UCN traps to increases the thickness of liquid He on the wall edges and to cover the entire wall surface by sufficiently thick helium films. This completely protects UCNs from being absorbed inside the trap walls. We estimate the required electric field and voltage for several possible designs of UCN traps. This improvement may give rise to a new generation of ultracold neutron traps with very long storage time. We also estimate the influence of this electric field on the dispersion of ripplons—the quanta surface waves, which give the main contribution to the inelastic UCN scattering at low temperature.

The interplay between superconductivity (SC) and spin/charge density wave (DW) in organic metals shows many similarities to high-$T_c$ superconductors. It also contains many puzzles, for example, the anisotropic SC onset observed and the severalfold increase of the upper critical field $H_{c2}$ in the coexistence region, as well as the microscopic origin of SC/DW phase separation there. In this paper, by the direct calculation of the Landau expansion for DW free energy, we argue that the phase transition between DW and metallic/SC phase in organic superconductors goes by first order at low-enough temperature, which explains the spatial segregation of DW and SC at large length scale, consistent with experimental observations. This first-order phase transition is not directly related to SC and happens even above the SC transition temperature.