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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., Comment: 11 pages, 3 figures

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., Comment: 12 pages, 3 figures

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 $z$-axis, used to explain the anisotropic superconductivity onset. We show that anisotropic resistivity drop at the SC transition 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., Comment: 14 Pages, 6 Figures

We study the coexistence of superconductivity (SC) and density-wave state and reconcile various puzzling experimental data in organic superconductors (TMTSF)$_{2}$PF$_{6}$ and (TMTSF)$_{2}$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 in far from the sample surface, and apply to many inhomogeneous superconductors, including high-$T_c$ cuprate or Fe-based ones., Comment: 7 pages with Appendix and 5 figures

About a half of the Fermi surface in rare-earth tritellurides RT e3 becomes gapped below the transition to a charge-density-wave (CDW) state, as revealed by ARPES data. However, the observed jump in resistivity during the CDW transition is less than 20%. Previously this phenomenon was explained by hypothesizing a very slow evolution of CDW energy gap below transition temperature in RTe3 compounds, which contradicts the X-ray measurements. Here we show that this weak change in resistivity can be explained in the framework of standard mean-field temperature dependence of the CDW energy gap in agreement with X-ray data. The change of resistivity caused by CDW is weak because the decrease in conducting electron density at the Fermi level is almost compensated by the decrease in their scattering rate. We calculate resistivity in RTe3 compounds using the Boltzmann transport equation and the mean-field description of the CDW state, and obtain a good agreement with experimental data., Comment: 6 Pages, 2 Figures, To be published in IOP Journal of Physics Conference Series

Using the self-consistent approximation we calculate conductivity in an anisotropic heterogeneous media with superconducting inclusions and compare the results with those obtained previously using the Maxwell approximation and with available experimental data on excess conductivity above $ T_c= $~8K in FeSe. Advantages and drawbacks of these two approximations are discussed. The obtained analytical formulas can be applied to various other anisotropic heterogeneous superconductors, including high-Tc layered superconductors., Comment: 6 pages, 4 figures; the work presented at the IV International Conference LaPlas-2018; to be published in the Journal of Physics: Conference Series (in press)

The magnetic oscillations in YBCO high-temperature superconductors have been widely studied over the last decade and consist of three equidistant low frequencies with a central frequency several times more intense than its two shoulders. This remains a puzzle in spite of numerous attempts to explain the corresponding small Fermi-surface pockets. Furthermore the ARPES data indicate only four Fermi-arcs with bilayer splitting, and show no sign of such small areas in the Fermi surface. Here we argue that the magnetic oscillations measured in under-doped bilayer high temperature superconductors, in particular YBa$_{2}$Cu$_{3}$O$_{6+\delta }$, provide a measure of the interplanar electronic coupling rather than the areas of fine-grain reconstruction of the Fermi surfaces coming from induced charge density waves. This identification is based on the relative intensities of the different peaks, as well as their angular dependence, which points to an effective Fermi surface that is larger than the oscillation frequencies, and is compatible with several indications from ARPES. The dominance of such frequencies with respect to the fundamental frequencies from the Fermi surface is natural for a strongly correlated quasi-two dimensional electronic systems where non-linear mixings of frequencies are more resistant to sample inhomogeneity., Comment: 12 pages. arXiv admin note: substantial text overlap with arXiv:1606.03942

The Fourier transform of the observed magnetic quantum oscillations (MQO) in YBa$_{2}$Cu$_{3}$O$_{6+\delta }$ high-temperature superconductors has a prominent low-frequency peak with two smaller neighbouring peaks. The separation and positions of these three peaks are almost independent of doping. This pattern has been explained previously by rather special, exquisitely detailed, Fermi-surface reconstruction. We propose that these MQO have a different origin, and their frequencies are related to the bilayer and inter-bilayer electron hopping rather than directly to the areas of tiny Fermi-surface pockets. Such so-called "slow oscillations" explain more naturally many features of the observed oscillations and allow us to estimate the inter-layer transfer integrals and in-plane Fermi momentum., Comment: 6 pages