Abstract
In highly anisotropic organic superconductor (TMTSF)2ClO4, 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)2ClO4 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 Tc 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 ξ, 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.
Highlights
Accepted: 13 January 2021Raising the superconducting transition temperature (Tc) has been the goal of active research for a century
Our paper concerns the OrS and is devoted to two problems: (i) show that Maxwell-Garnett approximation can be used to estimate superconducting volume fraction in coexistence regime of superconducting, metallic and spin/charge-density wave phases; (ii) analysis of corresponding experimental data [6,7] in the organic superconductor (TMTSF)2 ClO4 to study the effect of cooling rate and of disorder on the volume fraction, shape and size of SC domains
Please note that the condition φ 1 is fulfilled in a wide range of parameters, because in 3D anisotropic samples even the SC percolation threshold φc, corresponding to the onset of nearly zero resistance, is considerably smaller than unity. This is illustrated in our recent work [31], where φc in needle-shaped flat (TMTSF)2 PF6 samples from Refs. [14,18], typical for organic superconductors, was calculated numerically, assuming a rectangular sample shape and ellipsoidal SC inclusions of varying size at randomly distributed but fixed positions
Summary
Accepted: 13 January 2021Raising the superconducting transition temperature (Tc) has been the goal of active research for a century. Compounds like cuprates [1,2], iron-based superconductors [3], organic superconductors (hereafter denoted as OrS) [4] are some major high-Tc superconductors at ambient pressure These materials have several common properties: (i) layered crystal structure and, high conductivity anisotropy; (ii) interplay between various types of electron ordering, i.e., between spin/charge-density wave and superconductivity;. At fast cooling the thermal disorder remains in the samples, so that both ordered and disordered domains coexist It was corroborated by resistivity [63], specific heat[64] and x-ray scattering [65] experiments
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