On the Size of Superconducting Islands on the Density-Wave Background in Organic Metals

Most high-Tc 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 Pc, 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)2PF6 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.

[1]  P. Grigoriev,et al.  First-order phase transition between superconducting and charge/spin density wave states causes their coexistence in organic metals , 2023, Physical Review B.

[2]  A. Frolov,et al.  Inhomogeneous Superconductivity Onset in FeSe Studied by Transport Properties , 2023, Materials.

[3]  W. Biberacher,et al.  Coherent heavy charge carriers in an organic conductor near the bandwidth-controlled Mott transition , 2022, Physical Review B.

[4]  Y. Uwatoko,et al.  Pressure-Induced Superconductivity of the Quasi-One-Dimensional Organic Conductor (TMTTF)2TaF6 , 2022, Materials.

[5]  K. Kindo,et al.  Enhanced Superconducting Pairing Strength near a Pure Nematic Quantum Critical Point , 2022, Physical Review X.

[6]  T. Naito.  Modern History of Organic Conductors: An Overview , 2021, Crystals.

[7]  R. Gross,et al.  Experimental evidence for Zeeman spin–orbit coupling in layered antiferromagnetic conductors , 2021, npj Quantum Materials.

[8]  Y. Ovchinnikov,et al.  Nano-based Josephson Tunneling Networks and High Temperature Superconductivity , 2021 .

[9]  P. Grigoriev,et al.  Anisotropic zero-resistance onset in organic superconductors , 2020, Physical Review B.

[10]  C. Kao,et al.  Observation of two types of charge-density-wave orders in superconducting La2-xSrxCuO4 , 2019, Nature Communications.

[11]  P. Zavalij,et al.  Sixfold enhancement of superconductivity in a tunable electronic nematic system , 2019, Nature physics.

[12]  K. Ishida,et al.  Enhancement of superconductivity by pressure-induced critical ferromagnetic fluctuations in UCoGe , 2019, Physical Review B.

[13]  W. Biberacher,et al.  Fermi surface properties of the bifunctional organic metal κ−(BETS)2Mn[N(CN)2]3 near the metal-insulator transition , 2018, Physical Review B.

[14]  C. Kao,et al.  Observation of intertwined density-wave orders and superconductivity in La$_{2-x}$Sr$_x$CuO$_4$ , 2018, 1810.10600.

[15]  R. T. Clay,et al.  From charge- and spin-ordering to superconductivity in the organic charge-transfer solids , 2018, Physics Reports.

[16]  A. Frolov,et al.  Excess Conductivity of Anisotropic Inhomogeneous Superconductors Above the Critical Temperature , 2017, Physics of the Solid State.

[17]  P. Hirschfeld,et al.  Using controlled disorder to probe the interplay between charge order and superconductivity in NbSe2 , 2017, Nature Communications.

[18]  K. Bechgaard,et al.  Crossover from impurity-controlled to granular superconductivity in (TMTSF ) 2 ClO 4 , 2017, 1709.03361.

[19]  O. Volkova,et al.  Anisotropic effect of appearing superconductivity on the electron transport in FeSe , 2017 .

[20]  E. Weschke,et al.  Synchrotron x-ray scattering study of charge-density-wave order in HgBa$_2$CuO$_{4+\delta}$ , 2017, 1702.03348.

[21]  O. Volkova,et al.  Gossamer high-temperature bulk superconductivity in FeSe , 2016, 1610.06117.

[22]  T. K. Radhakrishnan,et al.  A Review of Classical and Nonclassical Nucleation Theories , 2016 .

[23]  E. Abrahams,et al.  High Temperature Superconductivity in Iron Pnictides and Chalcogenides , 2016, 1604.03566.

[24]  G. Bianconi,et al.  Inhomogeneity of charge-density-wave order and quenched disorder in a high-Tc superconductor , 2015, Nature.

[25]  A. Chubukov,et al.  Enhancement of superconductivity at the onset of charge-density-wave order in a metal , 2015, 1507.03583.

[26]  X. Zhou,et al.  Electronic structure and superconductivity of FeSe-related superconductors , 2015, Journal of physics. Condensed matter : an Institute of Physics journal.

[27]  R. Greene,et al.  Charge ordering in the electron-doped superconductor Nd2–xCexCuO4 , 2014, Science.

[28]  T. Schmitt,et al.  Connection between charge-density-wave order and charge transport in the cuprate superconductors , 2014, 1404.7658.

[29]  D. Graf,et al.  Coexistence of spin density waves and superconductivity in (TMTSF)2PF6. , 2014, Physical review letters.

[30]  R. Gross,et al.  Correlation between Fermi surface transformations and superconductivity in the electron-doped high- T c superconductor Nd 2 − x Ce x CuO 4 , 2014, 1403.7398.

[31]  J. Yamada,et al.  Coexistence of superconductivity and spin-density wave in (TMTSF)2ClO4: Spatial structure of the two-phase state , 2013, 1310.3710.

[32]  S. V. Sanduleanu,et al.  Role of anion ordering in the coexistence of spin-density-wave and superconductivity in (TMTSF)2ClO4 , 2013, 1310.3434.

[33]  S. Blundell,et al.  Low-field superconducting phase of (TMTSF)2ClO4. , 2013, Physical review letters.

[34]  C. Mazzoli,et al.  Momentum-dependent charge correlations in YBa2Cu3O6+δ superconductors probed by resonant X-ray scattering: evidence for three competing phases. , 2012, Physical review letters.

[35]  P. Monceau.  Electronic crystals: an experimental overview , 2012, 1307.0929.

[36]  E. M. Forgan,et al.  Direct observation of competition between superconductivity and charge density wave order in YBa2Cu3O6.67 , 2012, Nature Physics.

[37]  A. Umantsev.  Field Theoretic Method in Phase Transformations , 2012, Lecture Notes in Physics.

[38]  S. Brazovskii,et al.  Domain walls at the spin-density-wave endpoint of the organic superconductor (TMTSF)2PF6 under pressure , 2010, 1002.3767.

[39]  D. Jeong,et al.  Structural and Electrical Properties of the Single-crystal Organic Semiconductor Tetramethyltetraselenafulvalene (TMTSF) , 2009 .

[40]  R. Greene,et al.  Progress and perspectives on electron-doped cuprates , 2009, 0906.2931.

[41]  K. Murata,et al.  Recent progress in high-pressure studies on organic conductors , 2009, Science and technology of advanced materials.

[42]  N. Yoneyama,et al.  Spatial mapping of electronic states in κ-(BEDT-TTF)2X using infrared reflectivity , 2009, Science and technology of advanced materials.

[43]  P. Grigoriev.  Superconductivity on the density wave background with soliton-wall structure , 2008, 0811.4335.

[44]  T. Kondo,et al.  Imaging nanoscale Fermi-surface variations in an inhomogeneous superconductor , 2008, 0811.1585.

[45]  P. Grigoriev.  Properties of superconductivity on a density wave background with small ungapped Fermi surface parts , 2008, 0803.0838.

[46]  T. Fujii,et al.  Enhancement of superconducting transition temperature due to the strong antiferromagnetic spin fluctuations in the noncentrosymmetric heavy-fermion superconductor CeIrSi3: A 29Si NMR study under pressure. , 2008, Physical review letters.

[47]  L. Gor’kov,et al.  Nature of the superconducting state in the new phase in(TMTSF)2PF6under pressure , 2006, cond-mat/0610837.

[48]  S. Wolf,et al.  Inhomogeneous superconductivity and the “pseudogap” state of novel superconductors , 2006, cond-mat/0609260.

[49]  P. Grigoriev,et al.  Phase diagram and structure of the charge-density-wave state in a high magnetic field in quasi-one-dimensional materials: A mean-field approach , 2005 .

[50]  W. Biberacher,et al.  Superconductivity in the charge-density-wave state of the organic metal α − ( BEDT − TTF ) 2 K Hg ( SCN ) 4 , 2005, cond-mat/0509769.

[51]  M. Naughton,et al.  Coexistence of superconductivity and antiferromagnetism probed by simultaneous nuclear magnetic resonance and electrical transport in (TMTSF)2PF6 system. , 2005, Physical review letters.

[52]  L. Gor’kov,et al.  Soliton phase near antiferromagnetic quantum critical point in Q1D conductors , 2005, cond-mat/0502472.

[53]  M. Kartsovnik.  High magnetic fields: a tool for studying electronic properties of layered organic metals. , 2004, Chemical reviews.

[54]  K. Kuroki,et al.  Microscopic theory of spin-triplet f-wave pairing in quasi-one-dimensional organic superconductors , 2004, cond-mat/0402672.

[55]  J. Fabre,et al.  From Mott insulator to superconductivity in (TMTTF)2BF4: high pressure transport measurements , 2003 .

[56]  M. Lang,et al.  Organic superconductors , 2003, cond-mat/0302157.

[57]  M. Ausloos,et al.  Charge- and spin-density waves in existing superconductors: competition between Cooper pairing and Peierls or excitonic instabilities , 2002 .

[58]  K. Miyagawa,et al.  Proximity of pseudogapped superconductor and commensurate antiferromagnet in a quasi-two-dimensional organic system. , 2002, Physical review letters.

[59]  M. Naughton,et al.  Critical field enhancement near a superconductor-insulator transition. , 2002, Physical review letters.

[60]  M. Naughton,et al.  Triplet superconductivity in an organic superconductor probed by NMR Knight shift. , 2001, Physical review letters.

[61]  H. Eisaki,et al.  Imaging the granular structure of high-Tc superconductivity in underdoped Bi2Sr2CaCu2O8+δ , 2001, Nature.

[62]  K. Bechgaard,et al.  Coexistence of superconductivity and spin density wave orderings in the organic superconductor (TMTSF)2PF6 , 2001, cond-mat/0109031.

[63]  M. Ausloos,et al.  Charge- and spin-density-wave superconductors , 2001 .

[64]  D. Oxtoby.  Nucleation of First-Order Phase Transitions , 1998 .

[65]  M. Naughton,et al.  Anisotropy of the Upper Critical Field in (TMTSF)2PF6 , 1997 .

[66]  Wang,et al.  Quantum Hall transitions in (TMTSF)2PF6. , 1996, Physical review. B, Condensed matter.

[67]  Danner,et al.  Critical imperfect nesting in (TMTSF)2PF6. , 1996, Physical review. B, Condensed matter.

[68]  Mckenzie.  Microscopic theory of the pseudogap and Peierls transition in quasi-one-dimensional materials. , 1995, Physical review. B, Condensed matter.

[69]  Alexander L. Efros,et al.  Physics and Geometry of Disorder: Percolation Theory , 1987 .

[70]  H. Gutfreund,et al.  Interchain coupling and the Peierls transition in linear-chain systems , 1975 .

[71]  N. Maeda.  Nucleation Theory , 2020, Nucleation of Gas Hydrates.

[72]  K. Baier.  Field Theoretic Method In Phase Transformations , 2016 .

[73]  A. Lebed.  The Physics of Organic Superconductors and Conductors , 2008 .

[74]  Hedo Masato,et al.  Electrical Resistivity of (TMTTF)2PF6 under High Pressure , 2007 .

[75]  S. Torquato.  Random Heterogeneous Materials , 2002 .

[76]  G. Grüner,et al.  Density Waves In Solids , 1994 .

[77]  J. Schrieffer,et al.  Theory of Polymers Having Broken Symmetry Ground States , 1981 .

[78]  T. Schneider,et al.  Physics in one dimension : proceedings of an international conference Fribourg, Switzerland, August 25-29, 1980 , 1981 .

[79]  Michael Tinkham,et al.  Introduction to Superconductivity , 1975 .

[80]  H. Eisaki,et al.  Imaging the granular structure of highT c superconductivity in underdoped Bi 2 Sr 2 CaCu 2 O 8 , 2022 .

[81]  R. Greene,et al.  Charge ordering in the electron-doped superconductor Nd 2 – x Ce x CuO 4 , 2022 .