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Emergence of an Interband Phase Difference and Its Consequences in Multiband Superconductors

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Vortices and Nanostructured Superconductors

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 261))

Abstract

Since the idea of a topology based on the interband phase difference was proposed for multiband superconductors without degenerate superconducting components, many feasible and interesting possibilities have been explored. The basic concepts involved are an interband phase difference soliton , the fractionalization of the unit magnetic flux quantum, and frustration between quantum phases of multiple components. The superconductivity field was be extended by introducing the idea of the fluctuation in the interband phase difference. This extension provides a bridge between superconducting condensates and other macroscopic quantum mechanical systems such as Bose–Einstein condensates with multiple components and particle physics systems governed by a nonabelian gauge field. The entropy supported by the interband fluctuation suggests a relationship between multiband superconductors and highly correlated systems. In this chapter, I comment on the past, present, and future situation of multicomponent superconductivity based on multiband superconductors .

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References

  1. M. Tinkham, Introduction to Superconductivirty (McGraw-Hill, Inc. New York, 1996)

    Google Scholar 

  2. J.F. Annett, N. Goldenfeld, A.J. Leggett, Experimental constrains on the paring state of the cuprate superconductors: an emergening consensus, in Physical Properties of High Temperature Superconductors, ed. by D.M. Ginsberg (World Scientific, Singapore, 1996), pp 375–461

    Google Scholar 

  3. A.J. Leggett, Number-phase fluctuations in two-band superconductors. Prog. Theor. Phys. 36, 901–930 (1966)

    Google Scholar 

  4. Y. Tanaka, Phase instability in multi-band superconductors. J. Phys. Soc. Jpn. 70, 2844–2847 (2001)

    Google Scholar 

  5. Y. Tanaka, Soliton in two-band superconductor. Phys. Rev. Lett. 88, 017002 (2001)

    Google Scholar 

  6. T. Yanagisawa, Quarks and fractionally quantized vortices in superconductors: an analogy between two worlds, in  Recent Advances in Quarks Research, ed. by H Fujikage, K Hyobanshi (Nova Science, New York, 2013), pp 113–46

    Google Scholar 

  7. A.J. Leggett, Interpretation of recent results on He3 below 3 mK: a new liquid phase? Phys. Rev. Lett. 29, 1227–1230 (1972)

    Google Scholar 

  8. D.D. Osheroff, R.C. Richardson, D.M. Lee, Evidence for a new phase of solid He3. Phys. Rev. Lett. 28, 885–888 (1972)

    Google Scholar 

  9. A.J. Leggett, A theoretical description of the new phases of liquid 3He. Rev. Mod. Phys. 47, 331–414 (1975)

    Google Scholar 

  10. A.J. Leggett, Nobel lecture: superfluid He3: the early days as seen by a theorist. Rev. Mod. Phys. 76, 999–1011 (2004)

    Google Scholar 

  11. J. Bardeen, L.N. Cooper, J.R. Schrieffer, Microscopic theory of superconductivity. Phys. Rev. 106, 162–164 (1957)

    Google Scholar 

  12. J. Bardeen, L.N. Cooper, J.R. Schrieffer, Theory of superconductivity. Phys. Rev. 108, 1175–1204 (1957)

    Google Scholar 

  13. P.W. Anderson, P. Morel, Generalized Bardeen-Cooper-Schrieffer states and aligned orbital angular momentum in the proposed low-temperature phase of liquid He3. Phys. Rev. Lett. 5, 136–138 (1960)

    Google Scholar 

  14. P.W. Anderson, P. Morel, Generalized Bardeen-Cooper-Schrieffer states and the proposed low-temperature phase of liquid He3. Phys. Rev 123, 1911–1934 (1961)

    Google Scholar 

  15. R. Balian, N.R. Werthamer, Superconductivity with pairs in a relative p wave. Phys. Rev. 131, 1553–1564 (1963)

    Google Scholar 

  16. F. Steglich, J. Aarts, C.D. Bredl, W. Lieke, D. Meschede, W. Franz, H. Schäfer, Superconductivity in the presence of strong Pauli paramagnetism: CeCu2Si2. Phys. Rev. Lett. 43, 1892–1896 (1979)

    Google Scholar 

  17. H.R. Ott, H. Rudigier, Z. Fisk, J.L. Smith, UBe13: an unconventional actinide superconductor. Phys. Rev. Lett. 50, 1595–1598 (1983)

    Google Scholar 

  18. H.R. Ott, H. Rudigier, T.M. Rice, K. Ueda, Z. Fisk, J.L. Smith, p-wave superconductivity in UBe13. Phys. Rev. Lett. 52, 1915–1918 (1984)

    Google Scholar 

  19. R. Joynt, L. Taillefer, The superconducting phases of UPt3. Rev. Mod. Phys 74, 235–294 (2002)

    Google Scholar 

  20. M. Sigrist, K. Ueda, Phenomenological theory of unconventional superconductivity. Rev. Mod. Phys. 63, 239–311 (1991)

    Google Scholar 

  21. A.P. Mackenzie, Y. Maeno, The superconductivity of Sr2RuO4 and the physics of spin-triplet pairing. Rev. Mod. Phys. 75, 657–712 (2003)

    Google Scholar 

  22. L.-F. Zhang, V.F. Becerra, L. Covaci, M.V. Milošević, Electronic properties of emergent topological defects in chiral p-wave superconductivity. Phys. Rev. B 94, 24520 (2016)

    Google Scholar 

  23. D.F. Agterberg, V. Barzykin, L.P. Gor’kov, Conventional mechanisms for exotic superconductivity. Phys. Rev. B 60, 14868–14871 (1999)

    Google Scholar 

  24. C.C. Tsuei, J.R. Kirtley, Pairing symmetry in cuprate superconductors. Rev. Mod. Phys. 72, 969–1016 (2000)

    Google Scholar 

  25. Q.P. Li, B.E.C. Koltenbah, R. Joynt, Mixed s-wave and i d-wave superconductivity in high-Tc systems. Phys. Rev. B 48, 437–455 (1993)

    Google Scholar 

  26. S. Yip, A. Garg, Superconducting states of reduced symmetry: general order parameters and physical implications. Phys. Rev. B 48, 3304–3308 (1993)

    Google Scholar 

  27. C.J. Myatt, E.A. Burt, R.W. Ghrist, E.A. Cornell, C.E. Wieman, Production of two overlapping Bose-Einstein condensates by sympathetic cooling. Phys. Rev. Lett. 78, 586–589 (1997)

    Google Scholar 

  28. D.S. Hall, M.R. Matthews, J.R. Ensher, C.E. Wieman, E.A. Cornell, Dynamics of component separation in a binary mixture of Bose-Einstein condensates. Phys, Rev. Lett 81, 1539–1542 (1998)

    Google Scholar 

  29. M.R. Matthews, B.P. Anderson, P.C. Haljan, D.S. Hall, C.E. Wieman, E.A. Cornell, Vortices in a Bose-Einstein condensate. Phys. Rev. Lett. 83, 2498–2501 (1999)

    Google Scholar 

  30. K. Doi, Y. Natsume, Calculation of Bose-Einstein condensations and characteristic features of fluctuations for systems with and without a vortex in two-component alkali atom gases. J. Phys. Soc. Jpn. 70, 167–172 (2001)

    Google Scholar 

  31. K. Kasamatsu, M. Tsubota, M. Ueda, Vortex phase diagram in rotating two-component Bose-Einstein condensates. Phys. Rev. Lett. 91, 150406 (2003)

    Google Scholar 

  32. M. Cipriani, M. Nitta, Crossover between integer and fractional vortex lattices in coherently coupled two-component Bose-Einstein condensates. Phys. Rev. Lett. 111, 170401 (2013)

    Google Scholar 

  33. D.T. Son, M.A. Stephanov, Domain walls of relative phase in two-component Bose-Einstein condensates. Phys. Rev. A 65, 63621 (2002)

    Google Scholar 

  34. P. Öhberg, L. Santos, Dark solitons in a two-component Bose-Einstein condensate. Phys. Rev. Lett. 86, 2918–2921 (2001)

    Google Scholar 

  35. B.D. Esry, C.H. Greene, J.J.P. Burke, J.L. Bohn, Hartree-Fock theory for double condensates. Phys. Rev. Lett. 78, 3594–3597 (1997)

    Google Scholar 

  36. C.K. Law, H. Pu, N.P. Bigelow, J.H. Eberly, “Stability signature” in two-species dilute Bose-Einstein condensates. Phys. Rev. Lett. 79, 3105–3108 (1997)

    Google Scholar 

  37. H. Pu, N.P. Bigelow, Properties of two-species Bose condensates. Phys. Rev. Lett. 80, 1130–1133 (1998)

    Google Scholar 

  38. D.R. Tilley, J. Tilley, Superfluidity and superconductivity 3rd edn. (Adams Hilger, Bristol and New York, 1990)

    Google Scholar 

  39. O.V. Lounasmaa, E. Thuneberg, Vortices in rotating superfluid 3He. Proc. Natl. Acad. Sci. U.S.A 96, 7760–7767 (1990)

    Google Scholar 

  40. M.M. Salomaa, G.E. Volovik, Quantized vortices in superfluid 3He. Rev. Mod. Phys. 59, 533–613 (1987)

    Google Scholar 

  41. T.A. Tokuyasu, D. Hess, J.A. Sauls, Vortex states in an unconventional superconductor and the mixed phases of UPt3. Phys. Rev. B 41, 8891–8903 (1990)

    Google Scholar 

  42. J.A. Sauls, M. Eschrig, Vortices in chiral, spin-triplet superconductors and superfluids. New J. Phys. 11, 75008 (2009)

    Google Scholar 

  43. C.N. Yang, R.L. Mills, Conservation of isotopic spin and isotopic gauge invariance. Phys. Rev. 96, 191–195 (1954)

    Google Scholar 

  44. S. Weinberg, A model of leptons. Phys. Rev. Lett. 19, 1264–1266 (1967)

    Google Scholar 

  45. M. Gell-Mann, A schematic model of baryons and mesons. Phys. Lett. 8, 214–215 (1964)

    Google Scholar 

  46. M. Eto, Y. Hirono, M. Nitta, S. Yasui, Vortices and other topological solitons in dense quark matter. Prog. Theor. Exp. Phys. 2014, 012D01 (2014)

    Google Scholar 

  47. S. Sasaki, H. Suganuma, H. Toki, Dual Ginzburg-Landau theory with QCD-monopoles for dynamical chiral-symmetry breaking. Prog. Theor. Phys. 94, 373–384 (1995)

    Google Scholar 

  48. Y. Koma, H. Toki, Weyl invariant formulation of the flux-tube solution in the dual Ginzburg-Landau theory. Phys. Rev. D 62, 54027 (2000)

    Google Scholar 

  49. Y. Koma, M. Koma, D. Ebert, H. Toki, Effective string action for the U(1) × U(1) dual Ginzburg–Landau theory beyond the London limit. Nuclear Physics B 648, 189–202 (2003)

    Google Scholar 

  50. M. Nitta, Fractional instantons and bions in the O(N) model with twisted boundary conditions. JHEP 2015, 1–38 (2015)

    Google Scholar 

  51. J. Ashcroft, M. Eto, M. Haberichter, M. Nitta, M.B. Paranjape, Head butting sheep: kink collisions in the presence of false vacua. J. Phys. A: Math. Theory 49, 365203 (2016)

    Google Scholar 

  52. T.W.B. Kibble, Topology of cosmic domains and strings. J. Phys. A: Math. Gen. 9, 1387–1398 (1976)

    Google Scholar 

  53. A. Dey, S. Mahapatra, T. Sarkar, Very general holographic superconductors and entanglement thermodynamics. JHEP 12, 1–32 (2014)

    Google Scholar 

  54. G.L. Giordano, A.R. Lugo, Holographic phase transitions from higgsed, non abelian charged black holes. JHEP 7, 1–29 (2015)

    Google Scholar 

  55. Y. Tanaka, Multicomponent superconductivity based on multiband superconductors. Supercond. Sci. Technol. 28, 034002 (2015)

    Google Scholar 

  56. H. Ihara, K. Tokiwa, H. Ozawa, M. Hirabayashi, H. Matuhata, A. Negishi, Y.S. Song, New high-Tc superconductor Ag1−xCuxBa2Can−1CunO2n+3−δ family with Tc > 117 K. Jpn. J. Appl. Phys 33, L300–L303 (1994)

    Google Scholar 

  57. H. Ihara, K. Tokiwa, H. Ozawa, M. Hirabayashi, A. Negishi, H. Matuhata, Y.S. Song, New high-Tc superconductor family of Cu-Based Cu1−xBa2Can−1CunO2n+ 4−δ with Tc > 116 K. Jpn. J. Appl. Phys 33, L503–L506 (1994)

    Google Scholar 

  58. N. Hamada, H. Ihara, Electronic band structure of CuBa2Ca3Cu4O10+x(x = 0, 1). Physica B 284, 1073–1074 (2000)

    Google Scholar 

  59. N. Hamada, H. Ihara, Electronic band structure of CuBa2Can−1CunO2n+2 and CuBa2Can−1CunO2n+1F (n = 3 − 5). Physica C 357, 108–111 (2001)

    Google Scholar 

  60. Y. Tokunaga, K. Ishida, Y. Kitaoka, K. Asayama, K. Tokiwa, A. Iyo, H. Ihara, Effect of carrier distribution on superconducting characteristics of the multilayered high-T c cuprate (Cu0.6C0.4)Ba2Ca3Cu4O12+y: 63Cu-NMR study. Phys. Rev. B 61, 9707–9710 (2000)

    Google Scholar 

  61. Y. Tanaka, A. Iyo, N. Shirakawa, M. Ariyama, M. Tokumoto, S.I. Ikeda, H. Ihara, Specific heat study on CuxBa2Can−1CunOy. Physica C 357, 222–225 (2001)

    Google Scholar 

  62. K. Momma, F. Izumi, VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 44, 1272–1276 (2011)

    Google Scholar 

  63. Y. Tanaka, Tl-based, Hg-based and multilayer (Cu-base and F-based) cuprate superconductors, in Physics of Vortex State in Superconductors, ed. by K. Kadowaki (Shokabo, Tokyo, in Japanese, 1996) in press

    Google Scholar 

  64. H. Suhl, B.T. Matthias, L.R. Walker, Bardeen-Cooper-Schrieffer theory of superconductivity in the case of overlapping bands. Phys. Rev. Lett. 3, 552–554 (1959)

    Google Scholar 

  65. A. Vargunin, T. Örd, K. Rägo, Thermal fluctuations of order parameters in two-gap superconductors. J. Supercond. Nov. Magn. 24, 1127–1131 (2011)

    Google Scholar 

  66. A. Vargunin, K. Rägo, T. Örd, Two-gap superconductivity: interband interaction in the role of an external field. Supercond. Sci. Technol. 26, 65008 (2013)

    Google Scholar 

  67. J. Goryo, S. Soma, H. Matsukawa, Deconfinement of vortices with continuously variable fractions of the unit flux quanta in two-gap superconductors. EPL 80, 17002 (2007)

    Google Scholar 

  68. M. Nitta, M. Eto, T. Fujimori, K. Ohashi, Baryonic bound state of vortices in multicomponent superconductors. J. Phys. Soc. Jpn. 81, 84711 (2012)

    Google Scholar 

  69. S.B. Gudnason, M. Nitta, Fractional Skyrmions and their molecules. Phys. Rev. D 91, 85040 (2015)

    Google Scholar 

  70. E. Babaev, L.D. Faddeev, A.J. Niemi, Hidden symmetry and knot solitons in a charged two-condensate Bose system. Phys. Rev. B 65, 067001 (2002)

    Google Scholar 

  71. E. Babaev, Vortices with fractional flux in two-gap superconductors and in extended Faddeev model. Phys. Rev. Lett. 89, 100512 (2002)

    Google Scholar 

  72. E. Babaev, J. Carlström, J. Garaud, M. Silaev, J.M. Speight, Type-1.5 superconductivity in multiband systems: magnetic response, broken symmetries and microscopic theory—a brief overview. Physica C 479, 2–14 (2012)

    Google Scholar 

  73. E. Babaev, M. Speight, Semi-meissner state and neither type-I nor type-II superconductivity in multicomponent superconductors. Phys. Rev. B 72, 180502 (2005)

    Google Scholar 

  74. P.J. Pereira, L.F. Chibotaru, V.V. Moshchalkov, Vortex matter in mesoscopic two-gap superconductor square. Phys. Rev. B 84, 144504 (2011)

    Google Scholar 

  75. L.F.C.L.F. Chibotaru, V.H.D.V.H. Dao, A. Ceulemans, Thermodynamically stable noncomposite vortices in mesoscopic two-gap superconductors. EPL 78 (2007) 47001

    Google Scholar 

  76. L.F. Chibotaru, V.H. Dao, Stable fractional flux vortices in mesoscopic superconductors. Phys. Rev. B 81, 20502 (2010)

    Google Scholar 

  77. A. De Col, V.B. Geshkenbein, G. Blatter, Dissociation of vortex stacks into fractional-flux vortices. Phys. Rev. Lett. 94, 97001 (2005)

    Google Scholar 

  78. R. Geurts, M.V. Milošević, F.M. Peeters, Vortex matter in mesoscopic two-gap superconducting disks: influence of Josephson and magnetic coupling. Phys. Rev. B 81, 214514 (2010)

    Google Scholar 

  79. R.M. da Silva, M.V. Milošević, D. Dominguez, F.M. Peeters, J.A. Aguiar, Distinct magnetic signatures of fractional vortex configurations in multiband superconductors. Appl. Phys. Lett. 105, 232601

    Google Scholar 

  80. T. Yanagisawa, Theory of multi-band superconductivity, in Recent Advances in Superconductivity Research ed. by C.B. Taylor (New York: Nova Science, 2013), pp. 219–48

    Google Scholar 

  81. T. Yanagisawa, Chiral sine-Gordon model. EPL 113, 41001 (2016)

    Google Scholar 

  82. Y. Tanaka, A. Crisan, D.D. Shivagan, A. Iyo, K. Tokiwa, T. Watanabe, Interpretation of abnormal AC loss peak based on vortex-molecule model for a multicomponent cuprate superconductor. Jpn. J. Appl. Phys 46, 134–135 (2007)

    Google Scholar 

  83. Y. Tanaka, A. Crisan, Ambiguity in the statistics of single-component winding vortex in a two-band superconductor. Physica B 404, 1033–1039 (2009)

    Google Scholar 

  84. T. Yanagisawa, Y. Tanaka, I. Hase, K. Yamaji, Vortices and chirality in multi-band superconductors. J. Phys. Soc. Jpn. 81, 24712 (2012)

    Google Scholar 

  85. Y. Tanaka, A. Iyo, S. Itoh, K. Tokiwa, T. Nishio, T. Yanagisawa, Experimental observation of a possible first-order phase transition below the superconducting transition temperature in the multilayer cuprate superconductor HgBa2Ca4Cu5Oy. J. Phys. Soc. Jpn. 83, 74705 (2014)

    Google Scholar 

  86. Y. Tanaka, T. Yanagisawa, T. Nishio, Fluctuation-assisted gap evolution in frustrated multiband superconductors. Physica C 483, 86–90 (2012)

    Google Scholar 

  87. Y. Tanaka, T. Yanagisawa, T. Nishio, Unlocking interband phase difference in multiband superconductors. Physica C 485, 64–70 (2013)

    Google Scholar 

  88. V. Stanev, Z. Tešanović, Three-band superconductivity and the order parameter that breaks time-reversal symmetry. Phys. Rev. B 81, 134522 (2010)

    Google Scholar 

  89. V. Stanev, Model of collective modes in three-band superconductors with repulsive interband interactions. Phys. Rev. B 85, 174520 (2012)

    Google Scholar 

  90. S.-Z. Lin, X. Hu, Massless leggett mode in three-band superconductors with time-reversal-symmetry breaking. Phys. Rev. Lett. 108, 177005 (2012)

    Google Scholar 

  91. T. Yanagisawa, Y. Tanaka, Fluctuation-induced Nambu-Goldstone bosons in a Higgs–Josephson model. New J. Phys. 16, 123014 (2014)

    Google Scholar 

  92. V. Stanev, A.E. Koshelev, Complex state induced by impurities in multiband superconductors. Phys. Rev. B 89, 100505 (2014)

    Google Scholar 

  93. M. Silaev, E. Babaev, Unusual mechanism of vortex viscosity generated by mixed normal modes in superconductors with broken time reversal symmetry. Phys. Rev. B 88, 220504 (2013)

    Google Scholar 

  94. K. Kobayashi, M. Machida, Y. Ota, F. Nori, Massless collective excitations in frustrated multiband superconductors. Phys. Rev. B 88, 224516 (2013)

    Google Scholar 

  95. S.-Z. Lin, Ground state, collective mode, phase soliton and vortex in multiband superconductors. J. Phys.: Cond. Matt. 26, 493202 (2014)

    Google Scholar 

  96. T.A. Bojesen, A. Sudbø, Fluctuation effects in phase-frustrated multiband superconductors. J. Supercond. Nov. Magn. 28, 3193–3204 (2015)

    Google Scholar 

  97. T.A. Bojesen, E. Babaev, A. Sudbø, Phase transitions and anomalous normal state in superconductors with broken time-reversal symmetry. Phys. Rev. B 89, 104509 (2014)

    Google Scholar 

  98. A. Gurevich, V.M. Vinokur, Interband phase modes and nonequilibrium soliton structures in two-gap superconductors. Phys. Rev. Lett. 90, 047004 (2003)

    Google Scholar 

  99. Y. Tanaka, A. Iyo, D. Shivagan. P. Shirage, K. Tokiwa, T. Watanabe, N. Terada, Method for controlling inter-component phase difference soliton and inter-component phase difference soliton circuit device. US Patent 8902018 (2014)

    Google Scholar 

  100. Y. Tanaka, A. Iyo, N. Terada, S. Kawabata, A. Sundaresan, T. Watanabe, K. Tokiwa, Quantum turing machine. US Patent 7,400,282 (2008)

    Google Scholar 

  101. Y. Tanaka, D.D. Shivagan, A. Crisan, A. Iyo, P.M. Shirage, K. Tokiwa, T. Watanabe, N. Terada, Vortex molecule, fractional flux quanta, and interband phase difference soliton in multi-band superconductivity and multi-component superconductivity. J. Phys.: Conf. Ser. 150, 052267 (2009)

    Google Scholar 

  102. Y. Tanaka, T. Yanagisawa, Chiral ground state in three-band superconductors. J. Phys. Soc. Jpn. 79, 114706 (2010)

    Google Scholar 

  103. J.S. Bell, R. Jackiw, A PCAC puzzle: π0 → γγ in the σ-model in the sigma model. Il Nuovo Cimento A 60, 47–61 (1969)

    Google Scholar 

  104. S.L. Adler, Axial-vector vertex in spinor electrodynamics. Phys. Rev. 177, 2426–2438 (1969)

    Google Scholar 

  105. Y. Nambu, Quasi-particles and gauge invariance in the theory of superconductivity. Phys. Rev. 117, 648–663 (1960)

    Google Scholar 

  106. Field theories with ≪Sperconductor≫ solutions. J. Goldstone. Il Nuovo Cimento 19, 154–164 (1961)

    Google Scholar 

  107. I.Y. Nambu, G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. Phys. Rev. 122, 345–358 (1961)

    Google Scholar 

  108. H. Bluhm, Magnetic response measurements of mesoscopic superconducting and normal metal rings. Doctoral Degree Thesis, Stanford University, USA, 2013

    Google Scholar 

  109. S.V. Kuplevakhsky, A.N. Omelyanchouk, Y.S. Yerin, Soliton states in mesoscopic two-band-superconducting cylinders. Low Temp. Phys. 37, 667–677 (2011)

    Google Scholar 

  110. K.V. Samokhin, Phase solitons and subgap excitations in two-band superconductors. Phys. Rev. B 86, 064513 (2012)

    Google Scholar 

  111. V. Vakaryuk, V. Stanev, W.-C. Lee, A. Levchenko, Topological defect-phase soliton and the pairing symmetry of a two-band superconductor: role of the proximity effect. Phys. Rev. Lett. 109, 227003 (2012)

    Google Scholar 

  112. S.-Z. Lin, X. Hu, Phase solitons in multi-band superconductors with and without time-reversal symmetry. New J. Phys. 14, 063021 (2012)

    Google Scholar 

  113. H. Bluhm, N.C. Koshnick, M.E. Huber, K.A. Moler, Magnetic response of mesoscopic superconducting rings with two order parameters. Phys. Rev. Lett. 97, 237002 (2006)

    Google Scholar 

  114. J.R. Kirtley, C.C. Tsuei, J.Z. Sun, C.C. Chi, L.S. Yu-Jahnes, A. Gupta, M. Rupp, M.B. Ketchen, Symmetry of the order parameter in the high-Tc superconductor YBa2Cu3O7-d. Nature 373, 225–228 (1995)

    Google Scholar 

  115. C.C. Tsuei, J.R. Kirtley, C.C. Chi, L.S. Yu-Jahnes, A. Gupta, T. Shaw, J.Z. Sun, M.B. Ketchen, Pairing symmetry and flux quantization in a tricrystal superconducting ring of YBa2Cu3O7−δ. Phys. Rev. Lett. 73, 593–596 (1994)

    Google Scholar 

  116. C.C. Tsuei, J.R. Kirtley, Z.F. Ren, J.H. Wang, H. Raffy, Z.Z. Li, Pure dx2 − y2 order-parameter symmetry in the tetragonal superconductor TI2Ba2CuO6+δ. Nature 387, 481–483 (1997)

    Google Scholar 

  117. J.W. Guikema, H. Bluhm, D.A. Bonn, R. Liang, W.N. Hardy, K.A. Moler, Two-dimensional vortex behavior in highly underdoped YBa2Cu3O6+x observed by scanning Hall probe microscopy. Phys. Rev. B 77, 104515 (2008)

    Google Scholar 

  118. L. Luan, O.M. Auslaender, D.A. Bonn, R. Liang, W.N. Hardy, K.A. Moler, Magnetic force microscopy study of interlayer kinks in individual vortices in the underdoped cuprate superconductor YBa2Cu3O6+x. Phys. Rev. B 79, 214530 (2009)

    Google Scholar 

  119. H. Sickinger, A. Lipman, M. Weides, R.G. Mints, H. Kohlstedt, D. Koelle, R. Kleiner, E. Goldobin, Experimental evidence of a φ Josephson junction. Phys. Rev. Lett. 109, 227003 (2012)

    Google Scholar 

  120. V.V. Ryazanov, V.A. Oboznov, A.Y. Rusanov, A.V. Veretennikov, A.A. Golubov, J. Aarts, Coupling of two superconductors through a ferromagnet: Evidence for a π junction. Phys. Rev. Lett. 86, 2427–2430 (2001)

    Google Scholar 

  121. T.-L. Ho, V.B. Shenoy, Binary mixtures of Bose condensates of akali atoms. Phys. Rev. Lett. 77, 3276–3279 (1996)

    Google Scholar 

  122. H. Pu, N.P. Bigelow, Collective excitations, metastability, and nonlinear response of a trapped two-species Bose-Einstein condensate. Phys. Rev. Lett. 80, 1134–1137 (1998)

    Google Scholar 

  123. D.L. Feder, M.S. Pindzola, L.A. Collins, B.I. Schneider, C.W. Clark, Dark-soliton states of Bose-Einstein condensates in anisotropic traps. Phys. Rev. A 62, 53606 (2000)

    Google Scholar 

  124. Domain wall solitons in binary mixtures of Bose-Einstein condensates. Phys. Rev. Lett. 87 (2001) 140401

    Google Scholar 

  125. K. Maki, T. Tsuneto, Magnetic resonance and spin waves in the A phase of superfluid He3. Phys. Rev. B 11, 2539 (1975)

    Google Scholar 

  126. K. Maki, H. Ebisawa, Magnetic excitations in superfluid 3He. J. Low Temp. Phys. 23, 351–365 (1976)

    Google Scholar 

  127. K. Maki, P. Kumar, Magnetic solitons in superfluid He3. Phys. Rev. B 14, 118 (1976)

    Google Scholar 

  128. M. Przedborski, Planar topological defects in unconventional superconductors. Master’s Degree Thesis, Brock University, Canada, 2013

    Google Scholar 

  129. Y.A. Izyumov, V.M. Laptev, Vortex structure in superconductors with a many-component order parameter. Phase Transitions A Multinatl. J. 20, 95–112 (1990)

    Google Scholar 

  130. E. Babaev, Phase diagram of planar U (1) × U (1) superconductor: Condensation of vortices with fractional flux and a superfluid state. Nucl Phys. B 686, 397–412 (2004)

    Google Scholar 

  131. O. Festin, P. Svedlindh, S.-I. Lee, Flux noise in MgB2 film, in SPIE’s First International Symposium on Fluctuations and Noise, vol. 5112 (2003), pp. 338–345

    Google Scholar 

  132. A. Crisan, Y. Tanaka, A. Iyo, L. Cosereanu, K. Tokiwa, T. Watanabe, Anomalous vortex melting line in the two-component superconductor (Cu,C)Ba2Ca3Cu4O10+δ. Phys. Rev. B 74, 184517 (2006)

    Google Scholar 

  133. A. Crisan, Y. Tanaka, D.D. Shivagan, A. Iyo, L. Cosereanu, K. Tokiwa, T. Watanabe, Anomalous AC susceptibility response of (Cu,C)Ba2Ca2Cu3Oy: experimental indication of two-component vortex matter in multi-layered cuprate superconductors. Jpn. J. Appl. Phys 46, L451–L453 (2007)

    Google Scholar 

  134. D.D. Shivagan, A. Crisan, P.M. Shirage, A. Sundaresan, Y. Tanaka, A. Iyo, K. Tokiwa, T. Watanabe, N. Terada, Vortex molecule and i-soliton studies in multilayer cuprate superconductors. J. Phys. Conf. Ser. 97, 012212 (2008)

    Google Scholar 

  135. A. Gurevich, V.M. Vinokur, Phase textures induced by dc-current pair breaking in weakly coupled multilayer structures and two-gap superconductors. Phys. Rev. Lett. 97, 137003 (2006)

    Google Scholar 

  136. Y. Tanaka, I. Hase, T. Yanagisawa, G. Kato, T. Nishio, S. Arisawa, Current-induced massless mode of the interband phase difference in two-band superconductors. Physica C 516, 10–16 (2015)

    Google Scholar 

  137. Y. Tanaka, K. Tanaka, K. Tanaka, K. Tonooka, N. Kikuchi, K. Mashiko, A. Iyo, Y. Shimoi, Topological soliton model. Japan patent 5098946 (2012)

    Google Scholar 

  138. Y. Tanaka, K. Mashiko, A. Iyo, D.D. Shivagan, P.M. Shirage, N. Kikuchi, K. Tonooka, N. Terada, K. Tokiwa, T. Watanabe, Topological soliton model. Japan patent 5099483, 2012

    Google Scholar 

  139. K. Tanaka, Chaos, cosmos, and diversity (Research of soliton 5) (2012). https://www.shizecon.net/award/detail.html?id=244

  140. I.H. Yukawa, On the interaction of elementary particles. Proc. Phys.-Math. Soc. Jpn. 17, 48–57 (1935)

    Google Scholar 

  141. H. Yukawa, Models and methods in the meson theory. Rev. Mod. Phys. 21, 474–479 (1949)

    Google Scholar 

  142. J. Kondo, Superconductivity in transition metals. Prog. Theor. Phys. 29, 1–9 (1963)

    Google Scholar 

  143. J. Peretti, Superconductivity of transition elements. Phys. Lett. 2, 275–276 (1962)

    Google Scholar 

  144. F. Wenger, S. Östlund, d-wave pairing in tetragonal superconductors. Phys. Rev. B 47, 5977–5983 (1993)

    Google Scholar 

  145. Y. Imry, On the statistical mechanics of coupled order parameters. J. Phys. C: Solid State Phys. 8, 567–577 (1975)

    Google Scholar 

  146. W.-C. Lee, S.-C. Zhang, C. Wu, Paring state with a time-reversal symmetry breaking in FeAs-Based superconductors. Phys. Rev. Lett. 102, 217002 (2009)

    Google Scholar 

  147. K. Kuboki, M. Sigrist, Proximity-induced time-reversal symmetry breaking at Josephson junctions between unconventional superconductors. J. Phys. Soc. Jpn. 65, 361–364 (1996)

    Google Scholar 

  148. M. Matsumoto, H. Shiba, Coexistence of different symmetry order parameters near a surface in d-wave superconductors I. J. Phys. Soc. Jpn. 64, 3384–3396 (1995)

    Google Scholar 

  149. M. Matsumoto, H. Shiba, Coexistence of different symmetry order parameters near a surface in d-wave superconductors II. J. Phys. Soc. Jpn. 64, 4867–4881 (1995)

    Google Scholar 

  150. M. Matsumoto, H. Shiba, Coexistence of different symmetry order parameters near a surface in d-wave superconductors III. J. Phys. Soc. Jpn. 65, 2194–2203 (1996)

    Google Scholar 

  151. M. Fogelström, S.-K. Yip, Time-reversal symmetry-breaking states near grain boundaries between d-wave superconductors. Phys. Rev. B 57, R14060–R14063 (1998)

    Google Scholar 

  152. A. Huck, A. van Otterlo, M. Sigrist, Time-reversal symmetry breaking and spontaneous currents in s-wave/normal-metal/d-wave superconductor sandwiches. Phys. Rev. B 56, 14163–14167 (1997)

    Google Scholar 

  153. M. Sigrist, D.B. Bailey, R.B. Laughlin, Fractional vortices as evidence of time-reversal symmetry breaking in high-temperature superconductors. Phys. Rev. Lett. 74, 3249–3252 (1995)

    Google Scholar 

  154. D.B. Bailey, M. Sigrist, R.B. Laughlin, Fractional vortices on grain boundaries: the case for broken time-reversal symmetry in high-temperature superconductors. Phys. Rev. B 55, 15239–15247 (1997)

    Google Scholar 

  155. T.K. Ng, N. Nagaosa, Broken time-reversal symmetry in Josephson junction involving two-band superconductors. EPL 87, 17003 (2009)

    Google Scholar 

  156. Y. Tanaka, T. Yanagisawa, Chiral state in three-gap superconductors. Solid State Commun. 150, 1980–1982 (2010)

    Google Scholar 

  157. Y. Tanaka, P.M. Shirage, A. Iyo, Time-reversal symmetry-breaking in two-band superconductors. Physica C 470, 2023–2026 (2010)

    Google Scholar 

  158. J. Garaud, E. Babaev, Domain walls and their experimental signatures in s + is superconductors. Phys. Rev. Lett. 112, 017003 (2014)

    Google Scholar 

  159. J. Garaud, J. Carlström, E. Babaev, M. Speight, Chiral CP2 skyrmions in three-band superconductors. Phys. Rev. B 87, 014507 (2013)

    Google Scholar 

  160. S. Gillis, J. Jäykkä, M.V. Milošević, Vortex states in mesoscopic three-band superconductors. Phys. Rev. B 89, 024512 (2014)

    Google Scholar 

  161. N.V. Orlova, A.A. Shanenko, M.V. Milošević, F.M. Peeters, A.V. Vagov, V.M. Axt, Ginzburg-Landau theory for multiband superconductors: Microscopic derivation. Phys. Rev. B 87, 134510 (2013)

    Google Scholar 

  162. Y. Yerin, S.-L. Drechsler, G. Fuchs, Ginzburg-landau analysis of the critical temperature and the upper critical field for three-band superconductors. J. Low. Temp. Phys. 173, 247–263 (2013)

    Google Scholar 

  163. A. Vagov, A.A. Shanenko, M.V. Milošević, V.M. Axt, V.M. Vinokur, J.A. Aguiar, F.M. Peeters, Superconductivity between standard types: multiband versus single-band materials. Phys. Rev. B 93, 174503 (2016)

    Google Scholar 

  164. X. Hu, Z. Wang, Stability and Josephson effect of time-reversal-symmetry-broken multicomponent superconductivity induced by frustrated intercomponent coupling. Phys. Rev. B 85, 064516 (2012)

    Google Scholar 

  165. Y. Takahashi, Z. Huang, X. Hu, H–T phase diagram of multi-component superconductors with frustrated inter-component couplings. J. Phys. Soc. Jpn. 83, 034701 (2014)

    Google Scholar 

  166. Y. Takagashi, Theoretical study on vortex states in unconventional superconductors. Doctoral Degree of Thesis, Tsukuba Univ. Japan, 2014

    Google Scholar 

  167. D. Weston, E. Babaev, Classification of ground states and normal modes for phase-frustrated multicomponent superconductors. Phys. Rev. B 88, 214507 (2013)

    Google Scholar 

  168. T.A. Bojesen, E. Babaev, A. Sudbø, Time reversal symmetry breakdown in normal and superconducting states in frustrated three-band systems. Phys. Rev. B 88, 220511 (2013)

    Google Scholar 

  169. Y. Tanaka, T. Yanagisawa, A. Crisan, P.M. Shirage, A. Iyo, K. Tokiwa, T. Nishio, A. Sundaresan, N. Terada, Domains in multiband superconductors. Physica C 471, 747–750 (2011)

    Google Scholar 

  170. T. Yanagisawa, I. Hase, Massless modes and abelian gauge fields in multi-band superconductors. J. Phys. Soc. Jpn. 82, 124704 (2013)

    Google Scholar 

  171. K. Kobayashi, Y. Ota, M. Machinda, Analysis of collective excitation for multi band superconductor: frustrated spin model approach. Physica C 494, 13–16 (2013)

    Google Scholar 

  172. Y. Tanaka. Y. Tanaka, Superconducting frustration bit. Physica C 505, 55–64 (2014)

    Google Scholar 

  173. J.C. Wheatley, Experimental properties of the extraordinary phases of liquid 3He at millikelvin temperatures. Physica 69, 218–244 (1973)

    Google Scholar 

  174. T.J. Greytak, R.T. Johnson, D.N. Paulson, J.C. Wheatley, Heat flow in the extraordinary phases of liquid He3. Phys. Rev. Lett. 31, 452 (1973)

    Google Scholar 

  175. R.T. Johnson, D.N. Paulson, C.B. Pierce, J.C. Wheatley, Measurements along the melting curve of He3 at millikelvin temperatures. Phys. Rev. Lett. 30, 207–210 (1973)

    Google Scholar 

  176. R.L. Kleinberg, D.N. Paulson, R.A. Webb, J.C. Wheatley, Supercooling and superheating of the AB transition in superfluid 3He near the polycritical point. J. Low. Temp. Phys. 17, 521–528 (1974)

    Google Scholar 

  177. K. Tokiwa, A. Iyo, T. Tsukamoto, H. Ihara. Czech, Synthesis of HgBa2Ca3Cu4O10+δ (Hg-1234) and HgBa2Ca4Cu5O12+δ(Hg-1245) from oxygen controlled precursors under high pressure. J. Phys. 46 [Suppl. 3], 1491–1492 (1996)

    Google Scholar 

  178. R.G. Dias, A.M. Marques, Frustrated multiband superconductivity. Supercond. Sci. Technol. 24, 085009 (2011)

    Google Scholar 

  179. B.J. Wilson, M.P. Das, Time-reversal-symmetry-broken state in the BCS formalism for a multi-band superconductor. J. Phys. Condens. Matter 25, 425702 (2013)

    Google Scholar 

  180. J. Bardeen, J.R. Schrieffer, Recent developments in superconductivity. Prog. Low Temp. Phys. 3, 170–287 (1961)

    Google Scholar 

  181. A.J. Leggett, Diatomic molecules and cooper pairs. Modern trends in the theory of condensed matter 115, 13–27 (1980)

    Google Scholar 

  182. V.J. Emery, S.A. Kivelson, Importance of phase fluctuations in superconductors with small superfluid density. Nature 374, 434–437 (1995)

    Google Scholar 

  183. P. Nozieres, S. Schmitt-Rink, Bose condensation in an attractive fermion gas: from weak to strong coupling superconductivity. J. Low Temp. Phys. 59, 195–211 (1985)

    Google Scholar 

  184. D.M. Eagles, Possible pairing without superconductivity at low carrier concentrations in bulk and thin-film superconducting semiconductors. Phys. Rev. 186, 456–463 (1969)

    Google Scholar 

  185. M. Holland, S.J.J.M.F. Kokkelmans, M.L. Chiofalo, R. Walser, Resonance superfluidity in a quantum degenerate Fermi gas. Phys. Rev. Lett. 87, 120406 (2001)

    Google Scholar 

  186. C. Regal, Experimental realization of BCS-BEC crossover physics. PhD Thesis, University of Colorado, USA, 2006

    Google Scholar 

  187. T. Yanagisawa, Nambu-Goldstone-Leggett modes in multi-condensate superconductors. Nov. Supercond. Mater. 1, 95–106 (2015)

    Google Scholar 

  188. Y. Tanaka, A. Iyo, A. Crisan, K. Tokiwa, T. Watanabe, N. Terada, Method of generation and method of detection of interband phase difference soliton and interband phase difference circuir. US Patent 7,522,078, 2009

    Google Scholar 

  189. M.N. Regueiro, M. Jaime, M.A.A. Franco, J.J. Capponi, C. Chaillout, J.L. Tholence, A. Sulpice, P. Lejay, Pressure effects in high temperature superconductors. Physica C 235, 2093–2094 (1994)

    Google Scholar 

  190. Y. Tanaka, G. Kato, T. Nishio, S. Arisawa, Observation of quantum oscillations in a narrow channel with a hole fabricated on a film of multiband superconductors. Solid State Commun. 201, 95–97 (2015)

    Google Scholar 

  191. S.-Z. Lin, C. Reichhardt, Stabilizing fractional vortices in multiband superconductors with periodic pinning arrays. Phys. Rev. B 87, 100508 (2013)

    Google Scholar 

  192. A. Crisan, Y. Tanaka, A. Iyo, Exotic vortex matter: pancake vortex molecules and fractional-flux. J. Super. Nov. Magn. 24, 1–6 (2011)

    Google Scholar 

  193. E. Babaev, J. Jäykkä, M. Speight, Magnetic field delocalization and flux inversion in fractional vortices in two-component superconductors. Phys. Rev. Lett. 103, 237002 (2009)

    Google Scholar 

  194. M.A. Silaev, Stable fractional flux vortices and unconventional magnetic state in two-component superconductors. Phys. Rev. B 83, 144519 (2011)

    Google Scholar 

  195. V.N. Fenchenko, Y.S. Yerin, Phase slip centers in a two-band superconducting filament: application to MgB2. Physica C 480, 129–136 (2012)

    Google Scholar 

  196. Ref. [1], pp. 215–224

    Google Scholar 

  197. J. Bardeen, Critical fields and currents in superconductors. Rev. Mod. Phys. 34, 667–681 (1962)

    Google Scholar 

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Acknowledgements

This work was partially supported by JSPS KAKENHI Grant Number JP 16K06275. We would like to thank Editage (www.editage.jp) for English language editing.

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  1. National Institute of Advanced Industrial Science and Technology, AIST-Tsukuba-Central-2-30381020, 1-1-1 Umezono, Tsukuba, Ibaraki, 305-8568, Japan

    Yasumoto Tanaka

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    Adrian Crisan

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Tanaka, Y. (2017). Emergence of an Interband Phase Difference and Its Consequences in Multiband Superconductors. In: Crisan, A. (eds) Vortices and Nanostructured Superconductors. Springer Series in Materials Science, vol 261. Springer, Cham. https://doi.org/10.1007/978-3-319-59355-5_7

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