Nonmagnetic impurity scattering is known to shift up the Ginzburg−Landau parameter of a superconductor. In this case, when the system is initially in type I, it can change its magnetic response, crossing the intertype domain with between the two standard superconductivity types and arriving at type II. In the present work we demonstrate that the impact of disorder can be much more profound in the presence of the multiband structure of the charge carrier states. In particular, when the band diffusivities differ from each other, the intertype domain tends to expand significantly, including points with that belong to deep type-II in conventional single-band superconductors. Our finding sheds light on the nontrivial disorder effect and significantly complements earlier results on the enlargement of the intertype domain in clean multiband superconductors.
. [J]. Frontiers of Physics, 2024, 19(4): 43205.
P. M. Marychev, A. A. Shanenko, A. V. Vagov. Intertype superconductivity evoked by the interplay of disorder and multiple bands. Front. Phys. , 2024, 19(4): 43205.
B. Ketterson J.N. Song S., Superconductivity, Cambridge: Cambridge University Press, 1999
2
Auer J. , Ullmaier Y. . Magnetic behavior of type-II superconductors with small Ginzburg‒Landau parameters. Phys. Rev. B, 1973, 7(1): 136 https://doi.org/10.1103/PhysRevB.7.136
3
Krägeloh U. . Flux line lattices in the intermediate state of superconductors with Ginzburg‒Landau parameters near 1/2. Phys. Lett. A, 1969, 28(9): 657 https://doi.org/10.1016/0375-9601(69)90493-9
Kumpf U. . Magnetisierungskurven von Supraleitern zweiter Art mit kleinen Ginzburg‒Landau‒Parametern. Phys. Status Solidi B, 1971, 44(2): 829 https://doi.org/10.1002/pssb.2220440243
N. Ovchinnikov Yu. . Generalized Ginzburg-Landau equation and the properties of superconductors with Ginzburg‒Landau parameter κ close to 1. J. Exp. Theor. Phys., 1999, 88(2): 398 https://doi.org/10.1134/1.558809
Laver M. , J. Bowell C. , M. Forgan E. , B. Abrahamsen A. , Fort D. , D. Dewhurst C. , Mühlbauer S. , K. Christen D. , Kohlbrecher J. , Cubitt R. , Ramos S. . Structure and degeneracy of vortex lattice domains in pure superconducting niobium: A small-angle neutron scattering study. Phys. Rev. B, 2009, 79(1): 014518 https://doi.org/10.1103/PhysRevB.79.014518
10
H. Brandt E. , P. Das M. . Attractive vortex interaction and the intermediate mixed state of superconductors. J. Supercond. Nov. Magn., 2011, 24(1−2): 57 https://doi.org/10.1007/s10948-010-1046-8
11
Pautrat A. , Brûlet A. . Temperature dependence of clusters with attracting vortices in superconducting niobium studied by neutron scattering. J. Phys.: Condens. Matter, 2014, 26(23): 232201 https://doi.org/10.1088/0953-8984/26/23/232201
12
Y. Ge J. , Gutierrez J. , Lyashchenko A. , Filipov V. , Li J. , V. Moshchalkov V. . Direct visualization of vortex pattern transition in ZrB12 with Ginzburg-Landau parameter close to the dual point. Phys. Rev. B, 2014, 90(18): 184511 https://doi.org/10.1103/PhysRevB.90.184511
13
Reimann T. , Mühlbauer S. , Schulz M. , Betz B. , Kaestner A. , Pipich V. , Böni P. , Grünzweig C. . Visualizing the morphology of vortex lattice domains in a bulk type-II superconductor. Nat. Commun., 2015, 6(1): 8813 https://doi.org/10.1038/ncomms9813
14
Vagov A. , A. Shanenko A. , V. Milǒsevíc M. , M. Axt V. , M. Vinokur V. , A. Aguiar J. , M. Peeters F. . Superconductivity between standard types: Multiband versus single-band materials. Phys. Rev. B, 2016, 93(17): 174503 https://doi.org/10.1103/PhysRevB.93.174503
15
Y. Ge J. , N. Gladilin V. , E. Sluchanko N. , Lyashenko A. , Filipov V. , O. Indekeu J. , V. Moshchalkov V. . Paramagnetic Meissner effect in ZrB12 single crystal with non-monotonic vortex−vortex interactions. New J. Phys., 2017, 19(9): 093020 https://doi.org/10.1088/1367-2630/aa8246
16
Reimann T. , Schulz M. , F. R. Mildner D. , Bleuel M. , Brûlet A. , P. Harti R. , Benka G. , Bauer A. , Böni P. , Mühlbauer S. . Domain formation in the type-II/1 superconductor niobium: Interplay of pinning, geometry, and attractive vortex‒vortex interaction. Phys. Rev. B, 2017, 96(14): 144506 https://doi.org/10.1103/PhysRevB.96.144506
17
Wolf S. , Vagov A. , A. Shanenko A. , M. Axt V. , A. Aguiar J. . Vortex matter stabilized by many-body interactions. Phys. Rev. B, 2017, 96(14): 144515 https://doi.org/10.1103/PhysRevB.96.144515
18
Backs A. , Schulz M. , Pipich V. , Kleinhans M. , Böni P. , Mühlbauer S. . Universal behavior of the intermediate mixed state domain formation in superconducting niobium. Phys. Rev. B, 2019, 100(6): 064503 https://doi.org/10.1103/PhysRevB.100.064503
19
T. Saraiva T. , Vagov A. , M. Axt V. , A. Aguiar J. , A. Shanenko A. . Anisotropic superconductors between types I and II. Phys. Rev. B, 2019, 99(2): 024515 https://doi.org/10.1103/PhysRevB.99.024515
20
Vagov A. , Wolf S. , D. Croitoru M. , A. Shanenko A. . Universal flux patterns and their interchange in superconductors between types I and II. Commun. Phys., 2020, 3(1): 58 https://doi.org/10.1038/s42005-020-0322-6
21
Ooi S. , Tachiki M. , Konomi T. , Kubo T. , Kikuchi A. , Arisawa S. , Ito H. , Umemori K. . Observation of intermediate mixed state in high-purity cavity-grade Nb by magneto-optical imaging. Phys. Rev. B, 2021, 104(6): 064504 https://doi.org/10.1103/PhysRevB.104.064504
22
S. Brems X. , Mühlbauer S. , Y. Córdoba-Camacho W. , A. Shanenko A. , Vagov A. , Albino Aguiar J. , Cubitt R. . Current-induced self-organisation of mixed superconducting states. Supercond. Sci. Technol., 2022, 35(3): 035003 https://doi.org/10.1088/1361-6668/ac455e
23
J. Curran P. , M. Desoky W. , V. Milǒsevíc M. , Chaves A. , B. Lalöe J. , S. Moodera J. , J. Bending S. . Spontaneous symmetry breaking in vortex systems with two repulsive length scales. Sci. Rep., 2015, 5(1): 15569 https://doi.org/10.1038/srep15569
24
Wolf S.Vagov A.A. Shanenko A.M. Axt V.Perali A.A. Aguiar J., BCS‒BEC crossover induced by a shallow band: Pushing standard superconductivity types apart, Phys. Rev. B 95(9), 094521 (2017)
25
J. F. Cavalcanti P. , T. Saraiva T. , A. Aguiar J. , Vagov A. , D. Croitoru M. , A. Shanenko A. . Multiband superconductors with degenerate excitation gaps. J. Phys.: Condens. Matter, 2020, 32(45): 455702 https://doi.org/10.1088/1361-648X/aba776
26
Gurevich A. . Enhancement of the upper critical field by nonmagnetic impurities in dirty two-gap superconductors. Phys. Rev. B, 2003, 67(18): 184515 https://doi.org/10.1103/PhysRevB.67.184515
Vagov A. , A. Shanenko A. , V. Milǒsevíc M. , M. Axt V. , M. Peeters F. . Extended Ginzburg‒Landau formalism: Systematic expansion in small deviation from the critical temperature. Phys. Rev. B, 2012, 85(1): 014502 https://doi.org/10.1103/PhysRevB.85.014502
29
A. Shanenko A. , V. Milǒsevíc M. , M. Peeters F. , V. Vagov A. . Extended Ginzburg‒Landau formalism for two-band superconductors. Phys. Rev. Lett., 2011, 106(4): 047005 https://doi.org/10.1103/PhysRevLett.106.047005
30
Vagov A. , A. Shanenko A. , V. Milǒsevíc M. , M. Axt V. , M. Peeters F. . Two-band superconductors: Extended Ginzburg‒Landau formalism by a systematic expansion in small deviation from the critical temperature. Phys. Rev. B, 2012, 86(14): 144514 https://doi.org/10.1103/PhysRevB.86.144514
31
A. Golubov A. , Kortus J. , V. Dolgov O. , Jepsen O. , Kong Y. , K. Andersen O. , J. Gibson B. , Ahn K. , K. Kremer R. . Specific heat of MgB2 in a one- and a two-band model from first-principles calculations. J. Phys.: Condens. Matter, 2002, 14(6): 1353 https://doi.org/10.1088/0953-8984/14/6/320
