Quasiclassical theory of the upper critical field of high-field superconductors. Application to momentum-dependent scattering

Rieck, C. T.; Scharnberg, K.; Schopohl, N.

doi:10.1007/bf00683526

Cited by 47 publications

(45 citation statements)

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“…While the cylindrical Fermi surface sheets are dominating the behavior of B c2 at low temperatures, leading to a large anisotropy, at temperatures approaching T c the π bands due to their much larger c-axis Fermi velocity start to play a more important role, strongly reducing the B c2 anisotropy. Thus, the strong temperature dependence of the B c2 anisotropy appears as a cross-over from a low temperature σ band dominated regime to a higher temperature mixed σ and π band regime.In order to include the multi-band Fermi surface structure in the calculation of the upper critical field, we start our investigation from the fully momentum dependent multi-band formulation of the quasiclassical (Eilenberger) theory of the upper critical field [24]. For that purpose we have to solve the linearized multi-band gap equation in the presence of an external magnetic field, which reads ∆ α ( r) = −πT…”

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confidence: 99%

“…In order to include the multi-band Fermi surface structure in the calculation of the upper critical field, we start our investigation from the fully momentum dependent multi-band formulation of the quasiclassical (Eilenberger) theory of the upper critical field [24]. For that purpose we have to solve the linearized multi-band gap equation in the presence of an external magnetic field, which reads ∆ α ( r) = −πT…”

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confidence: 99%

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Fermi Surface Topology and the Upper Critical Field in Two-Band Superconductors: Application toMgB2

2003

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Recent measurements of the anisotropy of the upper critical field Bc2 on MgB2 single crystals have shown a puzzling strong temperature dependence. Here, we present a calculation of the upper critical field based on a detailed modeling of bandstructure calculations that takes into account both the unusual Fermi surface topology and the two gap nature of the superconducting order parameter. Our results show that the strong temperature dependence of the Bc2 anisotropy can be understood as an interplay of the dominating gap on the σ-band, which possesses a small c-axis component of the Fermi velocity, with the induced superconductivity on the π-band possessing a large c-axis component of the Fermi velocity. We provide analytic formulas for the anisotropy ratio at T = 0 and T = Tc and quantitatively predict the distortion of the vortex lattice based on our calculations.PACS numbers: 74.25.Op, 74.70.Ad Our understanding of the physical properties of the recently discovered superconductivity in MgB 2 has made rapid progress since its discovery [1]. Its high critical temperature T c = 39 K can be understood as arising from strong conventional electron-phonon coupling to a high frequency phonon mode [2,3,4]. Its pairing symmetry seems to be of conventional s-wave type [5,6]. However, in contrast to conventional superconductors, a number of recent experiments indicate that there exist two gaps of different size in this compound [7,8,9,10,11,12]. This possibility is supported by band structure calculations, which have shown that the Fermi surface of this compound consists of four bands: two σ-type two-dimensional cylindrical hole sheets and two π-type three dimensional tubular networks [13,14] in good overall agreement with recent de Haas-van Alphen experiments [15]. Microscopic calculations of the superconducting gap based on band structure calculations have shown recently that indeed one should expect a big superconducting gap living on the σ bands and a smaller one, induced by interband pairing interaction, living on the π bands [3,16]. Impurity scattering, which in conventional superconductors tends to average out strongly differing gap values, in this case becomes ineffective, because the σ and π bands possess different symmetries, making interband impurity scattering much weaker than intraband impurity scattering [17].Recent measurements of the upper critical field B c2 , particularly its anisotropy, on single crystal MgB 2 have shown a puzzling strong temperature dependence of the anisotropy ratio B ab c2 /B c c2 between the ab-plane and the c-axis upper critical field [18,19,20]. In conventional systems this ratio rarely changes by more than 10 to 20 percent as a function of temperature. In MgB 2 changes by more than a factor of 2 have been observed. It has been shown that such a strong temperature dependence of the anisotropy ratio can be obtained within a strongly anisotropic single gap model, possessing a small gap in c-axis direction and a big gap in ab-plane direction [21]. However, the gap anisotropy woul...

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Fermi Surface Topology and the Upper Critical Field in Two-Band Superconductors: Application toMgB2

2003

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“…Subsequent refinements were made to include various effects, such as the impurity dependence of µ 0 H c2 by Helfand et al [172,173] [180], and Schossmann et al [181], pand d-wave scattering by Rieck at al. [177] and the energy-dependence of N(E F ) by Schossmann et al [182]. A useful overview of these various mechanisms is provided by Rieck et al [177].…”

Section: Upper Critical Field Of Nb-snmentioning

confidence: 99%

“…[177] and the energy-dependence of N(E F ) by Schossmann et al [182]. A useful overview of these various mechanisms is provided by Rieck et al [177].…”

Section: Upper Critical Field Of Nb-snmentioning

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An experimental and computational study of srain sensitivity in superconducting Nb3Sn

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This work is the result of efforts by many people, both in a professional and a personal sense. During my time in Berkeley I had the opportunity to work with friendly and supportive people who were pushing back scientific boundaries, regarding the limits of superconducting high field technology. It is an odd but good experience to read papers from various authors detailing one scientific breakthrough or another, and then to meet them in person. Being a multi-cultural hub, Berkeley also allowed me to meet and become friends with people from all corners of this planet.Along the way, people have been instrumental in making this research happen. At LBNL, Jonathan Slack, Reuben Mendelsberg, and Andre Anders allowed me to use their lab for a rather extended period of time thus allowing for the fabrication of thin films, and have helped in various other ways along the years. The people at Ohio State University have helped by repeatedly performing heat capacity measurements on Nb 3 Sn bulk samples which were kindly supplied by Wilfried Goldacker of the Karlsruhe Institute of Technology. In particular I would like to thank Mike Susner of the Ohio State University, who came to the lab in the weekends just to make sure my samples would get measured. John Bonevich of the National Institute of Science and Technology was kind enough to perform characterization work on some of the Nb-Sn thin films we made, which included the STEM image on the cover. A lot of the experimental work was made possible with software and hardware designed at the University of Twente (such as VI by Bennie ten Haken), and I have gotten useful recommendations and assistance along the way, such as the advice on thin film fabrication from Frank Roesthuis. Professors Marcel ter Brake, Herman ten Kate, David Larbalestier, and Frances Hellman were kind enough to write letters of recommendation which contributed to getting the CSC student fellowship award. Vladimir Kresin of LBNL was kind enough to answer various questions related to the microscopic properties of Nb 3 Sn and comment on the description of microscopic theory in this thesis.Shane Cybart and Stephen Wu have assisted Edwin Dollekamp and myself in attempting to do some very fancy experiments. Edwin, from the University of Twente, took on a complicated research topic and I was impressed with how far he managed to get in that work, and Shane and Stephen invested time in the evenings and weekends to make it happen. Professor Orlandos previous investigations of Nb 3 Sn were an inspiration for some of the work described in this thesis, and he was kind enough to answer questions by email and over the phone. Derek Stewart of the Cornell NanoScale Science and Technology Facility helped me to get familiar with density functional theory calculations and computing clusters and made the suggestion of using Quantum Espresso ab-initio software. Robert Ryne and Steve Gourlay of LBNL helped me getting access to sizeable supercomputing resources at NERSC which were needed for this research.My friends and family st...

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Superconductivity of Magnesium Diboride: Theoretical Aspects

Dahm

Frontiers in Superconducting Materials

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In this work we review our present understanding of superconductivity in Magnesium Diboride from the theoretical perspective as it evolves from band structure calculations. Particular emphasis is placed on two gap superconductivity. Some of its peculiar consequences are discussed, in particular upper critical field anisotropy and microwave conductivity.Comment: 27 pages, 13 figures, review article to be published in: A. V. Narlikar (Ed.), Frontiers in Superconducting Materials, Springer, Berlin, 200

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Quasiclassical theory of the upper critical field of high-field superconductors. Application to momentum-dependent scattering

Cited by 47 publications

References 67 publications

Fermi Surface Topology and the Upper Critical Field in Two-Band Superconductors: Application toMgB2

Fermi Surface Topology and the Upper Critical Field in Two-Band Superconductors: Application toMgB2

An experimental and computational study of srain sensitivity in superconducting Nb3Sn

Superconductivity of Magnesium Diboride: Theoretical Aspects

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