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

Abstract

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...

Temperature-Dependent Anisotropy of the Penetration Depth and Coherence Length ofMgB2

“…Although there were some disagreements in early measurements, the most recent data [2, 3, 9] agree well with the theoretical predictions [4,5]. Significantly less experimental data has been reported on γ λ .…”

“…2,3,4,5). The maximum value of γ ξ ≃ 6 is found at the lowest temperatures where it is dominated by the anisotropy in the quasi two dimensional σ bands.…”

Coherent current states in a two-band superconductor

“…Various thermodynamic and transport properties of 2 MgB were studied in the framework of two-band BCS model [15][16][17][18][19][20][21][22]. Ginzburg-Landau functional for two-gap superconductors was derived within the weak-coupling BCS theory in dirty [23] and clean [24] superconductors.…”

Single-gap superconductivity inβ−Bi2Pd

“…The lower and upper critical fields also behave unusually leading for example to different superconducting anisotropies depending whether defined via * Corresponding author: samuely@saske.sk H c1 or H c2 , respectively [9]. Moreover such anisotropies are temperature dependent due to the interplay of the gaps which is varying in different parts of the field vs temperature phase diagram [10,11].…”