Point-contact Andreev-reflection spectroscopy in anisotropic superconductors: The importance of directionality (Review Article)
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(a) Fermi surface of MgB2. (b) Model Fermi surface used for the calculation of the theoretical spectra within the two-band 3D BTK model. (c) Theoretical PCARS curves generated at T = 4.2 K by using the two-band 3D BTK model with the gaps calculated in Ref. 7 , i.e., Δπ = 2.70 meV and Δσ = 7.09 meV and the model Fermi surface depicted in (b), for I||ab (bottom) and I||c (top). The bottom (blue) and the top thin (red) curves were obtained by using the same parameters, i.e., Z π = 0.37, Γ π = 1.65 meV, Z σ = 0.85, Γ σ = 2.10 meV, that allow reproducing the ab-plane spectrum of panel (d); the top thick (red) curve has parameters optimized to reproduce the shape of the c axis spectrum of panel (d), i.e., Z π = 0.17, Γπ = 0.5 meV, Z σ = 0.85, Γσ = 0.4 meV. (d) Symbols: two examples of PCARS spectra taken in MgB2 single crystals, with current injected along the ab plane (bottom) and along the c axis (top). The vertical scale is on the left axis; the top curve has been offset by 1 for clarity. Lines: two examples of STS spectra taken in different grains of a polycrystal (from Ref. 24 ). The vertical scale is on the right axis and the top curve has been offset for clarity. Vertical lines show the correspondence of the gap features in PCARS and STS spectra along the different directions.
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(a) Fermi surface of CaC6. The almost spherical surface originates from the nearly-free electron band (interlayer band) while the warped cylinders are mainly arising from the carbon π bands. As shown in Ref. 30, this distinction is however not strict. (b) Model Fermi surface used for the calculations within the 3D BTK model. For simplicity, we assumed two isotropic gaps of different amplitudes (indicated by different colors) to reside on the spherical surface and on the warped cylinders (here represented by a hyperboloid of revolution). Note that in the cell of panel (a) there are 7 cylinders for each spherical surface. (c) Theoretical spectra at T = 400 mK calculated by using the 3D BTK model and the schematic Fermi surface of panel (b). Apart from the gap values Δ1 = 1.7 meV and Δ2 = 1.3 meV that reside on the two portions of the FS, the parameters Z 1 = 0.60 and Z 2 = 0.95 were used. Note that these values are the same for both I||c and I||ab. Finally, the broadening parameters were set to zero. (d) Symbols: experimental PCARS spectra measured at 400 mK with current injected along the c axis (top) and along the ab plane (bottom). Thin lines are the theoretical spectra calculated as in panel (c) but using the broadening parameters Γ1 = 0.8 meV and Γ2 = 0.5 meV.
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(a) Fermi surface of Ca(Fe1.94Co0.06)2As2. The hole-like FS sheets in the center of the Brillouin zone is on the verge of a topological transition and is splitting into two closed pockets centered at the Z points. (b) The model Fermi surface used in the 3D BTK model, shown here only in the upper half of the Brillouin zone. Matt surfaces are the Fermi surface sheets, while the gridded surfaces indicate the amplitude of the relevant gap, which is isotropic on the electron-like FS but anisotropic on the hole-like one. (c) Theoretical curves calculated for I||ab (top) and I||c (bottom) using the Fermi surface of panel (b) and the gaps indicated in the labels. Here “1” and “2” refer to the holelike (electron-like) FS, respectively. The other parameters were: for curve 1, Γ1 = 1.25 meV, Z 1 = 0.05, Γ2 = 6.15 meV, Z 2 = 0.145; for curve 2, Γ1 = 1.7 meV, Z 1 = 0.05, Γ2 = 6.5 meV, Z 2 = 0.23. In both cases the angle between the normal to the interface and the a axis was taken to be α = π/8. The latter set of parameters was also used to calculate the c-axis spectrum (curve 3). (d) Two examples of experimental curves measured in single crystals of 6% Co-doped CaFe2As2, with the current injected along the ab planes.
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(a) Fermi surface of Ba(Fe1.92Co0.08)2As2, with the strongly warped hole-like FS sheets around Γ and the electron-like FS sheets at the corners of the Brillouin zone. (b) The model Fermi surface used in the 3D BTK model. Matt surfaces are the Fermi surface sheets, while the gridded surfaces indicate the amplitude of the relevant gap. The drawing refers to the case of isotropic gaps on both the bands. (c) Theoretical curves calculated for I||ab (1 and 2) and I||c (3and 4) and using the Fermi surface of panel (b). The gap amplitudes indicated in the labels were chosen in order to fit the position of the gap features in the experimental curves of panel (d). The other fitting parameters are the following: for curve 1, Γ1 = 1.85 meV, Z 1 = 0.03, Γ2 = 3.6 meV, Z 2 = 0.31; for curve 2, Γ1 = 1.75 meV, Z 1 = 0.08, Γ2 = 3.0 meV, Z 2 = 0.245; for curve 3, Γ1 = 2.8 meV, Z 1 = 0.05, Γ2 = 1.3 meV, Z 2 = 0; for curve 4, Γ1 = 3.85 meV, Z 1 = 0.1, Γ2 = 1.4 meV, Z 2 = 0. (d) Some examples of the experimental curves measured in 8% Co-doped BaFe2As2 with I||ab (top) and I||c (bottom). The lowest-lying curve was measured in epitaxial films 52 with x = 0.08 and Tc = (23.8±0.7) K, the others in single crystals.
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