Quasiclassical Elienberger Equations

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Quasiclassical Elienberger equations [129] for the green functions g(k , r, and order parameter , is a powerful tool to deal with inhomogeneous superconductors [130]. These functions depend on the so called, ‘Matsubara frequency’, , coordinate r, and wave vector k on the fermi surface. The dependence of green functions and order parameters on the wave vector k, makes them sensitive to the shape of fermi surface. This makes solution of Elienberger equations complicated in the system of complex Fermi surface, like MgB2. Frequently, the superconducting materials has strong impurity scattering and is described by the so called ‘dirty limit’. For such case, the impurity scattering within each fermi sheet averages out the angular dependences of …show more content…
This means, in this scenario the electron motion is diffusive and green functions are nearly isotropic. Usadel’s approach not only deals to ‘strongly dirty’ samples but also ‘moderately dirty’ samples. The theory of upper critical field for MgB2 was developed separately by Alex Gurevich [133], and Golubov and Koshelov [134]. Their theoretical models are based on multiband generalization of the quasiclassical Usadel equations. The main difference between these two approaches is that Gurevich model considers the small band anisotropy where as Golubov and Koshelov model addresses the case of very high anisotropy in quasi-2D band [134]. In this chapter, first I provide an over view of Gurevich theory [135] and I apply this theory to extract interband scattering rates and intraband diffusivities of MgB2 ultrathin …show more content…
To address the physics behind observed anomalous behavior of Hc2 (T), Gurevich, and Gloubov and Koshelov theory was developed. The unique benefit of this approach is that the details of complex Fermi surface of MgB2 is not necessary to calculate Hc2 [132]. The impurity scattering is accounted by the nature of normal state electronic diffusivities and which are controlled by their respective intraband scattering rates in the and π bands, and interband scattering rates , , and

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