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Abstract:
Nanocrystalline AlySn1-yO2-y/2 (y = 0.57, 0.4) was prepared by a co-precipitation method and subsequent calcination at temperatures of up to 650 degrees C. Transmission electron microscopy and X-ray diffraction reveal crystallite sizes of about 2 nm and a crystal structure equivalent to that of pure SnO2 cassiterite. The local structure was investigated by Al-27 and Sn-119 NMR as well as by Sn Mossbauer spectroscopy. The results show the formation of a solid solution with a random distribution of Al and Sn on the cation sites and a random distribution of oxygen vacancies on the anion sites. We formulate a kinetic theory for non-centrosymmetric superconductors at low temperatures in the clean limit. The transport equations are solved quite generally in spin- and particle-hole (Nambu) space by performing first a transformation into the band basis and second a Bogoliubov transformation to the quasiparticle-quasihole phase space. Our result is a particle-hole-symmetric, gauge-invariant and charge conserving description, which is valid in the whole quasiclassical regime (vertical bar q vertical bar << k(F) and (h) over bar omega << E-F). We calculate the current response, the specific heat capacity, and the Raman response function. For the Raman case, we investigate within this framework the polarization dependence of the electronic (pair-breaking) Raman response for the recently discovered non-centrosymmetric superconductors at zero temperature. Possible applications include the systems CePt3 Si and Li-2 Pd-x Pt3-x B, which reflect the two important classes of the involved spin- orbit coupling. We provide analytical expressions for the Raman vertices for these two classes and calculate the polarization dependence of the electronic spectra. We predict a two-peak structure and different power laws with respect to the unknown relative magnitude of the singlet and triplet contributions to the superconducting order parameter, revealing a large variety of characteristic fingerprints of the underlying condensate.
