Abstract
Consideration of the functional derivative of the zero-temperature reduced upper critical magnetic fieldh c2(0) with electron-phonon spectral density α2 F(ω) suggests that its value can be maximized, for a given areaA under α2 F(ω), with the choice of a delta-function spectral density. We show thath c2(0) is then independent ofA and that it increases steadily as the Einstein frequency ΩE of the delta function is lowered. We argue that there is a local maximum inh c2(0) at ΩE=0. The value at maximum is very sensitive to impurity content and increases sharply from a clean-limit value of 1.5 atT c /ΩE=1.33 to more than 3.45 in the dirty limit.
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Schossmann, M., Carbotte, J.P. & Schachinger, E. On the maximum reduced upper critical magnetic field in Eliashberg theory. J Low Temp Phys 70, 537–545 (1988). https://doi.org/10.1007/BF00682164
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DOI: https://doi.org/10.1007/BF00682164