Fluctuation-Induced Diamagnetism in Dirty Superconductors

An explicit evaluation is made of the fluctuation-induced diamagnetism from zeropoint fluctuations, which have been neglected in a previous calculation by Maki and Takayama. It is shown that in fact this contribution has another scaling field $\sim \frac{{\phi }_0}{l^2}$, as calculated previously by Lee and Payne and by Kurkijärvi, Ambegaokar, and Eilenberger. However, this term gives rise to an almost constant susceptibility (of the same order as Landau diamagnetism) in the field region of experimental interest [i.e., $H\sim H_{c2\mathrm{}}\mathrm{}\left(0\right)\mathrm{}$, the upper critical field at $T=0\mathrm{}$ K].