Finite-size effects and polycrystalline high-Tc materials.

Abstract

We examine the effect of thermal and quantal fluctuations on small super-conducting grains using a BCS-like Hamiltonian. A comparison between the static path approximation to the Hubbard-Stratonovich representation of the partition function (${\mathit{Z}}_{\mathrm{HS}}$) and the order-parameter representation (${\mathit{Z}}_{\mathrm{OP}}$) based on the Landau theory of phase transitions shows that one should use the expectation value of the pairing potential scrG instead of the BCS energy gap \ensuremath{\Delta} for the order parameter of a superconducting system. Unlike ${\mathit{Z}}_{\mathrm{HS}}$, ${\mathit{Z}}_{\mathrm{OP}}$ is not restricted to positive-definite pairing potentials and can be used for general momentum-dependent pairing potentials. We find that quantal fluctuations are negligible for the crystallites of the polycrystalline high-${\mathit{T}}_{\mathit{c}}$ materials and that the results obtained using ${\mathit{Z}}_{\mathrm{OP}}$ are a good approximation to the exact results. Both the sharpening of the peak in the specific heat and the increase in the critical temperature observed during the sintering process of polycrystalline high-${\mathit{T}}_{\mathit{c}}$ materials can be qualitatively understood by taking into account thermal fluctuations. In polycrystalline high-${\mathit{T}}_{\mathit{c}}$ materials there is an anomaly in the specific heat rising above the BCS peak which is not reproduced by including these finite-size effects.