the effect of gap fluctuations on specific heat of a superconducting nanograin

Recently, the finite size effects, via superconducting nanograins, have attracted much attention from physicists. the effect of the small size can enter via the interaction matrix element and the spectral energy. we suppose that the mean level spacing near the fermi energy is smaller than the bulk gap, allowing the bcs formalism to remain a valid approximation. for a nanograin, the gap function, in general, depends on the size of the system, and the fermi energy. by entering the effect of the small size on the gap equation for a rectangular nanograin, specific heat in terms of temperature and length of a superconducting nanograin is obtained. our results reveal that the spectral energy of the nanograin does not affect the change in the behavior of specific heat. however, the effect of the energy gap of nanograin strongly affects the behavior of specific heat. one of the interesting results is that at some fixed temperatures, the behaviour of specific heat shows a peak in a special length. also, we compare specific heat in 2- and 3-dimensional cases.