Deviation of Order parameter of s-wave superconducting nano-grain in quantum tunneling process: Coupling constant effects

Full text: When size of system is reduced, its mesoscopic behavior is strongly dictated by the finite electron number, and quantum fluctuation and quantum tunneling process can be occur. Dynamic behavior of nanometer-scale s-wave superconducting grain of the dimensions much less than the coherence length is considered. Grain is considered in the presence of a magnetic field and is weakly coupled to normal metallic plate, because of spin conservation. Andreev processes can be ignored. BCS approach is applied to a reduced BCS Hamiltonian for uniformly spaced, when grain is in superconducting state. Probability of departure from superconducting state of nano-grain and quantum tunneling from a pure superconducting state in frequency space are considered. Using self-consistent calculation based on complete integral representation of order parameter in frequency space, and considering deviation of matrix Green function of system (consist of grain and metal) as perturbation term at first approximation, due to quantum fluctuation, then deviation of order parameter of grain at absolute zero temperature have been plotted numerically in terms of frequency and coupling constant of Cooper pair of nano-grain. By using the deviation, we can conclude departure from superconducting state of grain and detect quantum phase transition. Also, for a fixed frequency and fixed density of states of grain, it is seen that difference between order parameter of pure superconducting state of nano-grain (before quantum tunneling process) and the last state (after considering quantum fluctuation) does not linearly depend on coupling constant of Cooper pair. (authors)