Inhomogeneous Superconductivity



Giant Proximity effect in phase fluctuating superconductors
Phys. Rev. Lett. 101, 097004 (2008)


    When a tunneling barrier between two superconductors is formed by a normal material that would be a superconductor in the absence of phase fluctuations, the resulting Josephson effect can undergo an enormous enhancement. We establish this novel proximity effect by a general argument as well as a numerical simulation and argue that it may underlie recent experimental observations of the giant proximity effect between two cuprate superconductors separated by a barrier made of the same material rendered normal by severe underdoping.


    


Proximity effect and Josephson junctions
Phys. Rev. B 73, 014503 (2006)

   

    Using the Bogoliubov–de Gennes equations for a tight-binding Hamiltonian we describe the proximity effect in weak links between a superconductor with critical temperature Tc and one with critical temperature Tc’, where Tc’>Tc . The weak link “N” is therefore a superconductor above its own critical temperature and the superconducting regions are considered to have either s-wave or d-wave symmetry. We note that the proximity effect is enhanced due to the presence of superconducting correlations in the weak link.


     




Andreev bound states in finite 2D & 3D size systems


    LDOS for a square normal region surrounded by s-wave superconductor:




    LDOS for a square normal region surrounded by d-wave superconductor:





    Recursion method (Lanczos/Chebyshev) for calculating Green's functions ( in progress )


    A very efficient method of solving the Bogoliubov-de Gennes equations (also other mean-field equations) is obtained by using the Kernel Polynomial Method. The Green’s function can be expanded in terms of Chebyshev series, with the coefficients calculated in a recursive manner. This method is similar in spirit with the Lanczos one (developed by Haydock, Annett and Gyorfy), but does not suffer from the numerical instability of the Lanczos procedure.