###### 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.