E. Vecino et al., Recursion method for nonhomogeneous superconductors: Proximity effect in superconductor-ferromagnet nanostructures - art. no. 184502, PHYS REV B, 6418(18), 2001, pp. 4502
We present a theoretical method to study the electronic local spectral dens
ity of hybrid nanostructures consisting of a normal (N) or ferromagnetic (F
) region deposited on top of a superconductor (S). Our approach is based on
a lattice Hamiltonian model which allows to describe the spatial variation
of the superconducting order parameter in nanostructures of arbitrary geom
etry. In order to obtain the local density of states we develop a generaliz
ation of the recursion method valid for systems containing superconducting
and ferromagnetic regions. As a first step we analyze the proximity effect
and the detailed behavior of Andreev states in one-dimensional (1D) N-S and
F-S structures. We study the transition from the 1D case to the limit of i
nfinite lateral dimensions in the ballistic regime. Finally we analyze the
spatial variation of the proximity effect as a function of the exchange fie
ld in F-S nanostructures. It is found that the oscillations in the induced
pairing amplitude in the scale of the ferromagnetic coherence length can be
correlated to the crossing of Andreev states through the Fermi energy as a
function of the ferromagnetic region size.