Localized single-particle excitations and the density of states for superconducting composites

The problem of localized single-particle excitations and the density of states (DOS) for an inhomogeneous system consisting of a spherical superconductor (with radius a and order parameter Δ1) embedded in another superconductor (order parameter Δ2) of infinite size is considered. With the assumption of constant values of Δ1 and Δ2, the Bogoliubov equations are solved for general values of 1 (the orbital angular momentum quantum number). For a fixed value of Δ1/Δ2 and different values of Δ2/E /sub F/ , the dependence of the excitatio energy ε(l = O)/Δ2 on the particle size k /sub F/ a is shown (K /sub F/ is the Fermi wave vector and E /sub F/ is the Fermi energy). For k /sub F/ a = 300, 450, and 800 and a fixed value of Δ2/E /sub F/ , the variations in the DOS by changing Δ1/Δ2 are also shown