The effect of the spatial variation of the order parameter on the tunneling density of states of superconducting alloys

In the first part of the paper we derive expressions of the Ginzburg-Landau (GL) type for the local tunneling density of states of superconducting alloys. These expressions are quite generally applicable at high excitation energies. One can see immediately that the density of states,N(r, ω), at any positionr and high energiesω is always larger than the local BCS density of states if the space dependence of the order parameter is governed by the GL-equation. This effect is largest for long mean free pathsl. In the second part of the paper we calculate the spatial average of the density of states,¯N, at all energiesω for a lattice of vortex lines in a magnetic field slightly below the upper critical field. The resulting curve of ¯N? N(0)]/N(0) versus co shows no gap and has a zero at about the gap value in zero field. Its value at ω=0 depends onl like ln(ξ₀/l) for l?ξ₀ N(0) denotes the normal density of states, and ξ₀ is the BCS coherence length].