Kinematic Change in Conduction-Electron Density of States due to Impurity Scattering. II. Problem of an Impurity Layer and Tunneling Anomalies

Abstract

The change of the conduction-electron density of states due to electron-impurity scattering has been investigated in a previous paper for one impurity; that calculation is extended now to the case of an impurity layer. A strong momentum dependence of the electron-impurity scattering is assumed, but no restrictions are placed on its energy dependence. Particular attention is paid to the spatial structure of the conduction-electron density of states around the impurity layer, which can be characterized by the same coherence length ${\ensuremath{\xi}}_{\ensuremath{\Delta}}$ introduced in the case of one impurity. The amplitude of this change shows a smoother dependence on distance measured from the impurity layer than in the case of one impurity, because of some coherent enhancement due to the scattering of different impurities. Therefore, this improves the chances for experimental observations. Theoretical aspects of adequate tunneling experiments on junctions doped by impurities are presented in detail with special emphasis on the determination of the coherence length ${\ensuremath{\xi}}_{\ensuremath{\Delta}}$. The perturbations caused by magnetic-impurity scattering is at present of primary interest. Some particular features concerning Kondo scattering and possible connections with giant zero-bias tunneling anomalies are discussed as well. In the case of resonant scattering, the most striking feature is that the conduction-electron-impurity scattering amplitude may be strongly enhanced in the unitarity limit due to the cooperative reduction in the conduction-electron density of states inside the impurity layer at the Fermi energy.