Exchange Model of Zero-Bias Tunneling Anomalies

An exchange model for zero-bias tunneling anomalies previously proposed by the author is examined in greater detail. The tunneling Hamiltonian is derived microscopically and its connection with the one proposed by Anderson is indicated. The interference scattering derived from the model is shown to be capable of explaining the magnitude and the temperature $T$ and voltage $V$ dependence of the anomalous conductance $G(V, T)$ found by Wyatt and by Rowell and Shen in $A-\left(\mathrm{oxide}A\right)-B$ junctions. Here $A$ is a transition metal, such as Ta or Nb, and $B$ a simple metal, such as Al. (Both metals are always in their normal state.) In addition, the dependence of $G(V, T)$ on magnetic field $H$ is studied in detail. Finally, the interpolated forms for $G(V, T, H)$ previously given are replaced by more exact numerically evaluated curves.