In this paper, two model tunneling junctions are studied. In the first model, a single magnetic impurity is assumed to be present near a sharp metal-barrier interface. In the second, phonons with a single Einstein frequency are assumed to exist throughout one electrode and into the barrier region. The effect of the electron-spin (phonon) interaction on the conductance has been calculated. It is found that the zero-bias conductance anomaly produced by the magnetic impurity in model I is a sensitive function of the magnetic-impurity position, being of one sign in the barrier and oscillating in the electrode. In model II, we find, contrary to what had been believed that, when the phonons are strictly confined to the metal electrode and a local electron-phonon coupling is assumed, the conductance decreases at the phonon emission threshold. This decrease quickly becomes an increase, however, if the phonons are allowed to penetrate significantly into the barrier.

• Received 30 December 1969

DOI:https://doi.org/10.1103/PhysRevB.2.907