Current-voltage characteristics of a tunnel junction with resonant centers

We calculate the I-V characteristics of a tunnel junction containing impurities in the barrier. We consider the indirect resonant tunneling involving the impurities. The Coulomb repulsion energy $E_c$ between two electrons with opposite spins simultaneously residing on the impurity is introduced by an Anderson Hamiltonian. At low temperatures $T \ll E_c$ the I-V characteristic is linear in $V$ both for $V<E_c$ and for $V>E_c$ and changes slope at $V=E_c$. This behavior reflects the energy spectrum of the impurity electrons - the finite value of the charging energy $E_c$. At $T \sim E_c$ the junction reveals an ohmic-like behavior as a result of the smearing out of the charging effects by the thermal fluctuations.