Potential barrier model incorporating localized states explaining tunnel anomalies

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Abstract
Most tunnel barriers contain localized electronic states nl(Δx, ε) in large amounts decreasing with distance Δx from the metal. The localized states hybridize with conduction electrons forming interface states with a decay width Δl∝exp(−2Δxκ) and a correlation energy ΔU* ∝ 1/εrΔx. For ΔU*>Δl these states are localized, which yields a strong coupling to surface plasmons, phonons, and spins. These states cause diffuse surface scattering and enhance exponentially [∝ Δ−1l ∝exp(+2Δxκ)] the tunnel matrix element by resonant tunneling jR as compared to tunneling jφ̄ through the whole potential barrier φ̄. Consequently at voltages ‖eU‖ <φ̄, jR(U,T) is identified by its stronger U and T dependencies and can even dominate over jφ̄. The enhanced interaction of the localized electrons with surface plasmons, phonons, and spins yield strong U, T, and time dependencies in the tunnel current which produce giant zero‐bias anomaly and spin‐flip zero‐bias anomaly; capacitance changes; inelastic processes, noise, and barrier reduction with increasing temperature; and pair weakening, leakage current, and reduction of the Josephson current.