Theory of Zero-Bias Anomaly in Magnetic Tunnel Junctions: Inelastic Tunneling via Impurities

TL;DR

This paper presents a nonperturbative theoretical study of inelastic electron tunneling via impurities in magnetic tunnel junctions, explaining zero-bias anomalies through phonon emission and electron-phonon interactions.

Contribution

It introduces a closed-time path integral approach to model inelastic tunneling and reproduces experimental zero-bias anomaly features in magnetic tunnel junctions.

Findings

Phonon emission spectrum shows a power-law infrared singularity.

Tunneling conductance increases with bias as |V|^{2g}.

Theory explains cusp-like and non-cusp-like zero-bias anomalies.

Abstract

Using the closed-time path integral approach, we nonperturbatively study inelastic tunneling of electrons via magnetic impurities in the barrier accompanied by phonon emission in a magnetic tunnel junction. The spectrum density of phonon emission is found to show a power-law infrared singularity $\sim\omega^{-(1-g)}$ with $g$ the dimensionless electron-phonon coupling. As a consequence, the tunneling conductance $G(V)$ increases with bias voltage $| V|$ as $G(V)-G(0)\sim| V|^{2g}$, exhibiting a discontinuity in slope at V=0 for $g\le 0.5$. This theory can reproduce both cusp-like and non-cusp-like feature of the zero-bias anomaly of tunneling resistance and magnetoresistance widely observed in experiments.