Particle tunneling through a polarizable insulator

TL;DR

This paper investigates electron tunneling through polarizable insulators, analyzing how coupling to excitations affects tunneling probability, with findings showing suppression effects and an orthogonality catastrophe in certain configurations.

Contribution

It introduces a model for electron tunneling through polarizable insulators that accounts for energy exchange with excitations, revealing new suppression mechanisms and orthogonality effects.

Findings

Weak coupling causes slight tunneling suppression via Debye-Waller factor.

Strong coupling increases effective barrier, further suppressing tunneling.

An insulating chain exhibits an orthogonality catastrophe similar to Fermi gas transitions.

Abstract

The tunneling probability between two leads connected by a molecule, a chain, a film, or a bulk polarizable insulator is investigated within a model of an electron tunneling from lead A to a state higher in energy, describing the barrier, and from there to lead B. To describe the possibility of energy exchange with excitations of the molecule or the insulator we couple the intermediate state to a single oscillator or to a spectrum of these, respectively. In the single-oscillator case we find for weak coupling that the tunneling is weakly suppressed by a Debye-Waller-type factor. For stronger coupling the oscillator gets 'stiff' and we observe a suppression of tunneling since the effective barrier is increased. The probability for the electron to excite the oscillator increases with the coupling. In the case of a film, or a bulk barrier the behavior is qualitatively the same as in the single oscillator case. An insulating chain, as opposed to a film or a bulk connecting the two leads,shows an 'orthogonality catastrophe' similar to that of an electronic transition in a Fermi gas.