Resonant Tunneling and Charging Effects, a Path Integral Approach

TL;DR

This paper develops a path integral real-time approach to analyze electron tunneling through small metallic islands, capturing Coulomb blockade, resonant tunneling, and electron interactions modeled as Luttinger liquids, revealing parameter renormalization and conductance broadening.

Contribution

It introduces a systematic diagrammatic path integral method to study quantum tunneling and Coulomb effects, including electron interactions, in mesoscopic systems.

Findings

Strong renormalization of system parameters.

Finite lifetime broadening of conductance features.

Power-law current-voltage characteristics in Luttinger liquids.

Abstract

Electron tunneling through small metallic islands with low capacitance is studied. The large charging energy in these systems is responsible for nonperturbative Coulomb blockade effects. We further consider the effect of electron interactions in the electrodes. In junctions with high resistance compared to the quantum resistance transport can be described by sequential tunneling. If the resistance is lower, quantum fluctuations, higher order coherent processes, and eventually resonant tunneling become important. We present a path integral real-time approach, which allows a systematic diagrammatic classification of these processes. An important process is ``inelastic resonant tunneling'', where different electrons tunnel coherently between the electrodes and the island. Physical quantities like the current and the average charge on the island can be deduced. We find a strong renormalization of the system parameters and, in addition, a finite lifetime broadening. It results in a pronounced broadening and smearing of the Coulomb oscillations of the conductance. These effects are important in an experimentally accessible range of temperatures. The electron interaction in the electrodes is modeled by a Luttinger liquid. It leads to non-analytic kernels in the effective action. The diagrammatic expansions can be performed also in this case, resulting in power-law current-voltage characteristics.