Circuit Effect On The Current-Voltage Characteristics Of Ultrasmall Tunnel Junctions

TL;DR

This paper derives a nonperturbative method to analyze the current-voltage characteristics of ultrasmall tunnel junctions considering circuit effects, matching experimental results for resistive environments.

Contribution

It introduces a nonperturbative approach using the generating functional method to account for circuit effects in tunnel junctions, extending beyond traditional perturbation theory.

Findings

Calculated conductance matches experimental data across voltages and temperatures.

Derived expressions relate renormalized energies to circuit parameters.

Provided a framework for analyzing complex circuit effects in tunnel junctions.

Abstract

We have used the method of generating functional in imaginary time to derive the current-voltage characteristics of a tunnel junction with arbitrary tunneling conductance, connected in series with an external impedance and a voltage source. We have shown that via the renormalized charging energy and the renormalized environment conductance, our nonperturbative expressions of the total action can be mapped onto the corresponding perturbative formulas. This provides a straightforward way to go beyond the perturbation theory. For the impedance being a pure resistance, we have calculated the conductance for various voltages and temperatures, and the results agree very well with experiments.