Cross correlations in mesoscopic charge detection

TL;DR

This paper investigates charge detection in a mesoscopic system, analyzing correlations between detector and SET currents, and proposes measuring SET barrier capacitances to enhance understanding of charge transport.

Contribution

It provides an exact solution for charge detection correlations in a mesoscopic SET system and highlights the importance of specific current correlations over Ramo-Shockley effective currents.

Findings

Current monitoring depends on correlations with SET barrier currents.

Correlations with Ramo-Shockley effective current are not essential.

Proposes measuring SET barrier capacitances for better charge detection.

Abstract

We study a tunnel contact that acts as charge detector for a single-electron transistor (SET) focusing on correlations between the detector current and the current through the SET. This system can be described fully by a Markovian master equation for the SET, while electron tunneling in the charge monitor represents a process with a stochastic rate, which can be solved exactly. It turns out that current monitoring is possible as long as the detector current correlates with the currents through either SET barrier. By contrast, correlations with the effective current according to the Ramo-Shockley theorem are not essential. Moreover, we propose the measurement of the SET barrier capacitances.