Energy and temperature fluctuations in the single electron box

TL;DR

This paper theoretically investigates how quantum tunneling causes temperature fluctuations in a single electron box, revealing non-equilibrium energy dynamics at the nanoscale with implications for experimental measurement.

Contribution

It introduces a full statistical description of energy and temperature fluctuations in a Coulomb blockade system, accounting for charging effects and reservoir temperature.

Findings

Quantum tunneling induces temperature fluctuations without net charge transfer.

Derived the full distribution of energy transfer and temperature fluctuations.

Analyzed low-frequency temperature fluctuations considering charging effects.

Abstract

In mesoscopic and nanoscale systems at low temperatures, charge carriers are typically not in thermal equilibrium with the surrounding lattice. The resulting, non-equilibrium dynamics of electrons has only begun to be explored. Experimentally the time-dependence of the electron temperature (deviating from the lattice temperature) has been investigated in small metallic islands. Motivated by these experiments we investigate theoretically the electronic energy and temperature fluctuations in a metallic island in the Coulomb blockade regime, tunnel coupled to an electronic reservoir, i.e. a single electron box. We show that electronic quantum tunnelling between the island and the reservoir, in the absence of any net charge or energy transport, induces fluctuations of the island electron temperature. The full distribution of the energy transfer as well as the island temperature is derived within the framework of full counting statistics. In particular, the low-frequency temperature fluctuations are analysed, fully accounting for charging effects and non-zero reservoir temperature. The experimental requirements for measuring the predicted temperature fluctuations are discussed.