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.
Highlights
A macroscopically large system, thermally coupled to a heat reservoir, is in thermal equilibrium with the reservoir when the system temperature is equal to the one of the reservoir
We have presented a theoretical analysis of the energy and temperature fluctuations of a single electron box, a metallic dot in the Coulomb blockade regime tunnel coupled to an electronic reservoir
The focus has been on the quasi-equilibrium regime, where the dynamics of the dot electron distribution, and the temperature, is driven by single electron tunnelling
Summary
A macroscopically large system, thermally coupled to a heat reservoir, is in thermal equilibrium with the reservoir when the system temperature is equal to the one of the reservoir. The observed relaxation time τe−ph of Te(t) towards the lattice temperature was of the order of 100 μs, several orders of magnitude longer than the typical τe−e, of the order of 1 ns or below [22] This large separation of time scales puts in prospect experiments with real time monitoring of Te(t), driven by electron tunnelling occurring on an intermediate time scale τE, fulfilling the inequality in Eq (1). As a general result we find that the temperature fluctuations increase for increasing charging effects, a consequence of both a wider range of energies of tunnelling electrons participating in the heat transfer and larger fluctuations in the number of tunnel events during the measurement.
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