Electron heating in metallic resistors at sub-Kelvin temperature

B. Huard (1) , H. Pothier (1) , Daniel Esteve (1) , K. E. Nagaev (2)

1 QUANTRONICS - Quantronics Group
2 IRE - Institute of Radioengineering and Electronics, Russian Academy of Sciences, Mokhovaya ulica 11, 125009 Moscow, Russia

In the presence of Joule heating, the electronic temperature in a metallic resistor placed at sub-Kelvin temperatures can significantly exceed the phonon temperature. Electron cooling proceeds mainly through two processes: electronic diffusion to and from the connecting wires and electron-phonon coupling. The goal of this paper is to present a general solution of the problem, in a form that can easily be used in practical situations. As an application, we compute two quantities that depend on the electronic temperature profile: the second and the third cumulant of the current noise at zero frequency, as a function of the voltage across the resistor. We also consider time dependent heating, an issue relevant for experiments in which current pulses are used, for instance in time-resolved calorimetry experiments.

Domaines: Systèmes mésoscopiques et effet Hall quantique [cond-mat.mes-hall]

B. Huard, H. Pothier, Daniel Esteve, K. E. Nagaev. Electron heating in metallic resistors at sub-Kelvin temperature. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2007, 76, pp.165426. ⟨10.1103/PhysRevB.76.165426⟩. ⟨hal-00168638v2⟩