Relationship Between the Heat Flow and the Current through a Superconducting Tunnel Junction

Nonequilibrium quasiparticles injected into the biased film of a superconducting tunnel junction (STJ) give rise to the electrical current across the insulating barrier. Each quasiparticle in superconductor is a quantum superposition of electron-like and hole-like excitations. This duality nature of quasiparticle leads to the process of quasiparticle multitunneling. Quasiparticle begins tunnel back and forth across the insulating barrier until it will be out of the game. After each tunneling from the biased film, quasiparticle loses its energy by emission of phonons until it reaches the gap energy. Because of the multitunneling, one quasiparticle can deposit the excess of its energy more than once. In this work, the theory of branching cascade processes is applied to the processes of the heat and the charge flow caused by the process of quasiparticle multitunneling. The relationship between the heat flow and the current through a superconducting tunnel junction is derived. It was shown that energetic X-rays at high counting rates may cause additional broadening of the spectral lines in STJ detectors due to temperature fluctuations through dependence of the gap energy on the temperature.