Recombination-Limited Energy Relaxation in a Bardeen-Cooper-Schrieffer Superconductor

Abstract

We study quasiparticle energy relaxation at subkelvin temperatures by injecting hot electrons into an Al island and measuring the energy flux from quasiparticles into phonons both in the superconducting and in the normal state. The data show strong reduction of the flux at low temperatures in the superconducting state, in qualitative agreement with the theory for clean superconductors. However, quantitatively the energy flux exceeds the theoretical predictions both in the superconducting and in the normal state, suggesting an enhanced or additional relaxation process.

A quantum diffractor for thermal flux

“…A thermal gradient is established by heating intentionally the source's electrons up to a fixed temperature T src , leading to an increase in the electronic temperature of S 1 up to T 1 4T bath . This is possible since S 1 is a superconducting electrode with small volume (V S1 % 0:2 mm 3 ), allowing for its electrons to be marginally coupled to the lattice phonons at low temperatures 20 . By contrast, S 2 and S 3 are strongly thermalized at T bath stemming from their large volume (B10 4 mm 3 ) 20 .…”

“…This is possible since S 1 is a superconducting electrode with small volume (V S1 % 0:2 mm 3 ), allowing for its electrons to be marginally coupled to the lattice phonons at low temperatures 20 . By contrast, S 2 and S 3 are strongly thermalized at T bath stemming from their large volume (B10 4 mm 3 ) 20 . Under these circumstances, T dr is mainly determined by the temperature T 1 in S 1 , which is affected by the heat flux _ Q S 1 !S 2 .…”

Excitation of Single Quasiparticles in a Small Superconducting Al Island Connected to Normal-Metal Leads by Tunnel Junctions

“…where AE is the material constant for electron-phonon coupling, ðzÞ the Riemann zeta function, n S ðEÞ the BCS (3) is obtained by kinetic Boltzmann equation calculations [31,32]. For an alternative derivation, see Supplemental Material [28].…”

Low Temperature Transport in Tunnel Junction Arrays: Cascade Energy Relaxation

“…They should be determined from the condition that the collision integral of the environmental modes with the e-h pairs accompanying the current flow becomes zero, and Eq. (1.6) yields N ω ∼ = n (12) ω . If T e ≪ V , then N ω can be approximated by the Bose-function with some effective temperature T eff at ω < V = T eff and N ω = 0 at ω > T eff (the emission of the excitations with the energy larger than V is forbidden), and…”

“…Intense studies of nano-structured and disordered systems including Josephson junctions [9,10], mesoscopic tunnel junctions [11] and superconductors [12], patterned superconducting films [13,14], highly disordered superconducting and semiconducting films [15][16][17][18][19][20] reveal a prime importance of the out-ofequilibrium properties of an environment to which the tunneling charge carriers relax the energy. In particular, experiments on disordered superconducting films revealed that at extremely low temperatures the I-V characteristics exhibit highly nonlinear behavior indicating that the transport charge carriers are decoupled from the phonon thermostat.…”