Inelastic scattering of quasiparticles in a superconductor with magnetic impurities

We show that inelastic scattering of quasiparticles by trace concentrations of magnetic impurities may result in significant changes in the nonequilibrium properties of superconductors. We used the approach of Müller-Hartmann and Zittartz to model Kondo scattering of conduction electrons by the magnetic impurities, and hence, to calculate the rates of (i) quasiparticle trapping into the localized impurity states, (ii) trap-enhanced recombination, (iii) pair breaking, and (iv) detrapping of localized quasiparticles by phonons, including both deformation-potential and spin-lattice couplings. Our results indicate that these processes will give rise to anomalies in the temperature dependence of kinetic parameters, which should be easily observable.

Figure 1

Feynman diagram for self-energy for electron-phonon interaction with Kondo impurities.

Figure 2

Quasiparticle trapping by magnetic impurity. A quasiparticle initially in the continuum spectrum at energy $ϵ$ undergoes an inelastic transition to a discrete level ${ϵ}_0$ with emission of a phonon $\hslash \Omega =ϵ-{ϵ}_0$.

Figure 3

Activation of a quasiparticle from the bound state at magnetic impurity by a phonon $\hslash \Omega =ϵ-{ϵ}_0$.

Figure 4

A quasiparticle in a continuum state at $ϵ$ recombines with a quasiparticle bound at a magnetic impurity at ${ϵ}_0$, emitting a phonon with energy $\hslash \Omega =ϵ+{ϵ}_0$.

Figure 5

Normalized trapping time and on-trap recombination coefficient as functions of the position of the impurity level.

Figure 6

Normalized trapping time and on-trap recombination coefficient as functions of characteristic time ${\tau }_1$ for coupling of the defect level to phonons due to deformation potential.

Figure 7

Normalized trapping time and on-trap recombination coefficient as functions of characteristic time ${\tau }_2$ for spin-lattice coupling.

Figure 8

Breaking of a Cooper pair by a phonon below the $2\Delta$ threshold.

Figure 9

Phonon self-energy.

Figure 10

Responsivity of a $\text{Nb}/{\text{Al}}_2{\text{O}}_3/\text{Nb}$ STJ as a function of photon energy.

Figure 11

Normalized responsivity of a symmetrical TaAl (30 nm) STJ vs temperature: $+$ are optical photons (4.1 eV); ◇ are x-ray (5.9 keV) photons.

Figure 12

The relaxation times as a function of reduced bath temperature for 150 nm Ta on Si (solid box, solid circle), 100 nm Al on Si (△), 250 nm Al on Si (▽), and 250 nm Al on sapphire (◇) samples. The inset shows the same data on a linear scale.