NON-EQUILIBRIUM PROPERTIES OFSUPERCONDUCTORS UNDER TUNNELLING INJECTION

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NON-EQUILIBRIUM PROPERTIES

OFSUPERCONDUCTORS UNDER TUNNELLING

INJECTION

V. Seminozhenko

To cite this version:

V. Seminozhenko.

NON-EQUILIBRIUM PROPERTIES OFSUPERCONDUCTORS UNDER

JOURNAL DE PHYSIQUE

Colloque C6, supplPment au

no

8,

Tome 39, aocit 1978, page C6-5 17

NON-EQUILIBRIUM PROPERTIES OFSUPERCONDUCTORS UNDER TUNNELLING INJECTION

V.P. Seminozhenko

Physico-Technical Institute of Low Temperatures, Ukr SSR

Academy of Sciences, 47, Lenin Prospect, Khrkov, 31 01 64, U. S. S. R.

RQsum6.- On Qtudie les Qtats hors dlQquilibre obtenus dans un supraconducteur par injection tunnel 1 partir d'un mQtal normal. On prQdit la variation des propribtgs cindtiques par rapport 1 l'btat dlQquilibre.

Abstract.- Non-equilibrium superconducting states under tunnelling injection from a normal metal are investigated.

A

principal change in the kinetic properties as against equilibrium states is predic- ted.

Studies on superconductor non-equilibrium sta- tes which have been activized in recent years show

that superconductors can display non-equilibrium pro- perties substantially differing from usual equilibri-

um ones.

Here we consider non-equilibrium superconduc- ting properties due to a tunnelling injection in a

junction consisting of a massive electrode of a normal metal and a superconducting film (N-I-S tunnel junc- tion, I indicating the insulator). The kinetic equa- tion for non-equilibrium steady states of an S-film due to a tunnelling injection from an N-metal has the simplest form at T = 0, in particular for eV>A :

I~CB(~V-E)-~~

(E)) = &{f ,NI

where f(&) is the distribution function of electronic excitations, E =

/E' +

A2

,

5

= p2/2m-EF,

A

is the energy gap,E the Fermienergy, B(E) the step

function,^

the

F

voltage at the junction, I.

-

D vF/d, D the barrier transparency, vF the Fermi velocity, d the thickness

of the S-film,

3

{f,~} the collision operator of electronic excitation-phonon interactions, N the pho- non distribution function.

The above non-linear integral equation may be solved for a variety of limiting cases. For some of them, the result may be presented in the form of

f(~) = f B(eV-E) where, e.g. :

Here y

-

0.3 V= ~ I ~ s ~ ~

,

~A is the electron- ~ I ~ / A ~ A ~ 0

phonon interaction constant, S the sound velocity, p the density,

M

= I. The negligibly weak dependence f(~) for E < e V is due to the fact that the electron

density of states in the normal metal near E _{FN is}

practically independent of energy (eV<<EFN). The absence of excitations above eV is due to the ap- proximation T = 0.

Being essentially non-equilibrium, the elec- tron distribution may, for instance, largely affect the ultrasound attenuation coefficient, as. In this

0

case, dependence of as/% (where a: is the attenua- tion coefficient in the normal metal) on frequency (w<<A) is given by :

This dependence is qualitatively represented in 0 figure 1 . The validity of inequality

as

> an is

Figure 1

reasonable because owing to the tunnelling injec- tion, the number of quasi-particles in the S-film near the Fermi level is larger than in the normal

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786231

equilibrium state. Calculation of the ultrasound attenuation jump at w = 28 shows that the jump ?S essentially blocked by the factor I

-

2f <I as against the equilibrium case. This effect is rela- ted to the very mechanism of the jump realization and the Pauli principle.

Proceeding from the obtained

distribution

function form, the distribution P(w) of recombina- tion phonons with frequency (at w >2A) generated from the superconducting film (figure 2) is calcu- lated :

{ B(ureV-P)B(2 eV-w) 2 arctg

-

1

+ O(w-2A) 0 (eV+A-w).rr

I

Figure 2

An important property of non-equilibrium superconductors is the spectrum dependence of the high-frequency conductivity :

Rn

m+

J&T=G

]

V

G

The form of this function qualitatively resemples the one in figure 1.

The effect of quasi-particle injection on the tunnelling characteristics in the most interesting. Thus, e..g., tunnelling injection into the middle film of the N-I-S-1'-S' structure can lead both to incre- asing quasi-particle tunnelling current through the S-1'-S' junction (A,, > A ) and to negative current

S