Nonequilibrium superconductivity in microwave field

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Submitted on 1 Jan 1979

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Nonequilibrium superconductivity in microwave field

V.M. Dmitriev, E.V. Khristenko

To cite this version:

V.M. Dmitriev, E.V. Khristenko. Nonequilibrium superconductivity in microwave field. Journal de

Physique Lettres, Edp sciences, 1979, 40 (4), pp.85-87. �10.1051/jphyslet:0197900400408500�.

�jpa-00231575�

L-85

Nonequilibrium

superconductivity

in

microwave field

_(*)

V. M. Dmitriev and E. V. Khristenko

Physico-Technical Institute of Low Temperatures, UkrSSR _Academy of _{Sciences, 47,} Lenin _Prospect, Kharkov, 310164, USSR

(Re~u le 10 aofit _1978, revise le 19 decembre, accepte le 22 decembre 1978)

Résumé. 2014 On a effectué l’étude

_{expérimentale}

et

_théorique

de la

_{supraconductivité}

hors _équilibre d’échantillons longs, étroits

_(L

>

_03BE(T))

et courts

_(L

_03BE(T))

en _{Sn, In,} Al en _présence de

_champs

alternatifs de _fréquences

comprises

entre 7 Mc et 150 Gc. On a établi les lois _{principales auxquelles} obéissent la stimulation et la

_suppression

de la

_{supraconductivité}

en fonction des dimensions, du matériau et de la

_pureté

des échantillons. On propose une

méthode de détermination du _temps de relaxation non _{élastique 03C403B5. On} a déterminé 03C403B5 = 8,3 10-10 s _{pour Sn}

et _03C403B5 = _4,62 10-9 _s

pour Al. On montre _{que les résultats}

_{expérimentaux}

sont en bon accord avec les théories

d’Eliashberg et d’Aslamasov-Larkin. Abstract. 2014 The

nonequilibrium superconductivity

of narrow

_long

_(L

>

_03BE(T))

and short

_(L

_03BE(T))

_samples

of Sn, In, Al has been studied in the

_frequency

_{range of 7 Mc} to 150 Gc. The

_{principal regularities}

for stimulation and

_suppression

of

_{superconductivity}

and their

_dependence

on the

sample

dimension, material and

purity

have

been found. A method for _estimating the inelastic relaxation time, 03C403B5, is

proposed.

It has been found that for Sn 03C403B5 = 8.3 10-10 s and for

Al 03C403B5

= 4.62 10-9 _s. The experimental data _are in

good

agreement with the

Eliash-berg

and the Aslamazov-Larkin theories.

LE JOURNAL DE PHYSIQUE - LETTRES _TOME

40, 15 FEVRIER 1979,

Classification

Physics Abstracts 74. 30G

It is shown that microwave-induced

_{nonequilibrium}

superconductivity

has common

_regularities

for

_long

uniform channels and

_bridges

of the dimension

L >

_~(7").

At

_frequencies

of ~ 10 Mc and

lower,

the

_{superconductivity}

is

_suppressed

as the radiation

power rises

by

the law

I~(P)

=

_I~(0)

r

pi~

power rises

by

the law

/~(P)

,=

_/~0)

1 -

p-resulted from the

Ginzburg-Landau

mechanism of

pair breaking.

When we increase the

_frequency,

this law is

disturbed,

and the current

_Ic(P)

is

_suppressed

less and less until it reaches

_le(O)

due to the radiation effect. As the

_frequency

increases

_further,

Ie(P)

>

_7,(0).

Such a

_frequency

is the lower critical

_frequency

_Wt of the effect

_fc(P)

>

_l~(0).

With further

_increasing

frequency,

this effect reaches a maximum at the

optimal

frequency

(00’ then reduces and vanishes at

the _upper critical

_frequency

_c~2. Under

_radiation,

not

_only

does the critical current

_increase,

but the critical

_temperature

_7~

increases

_by

the value

_A7~(P).

In the

_{Eliashberg technique [1]}

for order parameter A

one can _get the

_{following equation}

at zero current

through

the

_sample

_{[2] :}

where

b2-characterizes

the constant

_magnetic

field.

Diffe-rentiating

exp.

(1)

with respect to 0 and a, an

expres-sion can be found which determines the

optimal

frequency So

and

_jump

_{oco :}

Equations (2)

and

₍₃₎

_present the interaction between the

_{corresponding}

_{parameters ;}

to determine the

temperature, the

_parameters

should be substituted in

_(1).

The calculated results of

_{frequencies /i,/o?/2}

L-86 JOURNAL DE PHYSIQUE - LETTRES

and of

_ii,

_expressed

in

_frequency,

are shown for Sn

specimens

in

_figure

1,

where are

_plotted

both our

experimental

data and those from the literature.

In the calculations we use the

following

values : J = 3.063 x

~r~/1 2013 ~

_{(the equilibrium value),}

7,

=

_{3.8 K,}

1’£ = 8.3 x

10’~ s, D = 0.15.

The

stu-dies of the mechanism of formation of the lower

_{(co 1)}

and the _upper

_(ro2)

critical

_frequencies

make it

possible

to determine the time _Tg

_{by measuring}

the

frequency

c°1 for

the effect

I,,(P) > 4(0);

for

Al,

T, =

4.62

x

10-9

s.

-. As one can see from

₍₁₎

the

_phase

transition in the

nonequilibrium

case is the first-order transition with

respect

to the J

_jump.

It seems that there is a critical

current

_jump

also at the transition

_point

with the microwave radiation

_{[2, 4,}

_5].

To make this

_clear,

in the

_{Ginzburg-Landau technique}

we have written

the

_{following equation}

for

_{nonequilibrium}

super-current

where

and have studied it

_{carefully together}

with

_(1).

It is

seen from the

_depairing

_curves,

figure

_2,

that the

_only

difference between the

_equilibrium

and

nonequili-brium cases is that the critical current _goes to zero

at J = 0 for the first _case and _at

_J,

corresponding

to

the value of J

_jump,

for the second case. But for both cases the critical current increases from zero

conti-nuously. Figure

3 shows the increase of

_Tp

and

_Te

at 15.6 Gc. In our

_opinion

the

experimental

current

jumps

are due to the influence of rf heat. The compre-hensive

_{experimental study}

p Y of

_R(P)

( )

and

-2013/

(T)

cLD/D-~o

o

( )

dependences

near

_Tc

indicates that there are small

maxima on these

_dependences

which do not follow from

_(1).

It should be noted that the conditions under which the deviations from

(1)

are observed

_correspond

to those in which L

_ç(T).

Hence,

very short In

bridges

which

_displayed

the AC

_Josephson

effect

near

_T~

were studied

_{experimentally.}

For these

specimens

the stimulation of

_{superconductivity}

was

observed

_only

at T

_Tc

while near

_Tc

it was

sup-pressed.

In

_[6]

the effect of microwave radiation on the

critical current of nonuniform

_junctions

was

consi-dered and the

equations

were obtained for the effect

the

_physical

nature of which is the

change

in the

electron distribution function due to _{the energy}

diffusion

of electrons when

_they

are reflected

again

from the

_potential

well

_edges

in the microwave field. The

_experimental

results for nonuniform

_bridges

are

in

_satisfactory

_agreement with the

_theory

_[6].

The oscillations of the electrons in the

_potential

well facilitate the energy

diffusion,

and this _may

_explain

L-87

NONEQUILIBRIUM SUPERCONDUCTIVITY IN MICROWAVE FIELD

the fact that the stimulation of

_{superconductivity}

in

.

nonuniform

_junctions

can be observed much easier

than in uniform

_junctions.

The effect of material

parameters

(mean

free

_path

I and Fermi

_{velocity ’U’F)}

on the

_{superconductivity}

stimulation has been

ana-lysed.

For

_long

_specimens

the stimulation is shown

to be more effective at

_large

I and

_’BJF

and for short

specimens

to be more effective at small I.

In

_conclusion,

the effect found in

_[7]

is shown to be due to the influence of microwave radiation on the

electron distribution function in agreement with the results from

_[1,

_6].

References

[1] ELIASHBERG, G. M., Pisma v ZhETF 11 (1970) 186.

[2] DMITRIEV, V. M., KHRISTENKO, Y. V., Fiz. Niz. Temp. 4 ₍₁₉₇₈₎ 821.

[3] DAYEM, A. H., WIEGAND, T. _{H., Phys.} Rev. 155 (1967) 419.

[4] LATYSHEV, Yu. _{M., NAD’,} F. Ya., Pisma v ZhETF 19 ₍₁₉₇₄₎ 737; Zh. Eksp. Teor. Fiz. 71 (1976) 2158.

[5] KLAPWIJK, T. M., VAN DER BERGH, J. N., MOOIJ, J. E., J. Low

Temp. Phys. 25 ₍₁₉₇₇₎ 385.

[6] ASLAMAZOV, L. _{G., LARKIN,} A. _I., Zh. _Eksp. Teor. Fiz. 74

(1978) 2184.

[7] WYATT, A. F. G., DMITRIEV, V. M., MOORE, W. S., SHEARD,