The effect of an external magnetic field on the maximum current of SNINS junctions near the critical temperature
The behaviour of superconducting junctions of SNINS-type (where S is superconductor, N is normal metal, I is insulator) with anharmonic current-phase relations in the external magnetic field near the critical temperature was investigated. The dependence of the maximum current on the value of the m...
Gespeichert in:
| Datum: | 2018 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут фізики конденсованих систем НАН України
2018
|
| Schriftenreihe: | Condensed Matter Physics |
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/157460 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | The effect of an external magnetic field on the maximum current of SNINS junctions near the critical temperature / O.Yu. Pastukh, V.E. Sakhnyuk, A.V. Svidzinsky // Condensed Matter Physics. — 2018. — Т. 21, № 4. — С. 43702: 1–7 . — Бібліогр.: 31 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-157460 |
|---|---|
| record_format |
dspace |
| spelling |
nasplib_isofts_kiev_ua-123456789-1574602025-02-09T22:07:06Z The effect of an external magnetic field on the maximum current of SNINS junctions near the critical temperature Дослiдження впливу зовнiшнього магнiтного поля на максимальний струм SNINS-контактiв поблизу критичної температури Pastukh, O.Yu. Sakhnyuk, V.E. Svidzinsky, A.V. The behaviour of superconducting junctions of SNINS-type (where S is superconductor, N is normal metal, I is insulator) with anharmonic current-phase relations in the external magnetic field near the critical temperature was investigated. The dependence of the maximum current on the value of the magnetic flux in a wide range of electron transmission coefficient values was considered. Also, it was investigated how the presence of a normal layer of an arbitrary thickness in the scale of coherence length and in the presence of impurities in superconducting regions affect the sensitivity of the maximum current to the magnetic field magnitude. В роботi дослiджено поведiнку надпровiдних контактiв типу SNINS з ангармонiйною струм-фазовою залежнiстю у зовнiшньому магнiтному полi поблизу критичної температури. Проаналiзовано залежнiсть максимального струму вiд потоку зовнiшнього магнiтного поля для широкого iнтервалу змiни коефiцiєнта проходження електронiв. Також дослiджено, як впливає на чутливiсть струму до змiни магнiтного потоку наявнiсть нормального прошарку довiльної товщини в масштабi довжини когерентностi та наявнiсть у надпровiдних областях немагнiтних домiшок. Present research is supported by the State Fund for the Fundamental Research of Ukraine (award №F76/123-2017). 2018 Article The effect of an external magnetic field on the maximum current of SNINS junctions near the critical temperature / O.Yu. Pastukh, V.E. Sakhnyuk, A.V. Svidzinsky // Condensed Matter Physics. — 2018. — Т. 21, № 4. — С. 43702: 1–7 . — Бібліогр.: 31 назв. — англ. 1607-324X PACS: 74.50.+r DOI:10.5488/CMP.21.43702 arXiv:1812.08545 https://nasplib.isofts.kiev.ua/handle/123456789/157460 en Condensed Matter Physics application/pdf Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The behaviour of superconducting junctions of SNINS-type (where S is superconductor, N is normal metal, I is
insulator) with anharmonic current-phase relations in the external magnetic field near the critical temperature
was investigated. The dependence of the maximum current on the value of the magnetic flux in a wide range
of electron transmission coefficient values was considered. Also, it was investigated how the presence of a
normal layer of an arbitrary thickness in the scale of coherence length and in the presence of impurities in
superconducting regions affect the sensitivity of the maximum current to the magnetic field magnitude. |
| format |
Article |
| author |
Pastukh, O.Yu. Sakhnyuk, V.E. Svidzinsky, A.V. |
| spellingShingle |
Pastukh, O.Yu. Sakhnyuk, V.E. Svidzinsky, A.V. The effect of an external magnetic field on the maximum current of SNINS junctions near the critical temperature Condensed Matter Physics |
| author_facet |
Pastukh, O.Yu. Sakhnyuk, V.E. Svidzinsky, A.V. |
| author_sort |
Pastukh, O.Yu. |
| title |
The effect of an external magnetic field on the maximum current of SNINS junctions near the critical temperature |
| title_short |
The effect of an external magnetic field on the maximum current of SNINS junctions near the critical temperature |
| title_full |
The effect of an external magnetic field on the maximum current of SNINS junctions near the critical temperature |
| title_fullStr |
The effect of an external magnetic field on the maximum current of SNINS junctions near the critical temperature |
| title_full_unstemmed |
The effect of an external magnetic field on the maximum current of SNINS junctions near the critical temperature |
| title_sort |
effect of an external magnetic field on the maximum current of snins junctions near the critical temperature |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2018 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/157460 |
| citation_txt |
The effect of an external magnetic field on the maximum current of SNINS junctions near the critical temperature / O.Yu. Pastukh, V.E. Sakhnyuk, A.V. Svidzinsky // Condensed Matter Physics. — 2018. — Т. 21, № 4. — С. 43702: 1–7
. — Бібліогр.: 31 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT pastukhoyu theeffectofanexternalmagneticfieldonthemaximumcurrentofsninsjunctionsnearthecriticaltemperature AT sakhnyukve theeffectofanexternalmagneticfieldonthemaximumcurrentofsninsjunctionsnearthecriticaltemperature AT svidzinskyav theeffectofanexternalmagneticfieldonthemaximumcurrentofsninsjunctionsnearthecriticaltemperature AT pastukhoyu doslidžennâvplivuzovnišnʹogomagnitnogopolânamaksimalʹniistrumsninskontaktivpoblizukritičnoítemperaturi AT sakhnyukve doslidžennâvplivuzovnišnʹogomagnitnogopolânamaksimalʹniistrumsninskontaktivpoblizukritičnoítemperaturi AT svidzinskyav doslidžennâvplivuzovnišnʹogomagnitnogopolânamaksimalʹniistrumsninskontaktivpoblizukritičnoítemperaturi AT pastukhoyu effectofanexternalmagneticfieldonthemaximumcurrentofsninsjunctionsnearthecriticaltemperature AT sakhnyukve effectofanexternalmagneticfieldonthemaximumcurrentofsninsjunctionsnearthecriticaltemperature AT svidzinskyav effectofanexternalmagneticfieldonthemaximumcurrentofsninsjunctionsnearthecriticaltemperature |
| first_indexed |
2025-12-01T07:32:02Z |
| last_indexed |
2025-12-01T07:32:02Z |
| _version_ |
1850290288822583296 |
| fulltext |
Condensed Matter Physics, 2018, Vol. 21, No 4, 43702: 1–7
DOI: 10.5488/CMP.21.43702
http://www.icmp.lviv.ua/journal
The effect of an external magnetic field on the
maximum current of SNINS junctions near the
critical temperature
O.Yu. Pastukh, V.E. Sakhnyuk, A.V. Svidzinsky
Lesya Ukrainka Eastern European National University, 13 Voli Ave., 43000 Lutsk, Ukraine
Received May 24, 2018, in final form July 20, 2018
The behaviour of superconducting junctions of SNINS-type (where S is superconductor, N is normal metal, I is
insulator) with anharmonic current-phase relations in the external magnetic field near the critical temperature
was investigated. The dependence of the maximum current on the value of the magnetic flux in a wide range
of electron transmission coefficient values was considered. Also, it was investigated how the presence of a
normal layer of an arbitrary thickness in the scale of coherence length and in the presence of impurities in
superconducting regions affect the sensitivity of the maximum current to the magnetic field magnitude.
Key words: Josephson junctions, maximum current, magnetic flux, depairing effects
PACS: 74.50.+r
1. Introduction
The discovery of the Josephson effect [1] has greatly contributed to the development of superconduc-
tivity physics and opened a wide area for research in the field of the so-called weak superconductivity.
The place where these effects exist is the Josephson junctions or any other kind of weak links [2–4]. An
important characteristic of Josephson tunnel junctions is their behaviour in the external magnetic field.
As it turns out the maximum current in such structures is very sensitive to the change in the magnetic
field, and for the case of a sinusoidal current-phase relation can be written as [5]
Imax (Φ) = Imax (0)
����sin (πΦ/Φ0)
πΦ/Φ0
���� ,
where Φ is the magnetic flux through the junction, Φ0 is the magnetic flux quantum. From the above
expression one can see that the current drops to zero when the total magnetic flux is equal to an integer
number of quantum, i.e., Φ = nΦ0 and can reach the values from zero to the maximum value at a
change in the flow by only half the quantum Φ0. As a result, the use of this effect opens up wide
opportunities for the practical application of tunnel junctions [6–9]. A first experimental observation of
the magnetic field dependence of the maximum Josephson current was obtained in work [10]. Lately,
many experimental and theoretical investigations of this effect have been made for junctions of different
types, which are classified as so-called “short” [11–14], with dimensions that are small compared to the
Josephson penetration depth l � λJ and “long” [15–18], for which l � λJ. Nowadays, the investigations
of the behaviour of Josephson junctions in an external magnetic field for the case of annular tunnel
junctions [19, 20] and junctions with a ferromagnetic interlayer are also actively developed [21].
However, a detailed analysis shows that the simple sinusoidal current-phase relation is valid only under
certain conditions, which are implied on the parameters of the superconducting junction. For the case
of tunnel superconducting junction of SIS-type at the temperatures close to critical, the corresponding
condition is D � 1 (where D is the electron transmission coefficient through the dielectric layer). At
This work is licensed under a Creative Commons Attribution 4.0 International License . Further distribution
of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
43702-1
https://doi.org/10.5488/CMP.21.43702
http://www.icmp.lviv.ua/journal
http://creativecommons.org/licenses/by/4.0/
O.Yu. Pastukh, V.E. Sakhnyuk, A.V. Svidzinsky
non-small values of the electron transmission coefficient, in order to obtain the correct result for the
current, it is necessary to take into account the depairing effects, which under such conditions (D . 1)
are already significant. The study of the Josephson tunnel junction, taking into account these effects, was
carried out in [22, 23], which resulted in a nontrivial result for the current-phase relation instead of a
traditional sinusoidal dependence. It is obvious that the anharmonic current-phase relation will also be
reflected in the behaviour of the corresponding junctions in the magnetic field. In [24] it is shown that for
the “short” Josephson junction, an increase of electron transmission coefficient leads to an increase of the
current sensitivity to a change in the external magnetic field. For the “long” SIS junction in a magnetic
field [25], it is shown that the intense pair breaking significantly increases the penetration depth of the
magnetic field.
Nowadays, superconducting junctions of SNINS-type which combine tunnel effects and the proximity
effect are of great interest both in the fundamental and in the applied aspects of investigation. Equilibrium
properties of such junctions were studied in [26–28] while current-voltage characteristics of SNINS
junction for various thicknesses of the normal layer both in the tunneling and in the high-transparency
regimewere considered in [29, 30]. Our task in thiswork is to investigate the behaviour of superconducting
junctions of SNINS-type in the external magnetic field taking into account the depairing effects. Here we
consider how the presence of a wide range of electron transmission coefficient values and an arbitrary
thickness of the normal layer affects the sensitivity of the maximum current to the magnitude of the
magnetic field. The effect of nonmagnetic impurities is also taken into account.
2. Model and basic equations
Let us consider the investigated superconducting junction (figure 1). We choose the coordinate system
so that the superconductor occupies the region |z | > d/2, normal metal occupies the region |z | < d/2,
and the dielectric layer coincides with the plane x0y. Let the size of the junction in the x-direction be
equal to the unit of length and in the y-direction be equal to l. Let the external magnetic field be applied
along the x-axis, i.e., ®H = (H, 0, 0). The applied magnetic field is considered to be high so we can
assume that the penetration depth λJ of the magnetic field is much greater than the size of the junction.
In this case, we can neglect the self-induced magnetic field of the current passing through the junction
and consider the field inside the junction as uniformly equal to the external field applied to and around
the junction. For practical reasons, we take the vector potential oriented as follows: ®A = (0,−zH, 0). In
work [31], where the current states in the superconducting SNINS junction near the critical temperature
were investigated, it was shown that for certain values of junction parameters, the current-phase relation
is different from the traditional sinusoidal dependence. A pronounced anharmonicity of the current is
caused by the depairing effects action which are significant at small values of the normal metal thickness
and non-small values of the electron transmission coefficient. A significant role in this aspect also belongs
to the presence of nonmagnetic impurities in the junction. That is why the behaviour of superconducting
junctions with anharmonic current-phase relations in the external magnetic field becomes an interesting
topic of investigation. Let us consider how the values of the electron transmission coefficient, normal
Figure 1. Geometrical configuration of the SNINS junction.
43702-2
SNINS junction in an external magnetic field
metal thickness and the length of electron free path affect the dependence of the maximum current in
the junction on the magnetic flux. The result for the current-phase relation in SNINS junction is given
by [31]
j (ϕ) = sin ϕ
q1,∞ − q2,∞
2τq1,∞q2,∞
τ2 +
(
cos2 ϕ
2
q2
1,∞
+
sin2 ϕ
2
q2
2,∞
) 1 −
√
1 + 2τ2q2
1,∞q2
2,∞
(
q1,∞ tan2 ϕ
2 +q2,∞
q2
1,∞ tan2 ϕ
2 +q
2
2,∞
)2
τ2 + 1
2
(
1
q2,∞
− 1
q1,∞
)2
sin2 ϕ
, (2.1)
where τ = ξ0
ξ(T ) = [
12
7ζ (3)
1
χ(1/λ) (1 −
T
Tc
)]1/2 is the ratio of the coherence length and the characteristic
length in the Ginzburg-Landau theory, χ( 1λ ) =
8
7ζ (3)
∑∞
n=0
1
(2n+1)2(2n+1+1/λ)
, λ = l/ξ0 is a dimensionless
electron mean free path which determines a disorder of the superconductor with nonmagnetic impurities.
Coefficients q1,∞ and q2,∞ are given as follows:
q1,∞ =
1
2I1
{
I2 + I2(a) +
[I1 + I1(a)]2
I0 − I0(a)
}
,
q2,∞ =
1
2I1
{
I2 + I2(a,D) +
[I1 + I1(a,D)]2
I0 − I0(a,D)
}
.
In the above expressions, the notations for integrals which are determined by the kernels of linear integral
equations for the order parameter were used (see [31]).
In the presence of an external magnetic field, the phase difference between two superconductors
varies in the y direction and, as a result, there appears a component of the current in the direction of the
axis 0y. The dependence of the phase difference on the coordinates can be obtained from the relation
between the superfluid velocity ®υs and the magnetic field ®H [4]∫
®υsd®l = −
e
m
∫
®Hd®S.
As an integration area, we consider a parallelepiped, where one of its sides parallel to the axis 0y has
an infinitely small length dy and passes near the surface z = d/2 + 0. The opposite side is located at the
depth of the superconductor (we can assume ®υs = 0 and ®H = 0 on it). The other two sides are parallel to
the axis 0z, and the unit vector normal to the surface is in the direction of the axis 0x. After the integration
we choose in a similar way the integration area in the left-hand superconductor, and then we can find a
jump of superfluid velocity through the junction. On the other hand, from the definition ®υs = 1
2m∇ϕ−
e
m
®A
we can find a jump of superfluid velocity in terms of phase difference and vector potential. Thus, the
expression that in a differential form determines the dependence of the coherent phase difference on the
coordinates in the presence of a magnetic field is as follows:
∂ϕ
∂y
= −2eH (2δ + d) , (2.2)
where e is the electron charge, δ is the magnetic field penetration depth. Integrating relation (2.2) and
taking into account the direction of the applied magnetic field, we get
ϕ (y) = −2eH (2δ + d) y + ϕ0.
Substituting the above expression for the phase difference into (2.1), one can obtain an expression for the
current density j = j (H, y, ϕ0), taking into account the presence of an external magnetic field. In order
to find the total current through the superconducting junction, it is necessary to integrate the current
density over the entire area of the junction, taking into account its size. As a result, for the total current
as a function of the phase ϕ0 and magnetic field H, we have
I (H, ϕ0) =
1∫
0
dx
l∫
0
dy j (H, y, ϕ0) . (2.3)
43702-3
O.Yu. Pastukh, V.E. Sakhnyuk, A.V. Svidzinsky
Figure 2. Total current dependence of the magnetic flux and phase difference in SNINS junction.
Numerical integration of (2.3) makes it possible to analyze the effect of the junction parameters on
the dependence of the current on the magnetic flux. The corresponding graphical dependence of the total
current on the magnetic field and the phase difference is shown in figure 2, where the magnetic field H
is expressed through the total magnetic flux Φ = Hl (2δ + d) and the notation for the magnetic flux
quantum Φ0 = π/e is used.
As we can see in figure 2, with a change in the magnetic flux, there is an alternation of the maxima
and minima of the current, and the values of the maxima decrease with an increase of the magnetic flux.
For flux values Φ equal to an integer number of fluxons Φ0, maximum current reduces to zero, which
corresponds to the result of the classical work [10, 14]. Comparing the figures shown above, it becomes
obvious that with the decrease of the electron transmission coefficient, the peaks of the current become
sharper, and the decrease in the electron free path leads to the decrease in their magnitude.
Let us now analyze how the maximum current that can be born by a short SNINS junction depends
on the magnetic field. Obviously, in order to find it, it is necessary to equate the phase ϕ0 derivative of
I (H, ϕ0) to zero, that is, to find the critical value of the phase corresponding to the maximum current.
By making the calculations, one can obtain the graphical dependence of the maximum current in the
junction as a function of the magnetic flux. In figure 3 (a) the dependence of the maximum current as
0,5 1,0 1,5 2,0 2,5 3,0
0,00
0,25
0,50
0,75
1,00
(a)
I m
ax
(
)/I
m
ax
(0
)
0
D=0.2
D=0.5
D=0.9
=1
a=0.01 0
0,5 1,0 1,5 2,0 2,5 3,0
0,00
0,25
0,50
0,75
1,00
(b) =1
D=0.5
I m
ax
(
)/I
m
ax
(0
)
0
a=0.01 0
a=0.1 0
a= 0
Figure 3. Magnetic field dependence of the maximum current (normalized to the maximum current in
the absence of a field) for SNINS junction.
43702-4
SNINS junction in an external magnetic field
0,5 1,0 1,5 2,0 2,5 3,0
0,00
0,05
0,10
0,15
0,20
0,25
0,30 =1
I m
ax
(
)
0
D=0.5
a=0.01 0
0,5 1,0 1,5 2,0 2,5 3,0
0,00
0,01
0,02
0,03
0,04
0,05
0,06
0,07
=0.1
I m
ax
(
)
0
D=0.5
a=0.01 0
Figure 4. Dependence of the maximum current on the magnetic flux for different values of electron free
path.
a function of the magnetic flux is shown for the given value of the electron free path λ, normal layer
thickness a but different values of electron transmission coefficient D. An examination of the figure
shows that with an increase of D, the maximum current in the junction becomes much more sensitive
to the change in the magnetic flux, which is especially noticeable at the initial values of the magnetic
flux. This phenomenon was shown in [24], where the SIS junction was considered. The dependence of
the maximum current on the magnetic flux for different values of the normal layer thickness a with a
fixed value of the electron transmission coefficient D and electron free path λ is illustrated in figure 3 (b).
As one can see, the presence of the normal layer also affects the sensitivity of the current to the change
in the magnetic flux — with a decrease of the normal layer thickness sensitivity of Imax(Φ) increases.
From the numerical analysis for D = 0.9 and Φ/Φ0 = 0.3, we find out that the maximum current of the
junction decreases by 4 times, and for D = 0.2 and the same magnetic flux value, this decrease is only
25%. As a result, using in the measuring technique of superconducting SNINS junctions with non-small
values of the electron transmission coefficient opens up new horizons in various fields of science. From
the analysis of figure 3 (b), one can conclude that with an increase of the normal layer thickness, the
maximum current value Imax(Φ) begins to approach the value of the maximum current in the absence of
an external magnetic field Imax(0). Therefore, the corresponding graphs are higher. Let us now analyze
how the presence of non-magnetic impurities affects the magnitude of the maximum current.
Figure 4 displays the change of the magnitude and the shape of the maximum current with the change
in the electron free path for a given value of the electron transparency coefficient and the thickness of
the normal layer. One can see that an increase in the concentration of nonmagnetic impurities leads to
a noticeable decrease in the magnitude of the current maxima, while the form of the dependence shows
a small decrease in the sensitivity of the junction to the magnetic field. We can also consider numerical
comparisons. It is obvious that with a decrease in the electron free path from λ = 1 to λ = 0.1, the
maximum value Imax(Φ) decreases by more than 4 times. As for the shape of the dependence Imax(Φ), for
the value of the flow Φ/Φ0 = 0.4 at λ = 1, the maximum current decreases by 2.5 times the maximum
possible value, and when λ = 0.1, the current decrease does not exceed 50%.
3. Conclusions
In this paper, the behaviour of the superconducting SNINS junction in an external magnetic field near
the critical temperature has been investigated. It has been found that the presence of the dielectric layer and
the normal region in the junction significantly affect the magnitude of the maximum current and the shape
of the current dependence on the magnetic field. The increase in the electron transmission coefficient has
an especially noticeable impact on the sensitivity of the maximum current to the change in the magnetic
43702-5
O.Yu. Pastukh, V.E. Sakhnyuk, A.V. Svidzinsky
flux, which confirms the possibility of the practical application of such superconducting structures. In
addition, the effect of nonmagnetic impurities on the magnitude of the current was demonstrated. It
is shown that the change of the electron free path significantly affects the magnitude of the maximum
current in a junction, whereas the shape of the maximum current dependence on the magnetic flux
through the junction does not show significant changes. We can summarize that with an increase of the
electron transmission coefficient and a decrease of the normal layer thickness, when the depairing effects
are significant and the current-phase relation is anharmonic, the sensitivity of the junction to the change
in the magnetic flux increases. An interesting issue for a further research can be the behaviour of such
superconducting junctions in a magnetic field, taking into account the self-induced magnetic field caused
by the current passing through the junction.
Acknowledgements
Present research is supported by the State Fund for the Fundamental Research of Ukraine (award
№F76/123-2017).
References
1. Josephson B.D., Phys. Lett., 1962, 1, 251–253, doi:10.1016/0031-9163(62)91369-0.
2. Likharev K.K., Dynamics of Josephson Junctions and Circuits, Gordon and Breach, New York, 1986.
3. Likharev K.K., Ulrich B.T., Systemswith Josephson Junctions,MoscowUniversity Publications,Moscow, 1978,
(in Russian).
4. Svidzinsky A.V., Spatially Innhomogeneous Problems in the Theory of Superconductivity, Nauka, Moscow,
1982, (in Russian).
5. Josephson B.D., Rev. Mod. Phys., 1964, 36, 216–220, doi:10.1103/RevModPhys.36.216.
6. Barone A., Paterno G., Physics and Applications of the Josephson Effect, Wiley, New York, 1982.
7. Langenberg D.N., Scalapino D.J., Taylor B.N., Proc. IEEE, 1966, 54, 560, doi:10.1109/PROC.1966.4776.
8. Solymar L., Superconducting Tunneling and Applications, Chapman and Hall, London, 1972.
9. Schwartz B.B., Foner S., Superconductor Applications: SQUIDs andMachines, Plenum Press, New York, 1977.
10. Rowell J.M., Phys. Rev. Lett., 1963, 11, 200–202, doi:10.1103/PhysRevLett.11.200.
11. Fiske M.D., Rev. Mod. Phys., 1964, 36, 221, doi:10.1103/RevModPhys.36.221.
12. Schwidtal K., Finnegan R.D., J. Appl. Phys., 1969, 40, 2123, doi:10.1063/1.1657934.
13. Schwidtal K., Finnegan R.D., Phys. Rev. B, 1970, 2, 148, doi:10.1103/PhysRevB.2.148.
14. Balsamo E.P., Paternò G., Barone A., Russo M., Vaglio R., Phys. Status Solidi A, 1976, 35, K173,
doi:10.1002/pssa.2210350266.
15. Goldman A.M., Kreisman P.J., Phys. Rev., 1967, 164, 544, doi:10.1103/PhysRev.164.544.
16. Owen C.S., Scalapino D.J., Phys. Rev., 1967, 164, 538, doi:10.1103/PhysRev.164.538.
17. Schwidtal K., Phys. Rev. B, 1970, 2, 2526, doi:10.1103/PhysRevB.2.2526.
18. Atanasova P.K., Boyadjiev T.L., Zemlyanaya E.V., Shukrinov Y.M., In: Numerical Methods and Applications,
Dimov I., Dimova S., Kolkovska N. (Eds.), Springer, Berlin, Heidelberg, 2011, 347–352,
doi:10.1007/978-3-642-18466-6_41.
19. Martucciello N., Monaco R., Phys. Rev. B, 1996, 53, 3471, doi:10.1103/PhysRevB.53.3471.
20. Wallraff A., Koval Yu., Levitchev M., Fistul M.V., Ustinov A.V., J. Low Temp. Phys., 2000, 118, 543–553,
doi:10.1023/A:1004674908169.
21. Weides M., Kemmler M., Kohlstedt H., Waser R., Koelle D., Kleiner R., Goldobin E., Phys. Rev. Lett., 2006,
97, 247001, doi:10.1103/PhysRevLett.97.247001.
22. Sakhnyuk V.E., Holoviy V.M., J. Phys. Stud., 2011, 15, 2702 (in Ukrainian).
23. Barash Yu.S., Phys. Rev. B, 2012, 85, 100503, doi:10.1103/PhysRevB.85.100503.
24. Sakhnyuk V.E., Sci. Bull. Lesya Ukrainka East. Eur. Nat. Univ., Ser. Phys., 2013, 26, 50–54 (in Ukrainian).
25. Barash Yu.S., Phys. Rev. B, 2014, 89, 174516, doi:10.1103/PhysRevB.89.174516.
26. Zaikin A.D., Zharkov G.F., Zh. Eksp. Teor. Fiz., 1980, 78, 721–732 (in Russian), [Sov. Phys. JETP, 1980, 51,
364].
27. Golubov A.A., Kupriyanov M.Y., Zh. Eksp. Teor. Fiz., 1989, 96, 1420–1433 (in Russian), [Sov. Phys. JETP,
1989, 69, 805].
28. Akhramovich L.N., Svidzinsky A.V., Fiz. Nizk. Temp., 1988, 14, 815–821 (in Russian).
29. Bezuglyi E.V., Bratus’ E.N., Shumeiko V.S., Phys. Rev. B, 2017, 95, 014522, doi:10.1103/PhysRevB.95.014522.
43702-6
https://doi.org/10.1016/0031-9163(62)91369-0
https://doi.org/10.1103/RevModPhys.36.216
https://doi.org/10.1109/PROC.1966.4776
https://doi.org/10.1103/PhysRevLett.11.200
https://doi.org/10.1103/RevModPhys.36.221
https://doi.org/10.1063/1.1657934
https://doi.org/10.1103/PhysRevB.2.148
https://doi.org/10.1002/pssa.2210350266
https://doi.org/10.1103/PhysRev.164.544
https://doi.org/10.1103/PhysRev.164.538
https://doi.org/10.1103/PhysRevB.2.2526
https://doi.org/10.1007/978-3-642-18466-6_41
https://doi.org/10.1103/PhysRevB.53.3471
https://doi.org/10.1023/A:1004674908169
https://doi.org/10.1103/PhysRevLett.97.247001
https://doi.org/10.1103/PhysRevB.85.100503
https://doi.org/10.1103/PhysRevB.89.174516
https://doi.org/10.1103/PhysRevB.95.014522
SNINS junction in an external magnetic field
30. Zhitlukhina E., Devyatov I., Egorov O., Belogolovskii M., Seidel P., Nanoscale Res. Lett., 2016, 11, 58,
doi:10.1186/s11671-016-1285-0.
31. Pastukh O.Yu., Sakhnyuk V.E., Svidzinsky A.V., Phys. Lett. A, 2018, 382, 2149–2155,
doi:10.1016/j.physleta.2018.05.035.
Дослiдження впливу зовнiшнього магнiтного поля на
максимальний струм SNINS-контактiв поблизу критичної
температури
О.Ю. Пастух, В.Є. Сахнюк, А.В. Свiдзинський
Схiдноєвропейський нацiональний унiверситет iменi Лесi Українки, просп. Волi, 13, 43000 Луцьк, Україна
В роботi дослiджено поведiнку надпровiдних контактiв типу SNINS з ангармонiйною струм-фазовою зале-
жнiстю у зовнiшньому магнiтному полi поблизу критичної температури. Проаналiзовано залежнiсть ма-
ксимального струму вiд потоку зовнiшнього магнiтного поля для широкого iнтервалу змiни коефiцiєнта
проходження електронiв. Також дослiджено, як впливає на чутливiсть струму до змiни магнiтного потоку
наявнiсть нормального прошарку довiльної товщини в масштабi довжини когерентностi та наявнiсть у
надпровiдних областях немагнiтних домiшок.
Ключовi слова: контакт Джозефсона, максимальний струм, магнiтний потiк, ефекти розпаровування
43702-7
https://doi.org/10.1186/s11671-016-1285-0
https://doi.org/10.1016/j.physleta.2018.05.035
Introduction
Model and basic equations
Conclusions
|