Josephson effect in a weak link between borocarbides
A stationary Josephson effect is analyzed theoretically for a weak link between borocarbide superconductors. It is shown that different models of the order parameter result in qualitatively different current-phase relations.
Gespeichert in:
| Datum: | 2005 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2005
|
| Schriftenreihe: | Физика низких температур |
| Schlagworte: | |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/121396 |
| 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: | Josephson effect in a weak link between borocarbides / Yu.A. Kolesnichenko, S.N. Shevchenko // Физика низких температур. — 2005. — Т. 31, № 2. — С. 182-184. — Бібліогр.: 7 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-121396 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1213962017-06-15T03:02:45Z Josephson effect in a weak link between borocarbides Kolesnichenko, Yu.A. Shevchenko, S.N. Свеpхпpоводимость, в том числе высокотемпеpатуpная A stationary Josephson effect is analyzed theoretically for a weak link between borocarbide superconductors. It is shown that different models of the order parameter result in qualitatively different current-phase relations. 2005 Article Josephson effect in a weak link between borocarbides / Yu.A. Kolesnichenko, S.N. Shevchenko // Физика низких температур. — 2005. — Т. 31, № 2. — С. 182-184. — Бібліогр.: 7 назв. — англ. 0132-6414 PACS: 74.50.+r http://dspace.nbuv.gov.ua/handle/123456789/121396 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Свеpхпpоводимость, в том числе высокотемпеpатуpная Свеpхпpоводимость, в том числе высокотемпеpатуpная |
| spellingShingle |
Свеpхпpоводимость, в том числе высокотемпеpатуpная Свеpхпpоводимость, в том числе высокотемпеpатуpная Kolesnichenko, Yu.A. Shevchenko, S.N. Josephson effect in a weak link between borocarbides Физика низких температур |
| description |
A stationary Josephson effect is analyzed theoretically for a weak link between borocarbide superconductors.
It is shown that different models of the order parameter result in qualitatively different
current-phase relations. |
| format |
Article |
| author |
Kolesnichenko, Yu.A. Shevchenko, S.N. |
| author_facet |
Kolesnichenko, Yu.A. Shevchenko, S.N. |
| author_sort |
Kolesnichenko, Yu.A. |
| title |
Josephson effect in a weak link between borocarbides |
| title_short |
Josephson effect in a weak link between borocarbides |
| title_full |
Josephson effect in a weak link between borocarbides |
| title_fullStr |
Josephson effect in a weak link between borocarbides |
| title_full_unstemmed |
Josephson effect in a weak link between borocarbides |
| title_sort |
josephson effect in a weak link between borocarbides |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2005 |
| topic_facet |
Свеpхпpоводимость, в том числе высокотемпеpатуpная |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/121396 |
| citation_txt |
Josephson effect in a weak link between borocarbides / Yu.A. Kolesnichenko, S.N. Shevchenko // Физика низких температур. — 2005. — Т. 31, № 2. — С. 182-184. — Бібліогр.: 7 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT kolesnichenkoyua josephsoneffectinaweaklinkbetweenborocarbides AT shevchenkosn josephsoneffectinaweaklinkbetweenborocarbides |
| first_indexed |
2025-07-08T19:50:04Z |
| last_indexed |
2025-07-08T19:50:04Z |
| _version_ |
1837109567216943104 |
| fulltext |
Fizika Nizkikh Temperatur, 2005, v. 31, No. 2, p. 182–184
Josephson effect in a weak link between borocarbides
Yu.A. Kolesnichenko and S.N. Shevchenko
B. Verkin Institute for Low Temperature Physics and Engineering
of the National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkov 61103, Ukraine
E-mail: kolesnichenko@ilt.kharkov.ua
Received June 24, 2004
A stationary Josephson effect is analyzed theoretically for a weak link between borocarbide su-
perconductors. It is shown that different models of the order parameter result in qualitatively dif-
ferent current-phase relations.
PACS: 74.50.+r
Determination of the symmetry of the order param-
eter � in novel unconventional superconductors is im-
portant for the development of modern physics of su-
perconductivity because the dependence of �� �k on the
direction of the electron wave vector k on the Fermi
surface determines all of the kinetic and thermody-
namic characteristics of the superconductor. Calcula-
tion of the order parameter �� �k is a fundamental
problem and requires knowledge of the pairing poten-
tial. Some general information about �� �k can be ob-
tained from the symmetry of a normal state, i.e., ac-
cording to the Landau theory of secon-order phase
transitions [1], the order parameter transforms only
accoding to irreducible representations of the symme-
try group of the normal state (for review, see [2]).
Nevertheless, symmetry considerations reserve for the
order parameter considerable freedom in the selection
of irreducible representation and its basis functions.
Therefore in many papers authors consider different
models of the order parameter, which are based on
possible representations of crystallographic point
groups. The subsequent comparison of theoretical re-
sults with experimental data makes it possible to
choose between available models of the order parame-
ter. The Josephson effect in superconducting weak
links is one of the most suitable instruments for inves-
tigation of the symmetry of �� �k . It has heen shown,
for example, that current—phase relations jJ ( )� in
unconventional superconductors are quite different
for different models of �� �k , and hence the study of the
Josephson effect enables one to judge the applicability
of different models to the novel superconductors [3].
Borocarbides, such as YNi2B2C and LuNi2B2C,
exhibit unconventional superconductivity. There is
strong evidence that in these materials the order
parameter is highly anisotropic [4]. The order parame-
ter in these compounds has fourfold symmetry, and
there are deep minima along the [100] and [010] direc-
tions [4,5]. Both the symmetry of the borocarbide
crystal structure and the experimental results have
allowed the authors of Refs. [6] to suggest an
s g� -wave model of the order parameter to describe
the superconductivity in the borocarbides:
� � �
�
� � � �s g sin cos ( sin cos ),4 0 44
2
4 �
�
(1)
where and � are the polar and azimuthal angles of
an electron wave vector k; � s and � g are the s and g
components of the order parameter, and � �0 0� ( )T
describes the temperature-dependent amplitude value
of the order parameter.
Parameter
� � �s g/ is the key value here. If
� 1,
then the order parameter �( , ) � is an alternating-sign
quantity, which means that some reflected trajectories
experience the intrinsic phase difference. This result in
the suppression of the order parameter in the vicinity of
the interface between two superconductors similar to
what is known about the contact of two d-wave super-
conductors (see [7] and references therein); and in this
case the non-self-consistent calculation, presented be-
low, can be justified for the weak links in the form of
both the point contact and the plane boundary between
two banks. Another consequence of the intrinsic phase
difference is the appearance of the spontaneous phase
difference (which means that at equilibrium, when
jJ � 0 and dj /dJ �
0, the phase difference is not zero:
� �� �0 0) and the spontaneous interface current at
© Yu.A. Kolesnichenko and S.N. Shevchenko, 2005
equilibrium at � �� 0 (which is demonstrated below). If
� 1, then the order parameter is not an alternating-sign
quantity, �( , ) � � 0, and the non-self-consistent calcu-
lation can only be justified for the weak link in the form
of the point contact. In this case at the contact there is
also the component of the current along the interface
due to the anisotropy of the order parameter. However
this current is not spontaneous, which means that at the
equilibrium at � � 0 both Josephson and interface cur-
rent components equal to zero.
In what follows we study the stationary Josephson
effect in the weak link between two borocarbides,
described by the s g� -wave model (1) of the order
parameter, and compare the results with the Jo-
sephson current between d-wave superconductors
( sin )� �� 0 2� . We consider a perfect contact be-
tween two clean, differently orientated superconduc-
tors. The external order parameter phase difference �
is assumed to drop at the interface plane x � 0. The
theoretical description of the Josephson effect is based
on the Eilenberger equation, as it was described, for
example, in the Refs [7]. The standard procedure of
matching the solutions of the bulk Eilenberger equa-
tions at the boundary gives the Matsubara Green’s
function � ( )G� 0 at the contact at x � 0 [7]. The compo-
nent G g� �
11 0 0( ) ( )� of � ( )G� 0 determines the current
density at the boundary:
j k k| � , | |�x Fj j e N v�
� � � � ��0
0
0 04� � ��
�
Im g(0) (2)
Im ( ) ( )
sin
cos
,g kx
L R
L R n L R
0
2
� �
� �
sign
� �
� � � �
�
� �
(3)
where N0 is the density of states at the Fermi level,
� �... ,�k denotes averaging over the directions of Fermi
wave vector k, �k = k/k is the unit vector in the
direction of k, � �n T n� �( )2 1 are Matsubara frequen-
cies, � L R, stands for the order parameter in the left
(right) bank, and � �L R L Rn, ,� ��2 2 .
Making use of Eqs. (2), (3) we numerically plot
the current—phase relations for two components of
the current, jx (through the contact) and jy (along
the contact). We assume that the c axes of the left and
right superconducting banks are directed along the z
axis, that the a and b axes of the left superconductor
are directed along x and y axes, and that the ab basal
plane of the right superconductor is rotated by an an-
gle � with respect to the left superconductor. In Fig. 1
the current through the contact (Josephson current) is
plotted versus the phase difference for both d-wave
and s g� -wave models of the order parameter for low
temperature and a relative angle between supercon-
ducting banks � �� /4. The current—phase relations
are qualitatively different, which can be used as a test
to discriminate experimentally the true model, that
describes a borocarbide.
Generally speaking, there is a current jy tangential
to the boundary in addition to the current through the
contact jx [3]. The case of the contact of two d-wave
superconductors has heen considered in many papers
(see [7] and references therein). Here we consider in
more detail the Josephson effect for the s g� -wave
model. In this case the Josephson current depends
weakly on the relative angle between superconductors
�, while the current along the contact plane depends
strongly on �: jy � 0 for � � 0 and �/4 and attains the
maximal value at � �� /8. In Fig. 2 we plot both jx
and jy for the s g� -wave model of the order parame-
ter for low temperature and � �� /8. If
� 1, then the
tangential component of the current density in the
contact plane remains much smaller than the trans-
verse component for any values of the phase difference
� and of the relative angle between superconductors �.
At
� 1, as it is pointed out above, the spontaneous
Josephson effect in a weak link between borocarbides
Fizika Nizkikh Temperatur, 2005, v. 31, No. 2 183
0 0.2 0.4 0.6 0.8 1.0
� �/2
1.0
0.5
0
–0.5
–1.0
j
/j
x
�
s + g-wawe
d-wawea
b
c
a
b
c
Fig. 1. Josephson current density versus phase difference
for both the d-wave and s g� -wave models of the order
parameter (the solid line corresponds to
� 1 and the dot-
ted line corresponds to
� 2). T � 005 0. � , � �� /4. The
order parameters for the d-wave and s g� -wave models in
momentum space are shown in the insets.
= 0.1
�/2�
0 0.5 1.0
0.05
0
–0.05
0.5
0
–0.5
= 1
j/
j �
�/2�
jx
jy
0 0.5 1.0
Fig. 2. Current—phase relations for two components of
the current, jx (through the contact) and jy (along the
contact) for
� 1 and
� 01. , T � 005 0. � , � �� /8.
phase difference and spontaneous interface current ap-
pear. The effect is the most pronounced at
�� 1,
which we illustrate at Fig. 2.
Thus we have considered a weak link between two
clean differently orientated borocarbide superconduc-
tors. The current—phase relations were compared for
the d-wave and s g� -wave models of the order param-
eter. The dependences of the Josephson current on the
phase difference are qualitatively different for these
models. It is shown that because of the anisotropy of
the order parameter there is a current tangential to the
boundary for the s g� -wave model, which attains its
maximum at a relative angle between superconductors
equal to �/8. This interface current can exist in the
absence of Josephson current at equilibrium if
� 1.
The observation of such spontaneous current can be
used as a test of whether the order parameter is alter-
nating-sign or not.
We acknowledge fruitful discussions with A.N.
Omelyanchouk. This work was supported by CRDF
Project (Grant No UP1-2566-KH-03).
1. L.D. Landau and E.M. Lifshitz, Statistical Physics,
Part 1, Pergamon, New York (1979).
2. V.P. Mineev and K.V. Samokhin, Introduction to
Unconventional Superconductivity, Amsterdam, The
Netherlands: Gordon and Breach science Publishers
(1999).
3. Yu.A. Kolesnichenko, A.N. Omelyanchouk, and A.M.
Zagoskin, Fiz. Nizk. Temp. 30, 714 (2004) [Low
Temp. Phys 30, 535 (2004)].
4. Etienne Boaknin, R.W. Hill, Cyril Proust, C. Lupien,
Louis Taillefer, and P.C. Canfield, Phys. Rev. Lett.
87, 237001 (2001); K. Izawa, K. Kamata, Y. Na-
kajima, Y. Matsuda, T. Watanabe, M. Nohara, H.
Takagi, P. Thalmeier, and K. Maki, Phys. Rev. Lett.
89, 137006 (2002).
5. T. Jacobs, Balam A. Willemsen, S. Sridhar, R.
Nagarajan, L.C. Gupta, Z. Hossain, Chandan Mazumdar,
P.C. Canfield, and B.K. Cho, Phys. Rev. B52, 007022
(1995); In-Sang Yang, M.V. Klein, S.L. Cooper, P.C.
Canfield, B.K. Cho, and Sung-Ik Lee, Phys. Rev. B62,
1291 (2000); M. Nohara, M. Isshiki, H. Takagi, and
R.J. Cava, J. Phys. Soc. Jpn. 66, 1888 (1997); M.
Nohara, H. Suzuki, N. Mangkorntong, and H. Takagi,
Physica C341–348, 2177 (2000).
6. P. Pairor and M.B. Walker, Phys. Rev. B65, 064507
(2002); K. Maki, P. Thalmeier, and H. Won, Phys. Rev.
B65, 140502R (2002); Hyun C. Lee and Han-Yong Choi,
Phys. Rev. B65, 174530 (2002).
7. M.H.S. Amin, A.N. Omelyanchouk, S.N. Rashkeev, M.
Coury, and A.M. Zagoskin, Physica B318, 162 (2002);
Yu.A. Kolesnichenko, A.N. Omelyanchouk, and S.N.
Shevchenko, Fiz. Nizk. Temp. 30, 288 (2004) [Low
Temp. Phys. 30, 213 (2004)].
184 Fizika Nizkikh Temperatur, 2005, v. 31, No. 2
Yu.A. Kolesnichenko and S.N. Shevchenko
|