Andreev-spectroscopy study of unconventional superconductivity in MgB₂:(La,Sr)MnO₃ nanocomposite
Unconventional high-temperature superconductivity in MgB₂:La₀:₆₅Sr₀:₃₅MnO₃ (MgB:LSMO) nanocomposite has been found recently [Phys. Rev. B 86, 10502 (2012)]. In this report, the symmetry of the nanocomposite superconducting order parameter and plausible pairing mechanisms have been studied by the p...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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Krivoruchko, V.N. D’yachenko, A.I. Tarenkov, V.Yu. 2017-06-08T04:33:20Z 2017-06-08T04:33:20Z 2014 Andreev-spectroscopy study of unconventional superconductivity in MgB₂:(La,Sr)MnO₃ nanocomposite / V.N. Krivoruchko, A.I. D’yachenko, V.Yu. Tarenkov // Физика низких температур. — 2014. — Т. 40, № 10. — С. 1147-1154. — Бібліогр.: 38 назв. — англ. 0132-6414 PACS 74.45.+c, 74.78.–w, 74.20.Rp, 74.81.–g https://nasplib.isofts.kiev.ua/handle/123456789/119669 Unconventional high-temperature superconductivity in MgB₂:La₀:₆₅Sr₀:₃₅MnO₃ (MgB:LSMO) nanocomposite has been found recently [Phys. Rev. B 86, 10502 (2012)]. In this report, the symmetry of the nanocomposite superconducting order parameter and plausible pairing mechanisms have been studied by the point-contact Andreev-reflection (PCAR) spectroscopy. To clarify the experimental results obtained, we consider a model of a ferromagnetic superconductor, which assumes a coexistence of itinerant ferromagnetism and mixed-parity superconductivity. The Balian–Werthamer state, with quasiparticle gap topology of the same form as that of the ordinary s-wave state, fits the experimental data reasonably well. Utilizing the extended Eliashberg formalizm, we calculated the contribution of MgB₂ in the total composite’s conductivity and estimated the magnitude of the electron–phonon effects originated from MgB₂ in I–V characteristics of the composite at above-gap energies. It was found that distinctive features observed in the PC spectra of the MgB:LSMO samples and conventionally attributed to the electron–phonon interaction cannot be related to the MgB₂ phonons. It is argued that the detected singularities may be a manifestation of the electron-spectrum renormalizations due to strong magnetoelastic (magnon–phonon) interaction in LSMO. The authors thanks to M. Belogolovskii, A. Omelyanchouk, and Yu. Naidyuk for useful discussions. ru Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур III Международный семинар по микроконтактной спектроскопии Andreev-spectroscopy study of unconventional superconductivity in MgB₂:(La,Sr)MnO₃ nanocomposite Article published earlier |
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Andreev-spectroscopy study of unconventional superconductivity in MgB₂:(La,Sr)MnO₃ nanocomposite |
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Andreev-spectroscopy study of unconventional superconductivity in MgB₂:(La,Sr)MnO₃ nanocomposite Krivoruchko, V.N. D’yachenko, A.I. Tarenkov, V.Yu. III Международный семинар по микроконтактной спектроскопии |
| title_short |
Andreev-spectroscopy study of unconventional superconductivity in MgB₂:(La,Sr)MnO₃ nanocomposite |
| title_full |
Andreev-spectroscopy study of unconventional superconductivity in MgB₂:(La,Sr)MnO₃ nanocomposite |
| title_fullStr |
Andreev-spectroscopy study of unconventional superconductivity in MgB₂:(La,Sr)MnO₃ nanocomposite |
| title_full_unstemmed |
Andreev-spectroscopy study of unconventional superconductivity in MgB₂:(La,Sr)MnO₃ nanocomposite |
| title_sort |
andreev-spectroscopy study of unconventional superconductivity in mgb₂:(la,sr)mno₃ nanocomposite |
| author |
Krivoruchko, V.N. D’yachenko, A.I. Tarenkov, V.Yu. |
| author_facet |
Krivoruchko, V.N. D’yachenko, A.I. Tarenkov, V.Yu. |
| topic |
III Международный семинар по микроконтактной спектроскопии |
| topic_facet |
III Международный семинар по микроконтактной спектроскопии |
| publishDate |
2014 |
| language |
Russian |
| container_title |
Физика низких температур |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| format |
Article |
| description |
Unconventional high-temperature superconductivity in MgB₂:La₀:₆₅Sr₀:₃₅MnO₃ (MgB:LSMO) nanocomposite
has been found recently [Phys. Rev. B 86, 10502 (2012)]. In this report, the symmetry of the nanocomposite
superconducting order parameter and plausible pairing mechanisms have been studied by the point-contact
Andreev-reflection (PCAR) spectroscopy. To clarify the experimental results obtained, we consider a model
of a ferromagnetic superconductor, which assumes a coexistence of itinerant ferromagnetism and mixed-parity
superconductivity. The Balian–Werthamer state, with quasiparticle gap topology of the same form as that
of the ordinary s-wave state, fits the experimental data reasonably well. Utilizing the extended Eliashberg formalizm,
we calculated the contribution of MgB₂ in the total composite’s conductivity and estimated the magnitude
of the electron–phonon effects originated from MgB₂ in I–V characteristics of the composite at above-gap
energies. It was found that distinctive features observed in the PC spectra of the MgB:LSMO samples and conventionally
attributed to the electron–phonon interaction cannot be related to the MgB₂ phonons. It is argued that
the detected singularities may be a manifestation of the electron-spectrum renormalizations due to strong
magnetoelastic (magnon–phonon) interaction in LSMO.
|
| issn |
0132-6414 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/119669 |
| citation_txt |
Andreev-spectroscopy study of unconventional superconductivity in MgB₂:(La,Sr)MnO₃ nanocomposite / V.N. Krivoruchko, A.I. D’yachenko, V.Yu. Tarenkov // Физика низких температур. — 2014. — Т. 40, № 10. — С. 1147-1154. — Бібліогр.: 38 назв. — англ. |
| work_keys_str_mv |
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| first_indexed |
2025-11-24T02:24:16Z |
| last_indexed |
2025-11-24T02:24:16Z |
| _version_ |
1850840011532926976 |
| fulltext |
Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 10, pp. 1147–1154
Andreev-spectroscopy study of unconventional
superconductivity in MgB2:(La,Sr)MnO3 nanocomposite
V.N. Krivoruchko, A.I. D’yachenko, and V.Yu. Tarenkov
Donetsk Institute for Physics and Engineering, National Academy of Sciences of Ukraine
72 R. Luxemburg Str., Donetsk 83114, Ukraine
E-mail: krivoruc@gmail.com
Received May 20, 2014, published online August 21, 2014
Unconventional high-temperature superconductivity in MgB2:La0:65Sr0:35MnO3 (MgB:LSMO) nanocom-
posite has been found recently [Phys. Rev. B 86, 10502 (2012)]. In this report, the symmetry of the nanocom-
posite superconducting order parameter and plausible pairing mechanisms have been studied by the point-contact
Andreev-reflection (PCAR) spectroscopy. To clarify the experimental results obtained, we consider a model
of a ferromagnetic superconductor, which assumes a coexistence of itinerant ferromagnetism and mixed-parity
superconductivity. The Balian–Werthamer state, with quasiparticle gap topology of the same form as that
of the ordinary s-wave state, fits the experimental data reasonably well. Utilizing the extended Eliashberg for-
malizm, we calculated the contribution of MgB2 in the total composite’s conductivity and estimated the magni-
tude of the electron–phonon effects originated from MgB2 in I–V characteristics of the composite at above-gap
energies. It was found that distinctive features observed in the PC spectra of the MgB:LSMO samples and con-
ventionally attributed to the electron–phonon interaction cannot be related to the MgB2 phonons. It is argued that
the detected singularities may be a manifestation of the electron-spectrum renormalizations due to strong
magnetoelastic (magnon–phonon) interaction in LSMO.
PACS: 74.45.+c Proximity effects; Andreev reflection; SN and SNS junctions;
74.78.–w Superconducting films and low-dimensional structures;
74.20.Rp BCS theory and its development;
74.81.–g Inhomogeneous superconductors and superconducting systems, including electronic
inhomogeneities.
Keywords: unconventional superconductivity, heterostructures, Andreev reflection.
1. Introduction
Recently unconventional superconductivity in a binary
network composed of s-wave superconductor MgB2 and half-
metallic ferromagnet La0.65Sr0.35MnO3 was revealed [1].
Specifically, for MgB:LSMO (MgB2:La0.65Sr0.35MnO3)
composites with 3:1 and 4:1 weight ratio (0.896:0.104 and
0.92:0.08 volume ratio, respectively) of components some
principal effects have been found [1]. With an onset of the
MgB2 superconductivity, a spectacular drop of the sample
resistance has been detected and superconductivity has
been observed below 30 K. It was also found that the basic
nanocomposites’ characteristics (critical temperature, cur-
rent–voltage dependence, percolation threshold, etc.) are
strongly affected by the half-metallic (La,Sr)MnO3 and
cannot be quantitatively explained within the framework of
the conventional percolation scenario. Using the point-
contact (PC) spectroscopy, three energy gaps in the single-
electron spectrum Δ1(π), Δ2(σ), and Δtr have been clearly
revealed. Two of these gaps were identified as enhanced
gaps in the quasiparticle spectrum of the MgB2 in the
composite. The third gap Δtr was about three times larger
than the largest MgB2 gap, and its magnitude is the same
as those earlier detected in PCs data for (La,Ca)MnO3 [2]
and (La,Sr)MnO3 [3] with Pb or MgB2. A key feature is
also the temperature behavior of the Δtr gap, which does
not follow the BCS dependence.
As a possible explanation, it has been suggested [1–3]
that doped manganites may be an example of systems with
intrinsic fluctuated/incoherent superconductivity, i.e., with
intrinsic TΔ ≠ 0 but with global Tφ = 0 (here TΔ stands for
the temperature of an electron pairing, and Tφ is the tem-
perature of a long-range phase coherency). That is, at low
temperature in a half-metallic ferromagnet (La,Sr)MnO3,
© V.N. Krivoruchko, A.I. D’yachenko, and V.Yu. Tarenkov, 2014
V.N. Krivoruchko, A.I. D’yachenko, and V.Yu. Tarenkov
local spin-triplet p-wave pairing condensate already exists.
However, though the local gap amplitude is large, there is
no phase stiffness and the system is incapable of displaying
a long-range superconducting response. Nonetheless, local
phase rigidity survives and, being proximity coupled to
MgB2, the long-range coherency is restored. Inversely, the
manganite in a superconducting state with large pairing
energy enhances, due to proximity effect, the MgB2 super-
conductivity.
To clarify the symmetry of the MgB:LSMO nanocom-
posite superconducting order parameter, we have examined
a model which suggests that in the nanocomposite a super-
conducting phase develops in a low-symmetry environ-
ment with a missing inversion center. Namely, we consider
a model of a ferromagnetic superconductor described by
coexisting itinerant ferromagnetic and mixed-parity (a su-
perposition of spin-singlet s- and spin-triplet p-waves) su-
perconducting state. It is argued that a quasiparticle gap
topology similar to that in the superfluid phase of ³He [4]
most probably is realized in the composite’s superconduct-
ing phase.
In the BCS theory of superconductivity, electrons form
(Cooper) pairs through an attractive interaction mediated
by lattice vibrations. It is now generally accepted that the
only mechanism of formation of Cooper pairs in MgB2 is
an electron–phonon interaction (EPI) [5,6]. Concerning
ferromagnetic superconductors, Fay and Appel [7] predict-
ed that longitudinal ferromagnetic fluctuations could result
in a p-wave equal-spin-pairing superconducting state with-
in the ferromagnetic phase.
As well established at present [8], the self-energy ef-
fects reveal themselves through the distinctive peculiarities
in the PC current–voltage (I–V) dependence at eV >> Δ. To
elucidate a plausible pairing mechanism, which causes a
superconducting pairing in the composite, we analyze ex-
perimental singularities observed in PCs spectra of the
composite with nonmagnetic and ferromagnetic metallic
wires. It was found that distinctive peculiarities observed
in these PCs spectra and conventionally attributed to bo-
son’s self-energy effects cannot be related to the MgB2
phonons. It is suggested that the detected singularities may
be a manifestation of electron spectrum renormalizations
due to a strong magnon–phonon (magnetoelastic) interac-
tion in LSMO.
2. Specifics of experiment
The samples are composites of submicron MgB2 pow-
der and La0.65Sr0.35MnO3 nanoparticles (about 20–30 nm
in size). Details of the LSMO nanoparticles preparation
were described earlier [9]. Comparative investigations of
the nuclear magnetic resonance and nuclear spin-spin re-
laxation of 55Mn nuclei of nanopowder and polycrystalline
samples with the same composition confirmed the presence
of the ferromagnetic metallic state and phase separation,
which is typical for manganites, for particles of the size we
used [10]. Powders with different weight ratios of LSMO
and MgB2 were mixed and cold pressed (under pressure up
to 60 kbar) in stripes, and a number of samples of different
composition was obtained.
The point contacts are made by direct touch of
MgB:LSMO plate with sharpened needles of normal me-
tals In, Ag, and Nb, and half-metallic ferromagnet (hmF)
La0.65Ca0.35MnO3 (LCMO). Since not every touch pro-
duces the desired appearance of the energy-gap I–V char-
acteristics, we moved the electrodes relative to each other
in order to penetrate through the accidentally damaged
surface layer. This operation produces additional defects in
the contact region and, thus, shortens further the small
electron mean free path.
Small electron mean free path is one of a factor that
hampers PC spectroscopy of manganites. However, as was
earlier detected [6], even if the contact is obtained by the
so-called “soft” point-contact technique, in which the larg-
er (if compared to the electronic mean free path) “foot-
print” of the counter electrode is formed, these contacts
very often provide spectroscopic information. This means
that, on a microscopic scale, the real electrical contact oc-
curs through parallel nanometric channels (whose number
is unknown). The resistance of individual contacts is larger
than the total contact resistance and usually is in the suita-
ble range for Andreev reflection to occur. A selection of
the “spectroscopic” contacts we made based on accordance
of the PC’s spectra to theoretical one for Andreev PC. The
analysis of the PC spectra obtained (see Sec. 3.1) reveals
the presence of small dips in the conductance. It was ar-
gued [11] that such dips are caused by the contact not be-
ing in the ballistic limit. We assume that our contact are in
the diffusive regime [8].
A diffusive regime of electron current flow through a
PC corresponds to significant elastic scattering of electrons
in the PC area, with the inelastic electron scattering length
lin still exceeding the size of the contact d, i.e. d/lin << 1.
As is known [8], in the conventional case the contribution
to the current through a constriction (-c-) between a super-
conductor (S) and a normal (N) metal (S-c-N contact) can
be expressed, at eV >> Δ, as a sum of four terms:
( ) ( )1 0 1
exc exc
( )( ) / ( ) ( )N NI V V R I eV I I eV= + + + . (1)
Here RN stands for the PC normal state resistance; (1)
NI is
the negative increment to the current of the order of d/lin as
in the normal state because of EPI, i.e., due to an inelastic
electronic relaxation mechanisms; (0)
excI is the excess cur-
rent [12] constant at eV >> Δ. The term (1)
excI is the energy-
dependent correction to the excess current of the order of
(0)
excI (d/lin), which represents a contribution to the I−V curve
proportional to Δ/eV for bias eV >> Δ. Here elastic scatter-
ing due to a virtual emission and absorption of phonons
causes the above-gap singularities. The elastic term is pro-
1148 Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 10
Unconventional superconductivity of MgB:LSMO nanocomposite
portional to the energy-dependent part of the excess cur-
rent Iexc(eV) and appears because of frequency dependence
of the energy gap function Δ(ε = eV). At T = 0 the (normal-
ized) difference conductance related to the excess current
reads for the S-c-N contact [13–16]:
2
exc
2 2
( )( )
( )
N
dI
R
dV
∆ ε
ε =
ε + ε − ∆ ε
, ε = eV . (2)
Thus, similar to the tunneling spectroscopy, the self-
energy effects can reveal themselves as the peculiarities
already in the first derivatives of the PCs Iexc–V character-
istic at large biases eV >> Δ. Disappearance of peaks at
rising temperature or magnetic field proves that they do not
belong to the inelastic back scattering process, which
should have the same intensity both in superconducting
and in normal states [8]. Unfortunately, we are not able to
destroy the superconductivity by magnetic field or by in-
creasing temperature to distinguish directly elastic and
inelastic electron scattering process contribution into PCs
spectra. Nonetheless, we hope that some features observed
in PC’s dIexc/dV characteristics provide evidence that the
frequency dependence of the composite’s energy gap Δtr(ε)
differs from those for MgB2. Note, that the differential
conductance dIexc/dV characteristics of any point contact
(tunnel, ballistic, diffusive) are roughly similar in the re-
gion of ε = eV, where the contribution of ImΔ(ε) is ne-
gligible (see, e.g., [16]). For MgB2 this region is below
80 meV [5,6]. Just the energy range up to eV ≈ 80 meV,
where, for MgB2, the self-energy structure is determined
by Re Δ(ε), will be under consideration below.
3. Results and discussion
3.1. Supercurrent spin polarization
Let us recall here that, at energies below the supercon-
ducting gap, a charge transport through a N metal being in
contact with a S is possible only due to a specific process
called Andreev reflection (AR) [17]. AR is a two-particle
process in which, in the N metal, an incident electron
above the Fermi energy εF and an electron below εF with
opposite spins are coupled together and transferred across
the interface in the S side forming a Cooper pair in the
condensate. Simultaneously, a reflected hole with opposite
momentum and spin appears in the N metal. The charge
doubling at the interface enhances the subgap conductance
and this phenomenon has indeed been observed in the case
of a perfectly transparent interface. The picture is signifi-
cantly modified when spin comes into play. If the N metal
is a hmF there is full imbalance between spin-up and spin-
down electron populations, which suppresses the AR and
reduces the subgap conductance to zero. Particularly, LCMO
is a hmF. Thus, if a supercurrent in the composite is unpo-
larized [s-wave or a p-wave (S = 1, m = 0) component of
triplet pairing], in PCs of the composite with this hmF
electrode the AR will be suppressed and the subgap con-
ductance will be reduced below the normal-state value.
On the contrary, if at both sides of the contact charge cur-
rent is spin polarized, there is no restriction (because of
spin) on the AR and, as in a conventional case, an excess
current and a doubling of the normal-state conductance
have to be observed.
In Figs. 1 and 2, we demonstrate typical PCs I–V de-
pendences, Fig. 1, and the PC spectra, Fig. 2, of three re-
Fig. 1. (Color online) Current–voltage characteristics of three repre-
sentative PCs La0.65Ca0.35MnO3–composites (3:1); inset: the same
for PC-2.
–100 –50 0 50 100–80
–60
–40
–20
0
20
40
60
80
–6
–3
0
3
6
–100 –50 0 50 100
PC–2
PC-2
PC-3PC-1
V, mV
V, mVI,
m
A
I,
m
A
Fig. 2. (Color online) Normalized conductance GS/GN =
= (dI/dV)S/(dI/dV)N of the PCs shown in Fig. 1 at eV > Δtr. Inset:
the AR spectra of these PCs; arrows point to the conductance
drops corresponding to the superconducting gaps (the curves are
shifted for convenience).
20 30 40 50 60 70 80 90
1.0
1.1
1.2
1.3
1.4
–40 –20 0 20 40
3
6
9
12
15
PC-2
PC-3
PC-1
∆tr
PC-3
PC-2
PC-1
V, mV
V, mV
∆tr ∆tr
∆1( )p
∆ σ2( )
G
G
S
N
/
dI
dV/
, a
rb
. u
ni
ts
Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 10 1149
V.N. Krivoruchko, A.I. D’yachenko, and V.Yu. Tarenkov
presentative contacts between the composite (3:1) and hmF
electrode. As is seen in the figures, while the normal-state
resistivity of the PCs differs by factor up to order, the con-
tacts demonstrate common peculiarities (Fig. 1). Specifi-
cally, at low voltage, an excess current is unambiguously
detected for all contacts. For all prepared contacts, we have
observed almost doubling of the normal-state conductivity.
In addition, at low voltage, dips in the differential conduct-
ance are clearly detected. Note that the PC differential
conductance often shows sharp dips at voltage values larg-
er that the superconducting gap, but as a rule very close to
it. These dips are related to the superconducting properties
of the S electrode since they never show up in N–N junc-
tions, but the BTK theory is unable to reproduce them [6].
The different mechanisms leading to dips emergence are
discussed in literature [11,18]. It has been shown that if dip
is not too large (and a broadening parameter Г introduced
by Dynes et al. [19] is small) its position does not too
much differ from the true energy gap magnitude. Within
this approach, the single-electron energy gaps found are:
Δ1(π) ≈ 1.9–2.3 meV, Δ2(σ) ≈ 6.4–8.9 meV, and Δtr ≈
≈ 19.5–20.3 meV. As already mentioned, two of these
were identified as enhanced gaps originating from MgB2.
The third gap Δtr could not be related to s-wave supercon-
ductor MgB2. The temperature dependence of the Δtr gap
(see Fig. 8 in Ref. 1) does not follow the BCS dependence.
These data are a strong argument in favor of a spin-polar-
ized supercurrent in the MgB:LSMO composite. (A more
detailed discussion one can find in Ref. 1.)
We also measured PCs characteristics between non-
magnetic In, Ag, and Nb tips and the composite (3:1). Fi-
gure 3 shows representative dynamic conductance spectra,
dI/dV = G(V), of such PCs. As in the case of a hmF needle
(LCMO), at low voltage, doubling of the conductance and
dips corresponding to three superconducting gaps with
energies Δ1(π), Δ2(σ), and Δtr are observed, too.
The results shown in Figs. 1–3 are a noteworthy argu-
ment in favor of the mixed-parity superconducting state
(a superposition of both spin-singlet and spin-triplet states)
of the composite. Indeed, in the noncentrosymmetric su-
perconductor both even-parity and odd-parity pairings are
mixed, since no symmetry is available to distinguish be-
tween the two (see, e.g., [4,20]). Taking into account a
nanoscale inhomogeneity of the composite, we suggest that
the wave function of the composite superconducting state
is also a superposition of both spin-singlet and spin-triplet
contributions: Ψ ~ aΨs + bΨtr. The contributions from Ψs
and Ψtr components are independent and, thus, the total
supercurrent through the PC is
2 2 22 tr tr~ s sj a b a bΨ = Ψ + Ψ = ′ Ψ + ′ Ψ .
Generally, the relative weight of singlet and triplet com-
ponents in a pair wave function depends on the ratio of
the pairing interactions decomposed into even- and odd-
pairing channels. In our case, it is reasonable to assume
that relative weight of singlet and triplet components is
determined by a ration of the composite’s constituents. I.e.,
the s-wave component is due to a pairing in MgB2 while
the p-wave counterpart originated from an incoherent con-
densate in LSMO.
3.2. BW phase
Here we get in touch with a necessity to identify the p-
wave state. This question will be discussed in details else-
where. In short, our analysis has shown that in the case
of a given composite, most probably, we deal with the so-
called Balian–Werthamer (BW) state [21]. The BW super-
conducting state consists of an equal superposition of pairs
with spin S (|S| = 1) antiparallel to orbital momentum L.
A pair total angular momentum, which is a true quantum
number for a noncentrosymmetric superconductor, has no
favored direction J = S + L = 0. The gap function in
the BW state has a constant product † 2
0 .∆∆ = ∆ In this
phase the quasiparticles density of state (DOS) has the same
form as that of the ordinary s-wave superconductor and
the equilibrium thermodynamic properties of the BW state
and the s-wave superconductor are identical [4].
To test our conclusion, a fitting of the total composite
conductivity was done using different p-wave state symmet-
ry. We used in our model calculations Z = 0.1 for the effec-
Fig. 3. Dynamic conductance spectra of the PCs between non-
magnetic In, Ag, and Nb tips and the composite (3:1). Arrows
point to the conductance drops corresponding to the supercon-
ducting gaps Δ1(π), Δ2(σ) and Δtr, and the specific features ob-
served in the PCs spectra of the MgB:LSMO composite due to
magnetoelastic interaction (ph-mg) in LSMO (the curves are
shifted for convenience).
0 10 20 30 40 50
0.08
0.09
0.10
0.11
0.12
ph-mg
ph-mgph-mg
In–(3:1)
Ag (3:1)–
Nb (3:1)–
∆ σ2( )
∆tr
dI
dV
,
/
S
V, meV
∆ π1( )
1150 Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 10
Unconventional superconductivity of MgB:LSMO nanocomposite
tive barrier parameter and ΔMgB = 3.5 meV for MgB2 (this
“average” value of a superconducting gap is typical for
polycrystalline samples of MgB2 [5]). The best adjustment
was obtained if the energy gap of LSMO is equal to Δtr =
= 18 meV for the BW phase. An example of such fitting is
shown in Fig. 4. One can see that the case of the order pa-
rameter angular dependence as for the BW phase fits
the experimental curve very well. To avoid confusion with
the data shown in Fig. 4, note that both components jtr and
js exist at eV < ΔMgB, and only jtr ~ |Ψtr|
2 part remains at
ΔMgB < eV < Δtr. By another words, supercurrent through
a contact we can decomposed into two parts: fully unpola-
rized Iun and fully polarized Ipol. Fully polarized part exists
at |eV| < Δtr, while unpolarized only at |eV| < ΔMgB. That is
why in the figure GS/GN ≈ 3 at eV < ΔMgB. Note, in this
connection, that a several-fold relative enhancement in the
zero-bias conductance compared to its high-bias value is
typically observed if a contact is made between a good
normal metal and a superconductor with very large normal
state resistivity [11]. For example, a fivefold enhancement
is detected in a contacts made between an Y2PdGe3 poly-
crystalline superconductor and a Pt–Ir tip [11]. It is ex-
pected, that this enhancement arise from the critical current
alone. Yet, a detailed satisfactory understanding of the ori-
gin of this several-fold relative enhancement in the zero-
bias conductance is still lacking.
As already mentioned, due to the AR of quasiparticles
at the N/S interface, the excess current appears in N-c-S
contacts at eV > Δ. Its magnitude is proportional to the su-
perconducting energy gap [12]. In a general case, an ob-
served magnitude of the excess current is Iexc ≈ qΔ/eRN,
where the coefficient q depends on the symmetry of the or-
der parameter and the quality of the constriction. Using
this expression, it is easy to analyze the experimental data
shown in Fig. 1. We choose in our model calculation that
the pairing gap is equal to Δ₀ = 18 meV. Then, for PC-1
with Iexc ≈ 12.6 mA and RN ≈ 1.58 Ω we found q ≈ 1.1; for
PC-2 with Iexc ≈ 1.39 mA and RN ≈ 13.1 Ω we obtained q ≈
≈ 1.01; and for PC-3 with Iexc ≈ 11.5 mA and RN ≈ 1.74 Ω
we received q ≈ 1.14. On the other hand, using the expres-
sions of Ref. 22, one can calculate Iexc for a hmF/p-wave S
junction. For the BW phase we obtained: Iexc = 1.22Δ₀/eRN,
with Δ₀ = 18 meV, in reasonable agreement with the ex-
perimental results.
We also performed similar analysis for p-wave phases
with other topology of order parameter; in particular, when
the gap function has nodes on the Fermi surface. It was
found that the order parameter with nodes could not fit
the experimental results reasonably well. Thus, we think
the p-wave superconducting state with nodeless order pa-
rameter is realized in the MgB:LSMO nanocomposite at
T < 30 K.
3.3. Quasiparticles self-energy effects
The attractive features of PC spectroscopy is that the
second derivatives of the I–V characteristic at large biases
not only qualitatively but also semiquantitatively corre-
spond to the self-energy effects in the superconducting
order parameter [8]. These self-energy effects can be used
in standard programs [23] to solve the Eliashberg equa-
tions [24] for quantitative derivation of electron–boson-
interaction spectral function.
In the case of MgB:LSMO nanocomposite, it is obvious
that the system contains several (no less than three) weakly
connected charge carrier groups with quite different pro-
perties. Indeed, even for a separate MgB2, one has to con-
sider at least two types of charge carriers. One of those
(σ-band) is two-dimensional with a strong EPI, while the
other one (π-band) is three-dimensional with a weak EPI
but with larger density of state at the Fermi energy. The in-
ter-band scattering is weak and MgB2 behaves as a s-wave
superconductor with two distinct energy gaps (σ and π
gaps) [5,6]. As for LSMO constituent, in the framework of
the conventional double exchange model (see, e.g., [25]),
there is complete splitting of majority and minority spin
bands by large Hund’s energy (~ 1 eV). At low tempera-
ture, spin of itinerant electrons of ferromagnetic manga-
nites is completely polarized and the system is in a half-
metallic state. Thus, if superconductivity can exist at all in
this compound, it would most likely be of the p-wave triplet
type with parallel spin pairs. Accordingly, a multiband mo-
del comprised of a superposition of pairs with a spin-triplet
p-wave and spin-singlet s-wave components has to be ap-
plied in the case of MgB:LSMO system in a superconduct-
ing phase.
Fig. 4. (Color online) The PC experimental conductance and
the fitting with the nodeless p-wave order parameter. (For the
value of the parameters used, see the text.)
–100 –50 0 50 100
1.0
1.5
2.0
2.5
3.0
T = 4.2 K
V , meV
exp
calc
∆composite = 18 meV
∆MgB2 = 3.5 meV
(
/
)/
dI
dV
G
N
Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 10 1151
V.N. Krivoruchko, A.I. D’yachenko, and V.Yu. Tarenkov
However, direct application of the Eliashberg equations
in the case of a multiband superconductor is mathematical-
ly an ill-defined problem: it is not possible to obtain sever-
al band EPI functions α²Fij(Ω) from a single I(V) experi-
mental dependence. (Here α = α(Ω) describes the strength
of the electron interaction with a given phonon branch for
electron transport through the contact and Fij(Ω) stands for
the phonon DOS.)
Since the nature of the pairing interaction in half-me-
tallic manganite is unknown, we chose the following strat-
egy to shed light on the question addressed. The phonon
spectrum and the electron–phonon coupling in MgB2 are
well known at present (see Refs. 5, 16, 26–28). Using these
data, we first calculate the dI/dV–V characteristics of a PC
for the π- and σ-bands of MgB2. Comparing (extracting)
the contribution of the MgB2 phonons with (from) the ex-
perimental dI/dV–V data for the composite, we will be
able, at least in principle, to reveal the dI/dV–V nonlineari-
ties which are due to a superconducting state of the LSMO
constituent, if they are, and then to analyze them. With this
in mind, let us calculate the contribution from MgB2.
3.3.1. Contribution from the MgB2 phonons. According
to the conventional labeling [5], superconducting proper-
ties of MgB2 can be described by an effective two (σ- and
π-) bands model. Following the approach proposed by
Brinkman et al. [27], the total current through a tunnel
MgB2–N structure is a sum of the components and, hence,
the total normalized conductance can be written as a weight-
ed sum of the contributions of the σ- and π-bands, where
the weighting factors are determined by the plasma fre-
quencies along the corresponding crystallographic direc-
tions. Thus, the normalized tunnel contact conductance is
given by
( ) ( ),( )G A G A Gγ σ π
γ σ γ πω = ω + ω eVω = (3)
with γ = ab or c for a current flowing in the ab plane or in
the c direction, respectively. Within the approximation of
a δ-function barrier, the Gσ(ω) and Gπ(ω) are the partial
superconducting densities of states, respectively (for nume-
rical values of the weighting parameters see Table 1 in
Ref. 27). The contribution of the π-band is always domi-
nant even if tunneling is almost in the ab plane.
Within the two-band model, for the conductance of
a metallic MgB2–N PC, one can obtain the expressions
similar to Eqs. (3). However, now the partial conductance
for σ- and π-bands, Gσ(ω) and Gπ(ω) should be calculated
within the framework of the generalized BTK model as
discussed in Refs. 6, 27. The related normalized function
can be expressed as Eq. (2), however, with a given band’s
label Δj(ε), j = π or σ. The numerical values of the
weighting parameters, strictly spiking, changed, too.
It is well known, in the Eliashberg approach, even in
the weak-coupling regime a superconducting order param-
eter Δ(ω) is a (complex) function of energy with an ener-
gy-dependent real and imaginary parts. Thus Δj(ω) =
= Re Δj(ω) + I Im Δj(ω) for a current in c (j = π) or ab (j = σ)
directions. We calculated the gap functions Δj(ω) with an ex-
tension of the Eliashberg formalizm to a two bands super-
conductor (see, e.g., Ref. 27). These equations have been
solved numerically using the EPI functions found recently
in Refs. 27, 28 from the first principles calculations.
With the numerical data in hands for a MgB2–N con-
tact, we are able to reveal directly the self-effects due to
the MgB2 phonons in the experimental dI/dV–V data for
the MgB:LSMO composite. As follows from the data (not
shown here), at energies above the largest gap Δtr the con-
tribution of the MgB2 phonons into the total conductance
of the MgB:LSMO PCs is negligibly small. In fact, one
may expect this result because, as is seen from Eq. (2), at
ω >> Δσ the energy-dependent effects are of the order
(Δσ/ω)2. As far as the magnitude of the gap Δtr is about
three times larger than Δσ, at ω >> Δtr the contributions
related to MgB2 are weakened by an order.
3.3.2. Magnon–phonon self-energy effects. In diffusive
S-c-N contacts the self-energy effects might appear already
in the first derivative of their I–V characteristics (see, e.g.,
[15] and §12.1 in Ref. 8). Using the data obtained we at-
tempt to identify the structure of the composite’s PC spec-
tra at energies typical for phonons and magnons. Yet, this
is not so easy task.
The phonon spectra of ABO3 perovskite structure usual-
ly are separated into “external”, “bending” and “stretching”
modes with respect to cubic (Pm3m) symmetry [29,30].
The “external” mode represents a vibrating motion of the
A ion against the BO3 octahedra, and two “internal” modes
reflect internal motions of B and O ions in the octahedra
(“bending” and “stretching” modes, respectively). Depend-
ing on the ion size and the doping concentration, these trip-
ly degenerate modes split into pairs of nondegenerate and
doubly degenerate modes; moreover, they become broader
and overlap [30–34]. Furthermore, due to large unit cell,
additional modes emerge in the metallic phase of doped
manganites. The phonon structures of the doped sample are
broader and do not allow identifying strictly all the observ-
ed lines. Also the peak positions of phonons measured in
a powder system can be shifted with respect to the real
position in crystals [34,35].
In addition, there is much experimental and theoretical
evidence in favor of the fundamental role of magnetoelas-
tic coupling in physics of substituted manganite [25,36].
Strong magnon–phonon interaction is confirmed, in partic-
ular, by inelastic neutron scattering measurements, which
point that magnetoelastic coupling is important for under-
standing of the low-temperature lattice and spin dynamics
in ferromagnetic manganite. From the wave-vector depen-
dence of the magnon lifetime and its association with
the dispersions of selected optical phonon modes, it was
argued that the observed magnon softening and broadening
are due to strong magnon–phonon interactions [31–33].
1152 Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 10
Unconventional superconductivity of MgB:LSMO nanocomposite
In our case, the energy range where it is reasonable
to expect “magnon traces” in I–V characteristic is at
eV ~ [Δtr+Δ2(σ)] or at eV ~ [Δtr+Δ1(π)]. Indeed, for the
system under consideration, a crucial condition is the pro-
cess of conversion of the spinless (spin-singlet) Cooper
pair into spin-polarized (spin-triplet) Cooper pair and vice
versa (some kind of an “intrinsic proximity” effect; for more
detailed discussion see, e.g., reviews [37,38]). During this
conversion, spin waves are emitted or absorbed.
Comparing typical PCs spectra nonlinearities (Figs. 2
and 3) with the phonon and magnon DOS restored in neu-
tron measurements [29–33], we found a definite correla-
tion between nonlinearities in the PCs spectra and these
data. We think that specific peculiarities in the PC spectra
at 20.9–30.2 meV, 38.2–38.6 meV, and 44.5–45.7 meV
in Fig. 3 are due, most probably, to interaction of electrons
with magnetoelastic waves. As for the electron–boson traces
in PCs of composite with hmF LCMO, Fig. 2, here the num-
ber of distinctive peculiarities is significantly larger, and
they are difficult to be identified strictly. Further detail-
ed investigations are definitely needed to be sure that
the distinctive features observed in the PCs spectra of
the MgB:LSMO composite are due to electron–phonon or
electron–magnon interactions in LSMO.
4. Summary
In this report, we addressed a pairing symmetry and
a plausible pairing mechanism of a superconducting state
that realizes in the MgB2:La0.65Sr0.35MnO3 nanocompo-
site. Taking into account that a superconducting phase de-
velops in a low-symmetry environment with a missing
inversion center, we considered a model of a ferromagnetic
superconductor described by uniformly coexisting itinerant
ferromagnetism and a mixed-parity superconducting state.
In this state the order parameter, most probably, possesses
a nodeless topology and the single-electron DOS has the
same form as that of the ordinary s-wave superconductor.
Utilizing the extended Eliashberg formalizm, we calculated
the contribution of MgB2 in the total composite conducti-
vity and estimated a magnitude of the electron–phonon sing-
ularities originated from the MgB2 in the I–V characteris-
tics of the composite. It was found that distinctive features
observed in the PC spectra of the MgB:LSMO composite
can not be related to the phonons of MgB2. The singular-
ities observed in the I–V characteristics at above-gap ener-
gies may be a manifestation of the electron spectrum renorm-
alizations due to strong magnon–phonon (magnetoelastic)
interaction in La0.65Sr0.35MnO3. Yet, the conventional
point-contact spectroscopy investigations of the second
derivatives of the PC’s I–V characteristics at large biases
are definitely needed to identify the electron–phonon (elec-
tron–magnon) self-energy structure in a superconducting
state of the nanocomposite. The results propose a new
route to unconventional superconductivity and, we hope,
can motivate the search for new material for superconduct-
ing spintronics.
The authors thanks to M. Belogolovskii, A. Omelyan-
chouk, and Yu. Naidyuk for useful discussions.
1. V.N. Krivoruchko and V.Yu. Tarenkov, Phys. Rev. B 86,
10502 (2012).
2. V.N. Krivoruchko and V.Yu. Tarenkov, Phys. Rev. B 75,
214508 (2007).
3. V.N. Krivoruchko and V.Yu. Tarenkov, Phys. Rev. B 78,
054522 (2008).
4. V.P. Mineev and K.V. Samokhin, Introduction to Unconven-
tional Superconductivity, Gordon and Breach, New York
(1999).
5. X.X. Xi, Rep. Prog. Phys. 71, 116501 (2008).
6. D. Daghero and R.S. Gonnelli, Supercond. Sci. Technol. 23,
043001 (2010).
7. D. Fay and J. Appel, Phys. Rev. B 22, 3173 (1980).
8. Y.G. Naidyuk and I.K. Yanson, Point-Contact Spectroscopy,
Springer Series in Solid State Science, v. 145, New York:
Springer (2005).
9. M.M. Savosta, V.N. Krivoruchko, I.A. Danilenko, V.Yu. Ta-
renkov, T.E. Konstantinova, A.V. Borodin, and V.N. Varyu-
khin, Phys. Rev. B 69, 024413 (2004).
10. A.S. Mazur, V.N. Krivoruchko, and I.A. Danilenko, Fiz. Nizk.
Temp. 33, 1222 (2007) [Low Temp. Phys. 33, 931 (2007)].
11. G. Sheet, S. Mukhopadhyay, and P. Raychaudhuri, Phys.
Rev. B 69, 134507 (2004).
12. A.V. Zaitsev, Zh. Eksp. Teor. Fiz. 78, 221 (1980).
13. V.A. Khlus and A.N. Omelyanchuk, Fiz. Nizk. Temp. 9, 373
(1983) [Sov. J. Low Temp. Phys. 9, 189 (1983)].
14. V.A. Khlus, Fiz. Nizk. Temp. 9, 985 (1983) [Sov. J. Low
Temp. Phys. 9, 510 (1983)].
15. A.N. Omelyanchuk, S.I. Beloborod'ko, and I.O. Kulik, Fiz.
Nizk. Temp. 14, 1142 (1988) [Sov. J. Low Temp. Phys. 14,
630 (1988)].
16. I.K. Yanson, S.I. Beloborod’ko, Yu.G. Naidyuk, O.V. Dol-
gov, and A.A. Golubov, Phys. Rev. B 69, 100501(R) (2004).
17. A.F. Andreev, Sov. Phys. JETP 19, 1228 (1964).
18. G.J. Strijkers, Y. Ji, F.Y. Yang, C.L. Chien, and J.M. Byers,
Phys. Rev. B 63, 104510 (2001).
19. R.C. Dynes, V. Narayanamuri, and J.P. Garno, Phys. Rev.
Lett. 41, 1509 (1978).
20. L. Gor’kov and E. Rashba, Phys. Rev. Lett. 87, 037004
(2001).
21. R. Balian and N.R. Werthamer, Phys. Rev. 131, 1553 (1963).
22. S. Kashiwaya, Y. Tanaka, M. Koyanagi, and K. Kajimura,
Phys. Rev. B 53, 2667 (1996).
23. A.I. D’yachenko, cond-mat/0309479 (2003).
24. E.L. Wolf, Principles of Electron Tunneling Spectroscopy,
Oxford University Press, London (1985).
25. E. Dagotto, T. Hotta, and A. Moreo, Phys. Rep. 344, 1 (2001).
26. I.K. Yanson, V.V. Fisun, N.L. Bobrov, Yu.G. Naidyuk, W.N.
Kang, Eun-Mi Choi, Hyun-Jung Kim, and Sung-Ik Lee,
Phys. Rev. B 67, 024517 (2003).
Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 10 1153
V.N. Krivoruchko, A.I. D’yachenko, and V.Yu. Tarenkov
27. A. Brinkman, A.A. Golubov, H. Rogalla, O.V. Dolgov, J. Kor-
tus, Y. Kong, O. Jepsen, and O. K. Andersen, Phys. Rev. B
65, 180517(R) (2002).
28. O. De la Peña-Seaman, R. de Coss, R. Heid, and K.-P. Boh-
nen, Phys. Rev. B 82, 224508 (2010).
29. A.V. Boris, N.N. Kovaleva, A.V. Bazhenov, P.J.M. van Ben-
tum, Th. Rasing, S.-W. Cheong, A.V. Samoilov, and N.-C. Yeh,
Phys. Rev. B 59, R697 (1999).
30. A. Paolone, P. Roy, A. Pimenov, A. Loidl, O.K. Melnikov,
and A.Y. Shapiro, Phys. Rev. B 61, 11255 (2000).
31. M. Hennion, F. Moussa, P. Lehouelleur, F. Wang, A. Ivanov,
Y.M. Mukovskii, and D. Shulyatev, Phys. Rev. Lett. 94,
057006 (2005).
32. P. Dai, H.Y. Hwang, J. Zhang, J.A. Fernandez-Baca, S.-W.
Cheong, C. Kloc, Y. Tomoika, and Y. Tokura, Phys. Rev. B
61, 9553 (2000).
33. S. Petit, M. Hennion, F. Moussa, D. Lamago, A. Ivanov,
Y.M. Mukovskii, and D. Shulyatev, Phys. Rev. Lett. 102,
207201 (2009).
34. K.H. Kim, J.Y. Gu, H.S. Choi, G.W. Park, and T.W. Noh,
Phys. Rev. Lett. 77, 1877 (1996).
35. I. Fedorov, J. Lorenzana, P. Dore, G. De Marzi, P. Maselli,
P. Calvani, S.-W. Cheong, S. Koval, and R. Migoni, Phys.
Rev. B 60, 11875 (1999).
36. J. Zhang, F. Ye, H. Sha, P. Dai, J.A. Fernandez-Baca, and
E.W. Plummer, J. Phys.: Condens. Matter 19, 315204 (2007).
37. M. Eschrig, T. Löfwander, T. Champel, J.C. Cuevas, J. Kopu,
and G. Schön, J. Low Temp. Phys. 147, 457 (2007).
38. V.N. Krivoruchko, A.I. D'yachenko, and V.Yu. Tarenkov, Fiz.
Nizk. Temp. 39, 276 (2013) [Low Temp. Phys. 39, 211 (2013)].
1154 Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 10
1. Introduction
2. Specifics of experiment
3. Results and discussion
3.1. Supercurrent spin polarization
3.2. BW phase
3.3. Quasiparticles self-energy effects
4. Summary
|