Tracing the evolution of the two energy gaps in magnesium diboride under pressure
We have studied transport characteristics of mesoscopic multiple-mode superconducting contacts formed between two grains in bulk two-gap magnesium diboride. The experimental setup was realized by driving a normal-metal tip into MgB₂ polycrystalline sample and proved to be extremely stable, providing...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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irk-123456789-1220582017-06-27T03:02:54Z Tracing the evolution of the two energy gaps in magnesium diboride under pressure Kononenko, V. Tarenkov, V. Belogolovskii, M. Döring, S. Schmidt, S. Seidel, P. Сверхпроводимость, в том числе высокотемпературная We have studied transport characteristics of mesoscopic multiple-mode superconducting contacts formed between two grains in bulk two-gap magnesium diboride. The experimental setup was realized by driving a normal-metal tip into MgB₂ polycrystalline sample and proved to be extremely stable, providing possibility to perform pressure experiments at low temperatures. It is argued that in our procedure a small piece of the superconducting electrode is captured by the tip apex and, as a result, two junctions in series are formed: a junction between a tip and MgB₂ grain and a mesoscopic disordered contact between two superconducting pellets. Although the relative weight of the first junction resistance was considerably less, its contribution is shown to be important for the comparison of measured data with expected gap values. Two hallmarks of multiple Andreev reflections inside the MgB₂–c–MgB₂ contact (c stands for a high-transparent constriction), a zero-bias 1/√|V|-like singularity of the dc differential conductance and peaks connected to the two gap values, have been revealed. Finally, we report results of a hydrostatic compression experiment showing the evolution of the MgB₂ gap values with pressure. In contrast to the theoretical expectations, we have observed an increase of the smaller gap ∆π whereas the larger gap ∆σ decreased with increasing pressure as it should be for the electron–phonon pairing mechanism. We argue that the so-called separable model of anisotropy effects is insufficient to describe such changes and only improved two-band versions are capable to reproduce the pressure effect on the energy gaps in magnesium diboride. 2015 Article Tracing the evolution of the two energy gaps in magnesium diboride under pressure / V. Kononenko, V. Tarenkov, M. Belogolovskii, S. Döring, S. Schmidt, P. Seidel // Физика низких температур. — 2015. — Т. 41, № 4. — С. 343-349. — Бібліогр.: 27 назв. — англ. 0132-6414 PACS: 74.70.Ad, 81.07.Lk, 74.62.Fj http://dspace.nbuv.gov.ua/handle/123456789/122058 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Сверхпроводимость, в том числе высокотемпературная Сверхпроводимость, в том числе высокотемпературная |
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Сверхпроводимость, в том числе высокотемпературная Сверхпроводимость, в том числе высокотемпературная Kononenko, V. Tarenkov, V. Belogolovskii, M. Döring, S. Schmidt, S. Seidel, P. Tracing the evolution of the two energy gaps in magnesium diboride under pressure Физика низких температур |
| description |
We have studied transport characteristics of mesoscopic multiple-mode superconducting contacts formed between two grains in bulk two-gap magnesium diboride. The experimental setup was realized by driving a normal-metal tip into MgB₂ polycrystalline sample and proved to be extremely stable, providing possibility to perform pressure experiments at low temperatures. It is argued that in our procedure a small piece of the superconducting electrode is captured by the tip apex and, as a result, two junctions in series are formed: a junction between a tip and MgB₂ grain and a mesoscopic disordered contact between two superconducting pellets. Although the relative weight of the first junction resistance was considerably less, its contribution is shown to be important for the comparison of measured data with expected gap values. Two hallmarks of multiple Andreev reflections inside the MgB₂–c–MgB₂ contact (c stands for a high-transparent constriction), a zero-bias 1/√|V|-like singularity of the dc differential conductance and peaks connected to the two gap values, have been revealed. Finally, we report results of a hydrostatic compression experiment showing the evolution of the MgB₂ gap values with pressure. In contrast to the theoretical expectations, we have observed an increase of the smaller gap ∆π whereas the larger gap ∆σ decreased with increasing pressure as it should be for the electron–phonon pairing mechanism. We argue that the so-called separable model of anisotropy effects is insufficient to describe such changes and only improved two-band versions are capable to reproduce the pressure effect on the energy gaps in magnesium diboride. |
| format |
Article |
| author |
Kononenko, V. Tarenkov, V. Belogolovskii, M. Döring, S. Schmidt, S. Seidel, P. |
| author_facet |
Kononenko, V. Tarenkov, V. Belogolovskii, M. Döring, S. Schmidt, S. Seidel, P. |
| author_sort |
Kononenko, V. |
| title |
Tracing the evolution of the two energy gaps in magnesium diboride under pressure |
| title_short |
Tracing the evolution of the two energy gaps in magnesium diboride under pressure |
| title_full |
Tracing the evolution of the two energy gaps in magnesium diboride under pressure |
| title_fullStr |
Tracing the evolution of the two energy gaps in magnesium diboride under pressure |
| title_full_unstemmed |
Tracing the evolution of the two energy gaps in magnesium diboride under pressure |
| title_sort |
tracing the evolution of the two energy gaps in magnesium diboride under pressure |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2015 |
| topic_facet |
Сверхпроводимость, в том числе высокотемпературная |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/122058 |
| citation_txt |
Tracing the evolution of the two energy gaps in magnesium diboride under pressure / V. Kononenko, V. Tarenkov, M. Belogolovskii, S. Döring, S. Schmidt, P. Seidel // Физика низких температур. — 2015. — Т. 41, № 4. — С. 343-349. — Бібліогр.: 27 назв. — англ. |
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Физика низких температур |
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Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 4, pp. 343–349
Tracing the evolution of the two energy gaps
in magnesium diboride under pressure
V. Kononenko1, V. Tarenkov1, M. Belogolovskii1,2, S. Döring3,
S. Schmidt3, and P. Seidel3
1A. Galkin Donetsk Institute for Physics and Engineering, NASU, Kyiv UA-03680, Ukraine
E-mail: bel@fti.dn.ua
2G.V. Kurdyumov Institute for Metal Physics, Kyiv UA-03680, Ukraine
E-mail: belogolovskii@ukr.net
3Institut für Festkörperphysik, Friedrich-Schiller-Universität Jena, Jena D-07743, Germany
E-mail: Paul.Seidel@uni-jena.de
Received November 17, 2014, revised December 18, 2014,
published online February 23, 2015
We have studied transport characteristics of mesoscopic multiple-mode superconducting contacts formed be-
tween two grains in bulk two-gap magnesium diboride. The experimental setup was realized by driving a nor-
mal-metal tip into MgB2 polycrystalline sample and proved to be extremely stable, providing possibility to per-
form pressure experiments at low temperatures. It is argued that in our procedure a small piece of the
superconducting electrode is captured by the tip apex and, as a result, two junctions in series are formed: a junc-
tion between a tip and MgB2 grain and a mesoscopic disordered contact between two superconducting pellets.
Although the relative weight of the first junction resistance was considerably less, its contribution is shown to be
important for the comparison of measured data with expected gap values. Two hallmarks of multiple Andreev re-
flections inside the MgB2–c–MgB2 contact (c stands for a high-transparent constriction), a zero-bias 1 / V -like
singularity of the dc differential conductance and peaks connected to the two gap values, have been revealed. Fi-
nally, we report results of a hydrostatic compression experiment showing the evolution of the MgB2 gap values
with pressure. In contrast to the theoretical expectations, we have observed an increase of the smaller gap ∆π
whereas the larger gap ∆σ decreased with increasing pressure as it should be for the electron–phonon pairing
mechanism. We argue that the so-called separable model of anisotropy effects is insufficient to describe such
changes and only improved two-band versions are capable to reproduce the pressure effect on the energy gaps in
magnesium diboride.
PACS: 74.70.Ad Metals; alloys and binary compounds (including A15, MgB2, etc.);
81.07.Lk Nanocontacts;
74.62.Fj Effects of pressure.
Keywords: magnesium diboride, two-band/two-gap superconductor, high-transparency junctions, differential
conductance, hydrostatic pressure.
1. Introduction
Conventional BCS theory of phonon-mediated super-
conductivity considers a single-valued order parameter
∆ = const in the studied materials. In general, it is not cons-
tant but a momentum- and frequency-dependent function
( , )∆ ωk which can be determined using fully anisotropic
Eliashberg equations with the electron–phonon interaction
characteristic ( , , )′λ ωk k [1]. In some superconductors such
as magnesium diboride, experimental studies of the super-
conducting state reveal the presence of two separate gaps.
Usually, their appearance is associated with the presence of
two very different sheets of the Fermi surface with consid-
erably weak interaction between them [2]. In the simplest
version of the two-band model, each band is determined by
an independent set of parameters, including constant val-
ues of the coupling strength iλ (i = 1, 2) and those of the
Fermi velocity ,F iv (i = 1, 2). Besides, the two-band ap-
proach provides two additional parameters ijλ (i j≠ ),
interband coupling strengths, which are independent on
© V. Kononenko, V. Tarenkov, M. Belogolovskii, S. Döring, S. Schmidt, and P. Seidel, 2015
mailto:bel@fti.dn.ua
V. Kononenko, V. Tarenkov, M. Belogolovskii, S. Döring, S. Schmidt, and P. Seidel
the iλ values and can be varied freely within the model. It is
clear that the solely intraband pairing picture is not suffi-
cient to describe the main characteristics of two-band super-
conductors with a single critical temperature Tc. To repro-
duce some of the experimental features like the ratio of large
gap/small gap, it is necessary to consider both intraband
and interband pairing channels on an equal footing [3].
As was emphasized in the recent review [4], an alterna-
tive approach based on the account of anisotropy effects,
the so-called separable model, can be proposed and the dis-
crimination of the two approaches is very difficult in most
cases. Whereas in the two-band picture two distinct gaps
arise from the presence of two well-discriminated Fermi
bands, in the separable one it refers to the variation within
one band. The simplest way for introducing the anisotropy
into a single-band electron–phonon interaction characteris-
tic is to assume that ( , , ) (1 ) ( )(1 )a a ′′λ ω = + λ ω +k kk k with
( )λ ω being the Fermi surface average of ( , , )′λ ωk k [5]. An
important difference between the models resides in the fact
that in the latter case we have the only main parameter
( )λ ω that defines the average values of two narrow gap
sets (they may be roughly interpreted as two different gaps),
as the large gap/small gap ratio. On the contrary, for
the two-band model, we should discriminate between intra-
band and interband impurity scattering rates. Thus, the in-
terpretation of corresponding experimental data should be
carried out with caution in order to separate one approach
from the other [4].
This task is rather complicated, in particular, for such
spatially directed techniques like tunneling or point-contact
since the total quasiparticle current in related heterostruc-
tures is a sum of partial contributions from electronic groups
with different gap values i∆ (i = 1, 2). The weighing factor
is proportional to the corresponding squared plasma fre-
quency 2
,p iω [6] and the relative contribution of the elec-
tronic groups to the spectra of a two-gap superconductor
can be strongly anisotropic in the case of an anisotropic
Fermi surface. If so, an additional feature related to one of
two gaps can be undetectable for certain transport direc-
tions. But even if the two gap features are observed in the
point-contact or tunneling experiments it cannot be a deci-
sive measurement for the two-band interpretation since the
anisotropic single-band scenario cannot be completely ex-
cluded in this case [4]. The best way to understand whether
it is sufficient to describe a two-gap superconductor with a
single electron–phonon interaction characteristic ( )λ ω (the
separable model) or the interband coupling parameter be-
ing independent on the intraband ones (the two-band ap-
proach) would be measurements of the effect of a control-
lable external parameter on the energy-gap structure in
a superconductor.
In this work we show that hydrostatic high-pressure ex-
periments on magnesium diboride polycrystalline samples
provide additional opportunities to do more quantitative and
reliable study of the role of the interband coupling and new
arguments in support of the two-band model. In the next
section, we describe the studied MgB2 specimens, a pres-
sure chamber, and a procedure to create superconductor
(S)–constriction (c)–superconductor junction by pressing a
normal-metal (N) tip into a magnesium diboride micro-
crystal. In the third section, we analyze current–vs–voltage
and differential conductance–vs–voltage characteristics of
the S–c–S junctions at zero pressure. The fourth section
presents the data obtained in high-pressure measurements
that demonstrate the evolution of those two gaps in MgB2
with pressure. To our best knowledge, these are the first
experiments on the pressure effect on the gap structure in
MgB2. The main results of the work are summarized in the
last section.
2. Experimental
An initial MgB2 powder was synthesized during six
hours by high-temperature reaction between boron and
magnesium powders taken in stoichiometric ratio and grind-
ed properly. The sintering temperature was ≤ 800 °C and
the residual pressure was ~ 10–2 Pa. The polycrystalline
samples used in the present work were obtained by uniaxial
compression of the MgB2 powder. Annealed copper wires
were stacked on a polished carbide anvil parallel to one
other. The distance between the wires and their thickness
controlled spatial dimensions and geometry of the probed
area. Next, the MgB2 powder was poured between the
wires and covered by the upper anvil. Both anvils were
pressed against each other resulting in 6–7 GPa of pres-
sure. Under the pressure, the MgB2 powder was compacted
into mechanically durable bars with typical dimensions
about 10×1.0×0.1 mm.
The current–vs–voltage I–V characteristics and the dif-
ferential conductance G(V) = dI(V)/dV-versus-V spectra
were measured with a standard four-probe method and
a lock-in technique by superposing a small ac-modulation
of 10 µV on a slowly varying voltage bias V applied to the
sample. The dynamic conductance was determined through
numerical differentiation as well. Both results were com-
pared with each other.
Contact pads with resistances about 10–3 Ω were made
of a fine silver powder adding to corresponding MgB2 are-
as before the compression procedure. With decreasing tem-
perature, at 39cT T= ≈ K, the well-established critical
temperature value of the bulk magnesium diboride, resis-
tance of the specimens started to fall sharply but the transi-
tion to the entirely superconducting state always took place
at least a few degrees below the onset temperature (see the
main panel in Fig. 1). All measurements were performed
well below 30 K when the entire volume of the material
was in the superconducting state.
We believe that the comparatively wide resistive tran-
sitions of the MgB2 bars with the width of several K ori-
ginate from their granular nature. It is well known that
344 Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 4
Tracing the evolution of the two energy gaps in magnesium diboride under pressure
granular metal composites are characterized by two distinct
electronic transport regimes, percolation and tunneling ones,
depending on the relative amount of the metallic phase and
the nature of the grain interspace [7]. At sufficiently large
volume fraction of the metallic phase, such samples behave
as percolating systems with a well-defined critical concen-
tration above which macroscopic clusters of physically
connected conductive particles span the entire sample. This
“metallic regime” is characterized by the resistivity in-
creasing linearly with the temperature which is the case
at T > 80 K (see the left inset in Fig. 1). Essentially gra-
nular nature of our MgB2 samples with well connected
grains was confirmed by the scanning electron microscope
JSM-6490LV analysis (see the right inset in Fig. 1). We
show below that granularity of our MgB2 samples provides
the possibility to create contacts between individual super-
conducting granules.
The experimental setup was prepared by the following
way. A silver tip soldered to a spring made of beryllium
bronze was attached to the end portion of the MgB2 bar
welded to a glass fiber (Fig. 2). The contact resistance was
determined by the spring pressing strength and thus could
be varied in a very wide range. Note that in contrast to a
similar procedure in the paper [8], we have not released the
pressure after pushing the normal-metal tip into MgB2. In
our opinion, it was the reason why we have observed for-
mation of direct high-transparent inter-grain contacts while
the authors [8] registered a typical tunneling behavior in
the most cases.
As was declared in the introduction, the main driving
force behind our experiment was to study the pressure in-
fluence on superconducting gaps in magnesium diboride.
Because of that, we have paid special attention to the me-
chanical stability of the junctions. Upon reaching the opti-
mal values of the contact resistance about several tens of
Ohms the contact area was coated by a layer of the varnish.
After its polymerization, the contact was rigidly fixed and
the junctions demonstrated well reproduced characteristics
after several heating and cooling cycles as well as pressure
ones.
The high-pressure experiments were performed in a pres-
sure chamber with a piston and kerosene oil as pressure-
transmitting medium. 24 conductors were put into the cham-
ber allowing us to place additionally a manganin high-pres-
sure sensor and a platinum-wire thermometer. In the main
panel of Fig. 1 we demonstrate the pressure effect on the
normal-to-superconductor transition in our MgB2 samples.
Decreasing rates of the onset temperature cT (shown by
corresponding arrows) as well as those of the midpoints in
resistance–vs–T dependences were about 1 K/GPa in good
agreement with results by other authors for Tc in MgB2
(see an overview of relevant experimental data in [9,10]).
Thus, the relative change of both characteristics was about
0.03 1/GPa [9]. The normal-state resistance decrease was
of the same order ~ 0.02–0.03 1/GPa.
We note that the same compression-chamber technique
was successfully used by us earlier to study the pressure
effect on the differential resistance characteristics of point
contacts formed by a silver counter-electrode and high-Tc
cuprate ceramics in the superconducting state (see, e.g.,
[11,12]).
3. Conductance spectra at ambient pressure
Totally, at ambient pressure we have measured about
50 point contacts formed by a silver tip with magnesium
diboride bars. All current-voltage I(V) characteristics clearly
exhibited an excess current proving the presence of a high-
Fig. 1. Resistive normal-to-superconductor transition R of the gra-
nular MgB2 sample at ambient pressure (the solid line) and under
the pressure of 1.2 GPa (the dashed line). The left inset demon-
strates the resistance-vs-temperature dependence from T = 4.2 K
to room temperature; the right inset shows a SEM image of
a MgB2 sample.
Fig. 2. Top view of the Ag/MgB2 setup: substrate (1); Ag contact
pads (2); Cu pads (3); MgB2 bar (4); spring (5); silver tip (6).
Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 4 345
V. Kononenko, V. Tarenkov, M. Belogolovskii, S. Döring, S. Schmidt, and P. Seidel
transparent superconducting junction. The overwhelming
majority of the samples demonstrated also two prominent
features in the G(V) spectra: a strong zero-bias maximum
with G(V=0) which usually exceeded more than two times
the normal-state value ( )NG G eV σ≈ >> ∆ as the limit for
SN Andreev reflection transport and two small but well
pronounced peaks at voltages slightly above 3 and 7 meV.
The typical experimental dependence G(V) is shown in
Fig. 3(a), curve 1. Sometimes (only a few samples) we
have observed an additional third peak at approximately
9 meV. The junction with the most prominent feature at
9 meV (see Fig. 3(b), curve 1) was selected for subsequent
pressure experiments.
From the first sight, the studied samples are expected to
be contacts formed by a normal-metal tip, a superconduct-
ing grain, and a constriction c between them. In this well-
developed point-contact technique, the metallic tip is
brought into direct NS-contact which size should be small-
er than the electron mean free path. If a direct contact be-
tween the counter-electrode and a single-band supercon-
ductor is established, for voltages /V e< ∆ , at zero
temperature, only electron-into-hole and inverse scatter-
ings known as Andreev-reflection processes take place,
which double the differential interface conductance ( )G V
with respect to the NG value. Only for /V e> ∆ single
electrons may propagate from the normal part of the con-
tact to the superconducting one. As a result, the interface
conductance drops to its normal value at /V e>> ∆ . When
a finite barrier is present at the interface, we should ob-
serve a reduction of the low-voltage conductance and
a conductance peak at /V e= ∆ .
Our dI/dV–vs–V data do not agree with these expecta-
tions (see Fig. 3). Instead of a step-like behavior around
/V eπ= ∆ and a nearly doubled value for voltage biases
/V eπ< ∆ [15], we have observed, first, a huge zero-bias
conductance peak and, second, a set of nonlinear features
in the energy-gap region. As to the first issue, there can be
several explanations. The simplest one may be related to
a superconducting quenching effect in a narrow micro-
bridge between two metallic electrodes. As was argued in
Ref. 16 and references therein, the quenching mechanisms
can be classified in two classes: (a) electrodynamic flux-
flow vortex effects and (b) heat-driven thermal instabili-
ties. Both of them may be relevant in our experiments.
Ignoring the presence of the zero-bias anomaly, we could
interpret the two peaks in Fig. 3(a) as signatures of the two
gaps π∆ and σ∆ in MgB2 and the third nonlinearity in Fig.
3(b) as that related to the sum π σ∆ + ∆ . But following this
assumption, the value of π∆ would be overestimated and
that of σ∆ would be lower than generally accepted, e.g.
[14,15].
To solve this contradiction, we follow the papers [8,17]
and interpret the observation by assuming that our contacts
are formed by two junctions in series, a point contact be-
tween the normal-metal tip and a broken away supercon-
ducting grain and an S–c–S junction between two super-
conducting pellets. If so, the measured voltage bias equals
to ( ) ( ) ( )NS SSV I V I V I= + . In contrast to the paper [8], we
assume that we are dealing with two direct N–c–S and S–c–S
contacts without any significant barrier between the metal-
lic electrodes. The main characteristics of the first junction
are originating from the Andreev reflections at the NS in-
terface were described above. Charge transport in S–c–S
contacts includes multiple Andreev scattering processes at
two interfaces between superconducting electrodes [13]. It is
well known that, they manifest themselves in the so-called
“subharmonic gap structure”. In a S–c–S junction with si-
milar single-gap superconductors it consists of conductance
peaks at voltages 2 / ( )nV en= ± ∆ , n is an integer. In S1–c–
S2 asymmetric junctions with dissimilar gap values 1∆ and
2∆ on opposite sides of the scattering region [18] or those
with identical two-gap superconductors the number of the
singularities strongly increases, in particular, the new ones
are 12 / ( )en± ∆ , 22 / ( )en± ∆ , ( )1 22( ) / (2 1)e n± ∆ + ∆ + , etc.
Among them, the most pronounced processes are those
Fig. 3. (Color online) Representative conductance spectra of
Ag/MgB2 junctions at 4.2 K with two (a) and three (b) low-
voltage features, initial conductance-vs-voltage characteristics (1)
and corrected by the influence of the N–c–S contact (2). Dotted
curves represent 1 / V low-voltage asymptotic predicted in [13],
arrows show positions of π∆ , 2 π∆ , and σ∆ singularities expected
from calculations [14].
346 Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 4
Tracing the evolution of the two energy gaps in magnesium diboride under pressure
involving one Andreev reflection which result in conduct-
ance peaks at biases 1 / e∆ and 2 / e∆ (see Fig. 4 in [18]).
For voltages much less than the superconducting gaps the
dc differential conductance /dI dV of the S–c–S junction
was predicted to diverge as 1/ | |V [13]. This singularity
is a hallmark of the increased number of Andreev reflec-
tions at very small biases before a charge may enter one of
the superconducting electrodes. Of course, the effect will
be suppressed by any mechanism of inelastic scattering.
Nevertheless, in junctions shorter than inelastic scattering
length, there should be a voltage range where the conduct-
ance follows the 1/ | |V behavior, i.e., goes to infinity at
0V → .
If so, then the finite junction conductance at zero bias
should be completely determined by that of the N–c–S
contact. It allows us to estimate the ratio of the normal-
state resistances of N–c–S and S–c–S contacts /NS SSR R
which was in almost all cases 0.5≤ . Therefore, for the total
voltage drop 10V ≤ mV that on the N–c–S contact was
less than / eσ∆ , the resistance of the N–c–S contact was
constant and equal to / 2NSR . At the same time, the re-
sistance of the S–c–S contact is negligibly small [13], al-
lowing to assume that (0) 2 / NSG R= . Taking that into ac-
count, we were able to find the voltage bias on the S–c–S
contact ( ) ( ) / 2SS NSV I V I IR= − and related conductance
value 1( ) (1/ ( ) / 2)SS NSG I G I R −= − . In Fig. 3 we demon-
strate two examples of such correction procedure (curves 2).
We can see that after the correction the singularities be-
come more pronounced, they are shifted to lower biases
and the low-voltage asymptotic is consistent with the
1/ | |V dependence. Moreover, positions of the features at
about 3 and 7 meV now well correspond to / eπ∆ and
2 / eπ∆ values which, according to the theory [13], are
the most pronounced features in the conductance spectra of
S–c–S contacts with a disordered inter-electrode region.
The position of the local maximum at 9 mV seen in
Fig. 3(b) is shifted to the expected value of the large gap
/ eσ∆ . It should be noticed that the gap values are very
similar to those observed in STM/STS experiments, e.g.,
[19], and found for planar tunnel junctions (see, e.g., [20]).
We believe that the reproducibility of the zero-bias anoma-
ly and the shift of the gap-like features to correct gap posi-
tions give the evidence in favor of our hypothesis about
two junctions in series realized in our experiments and
show that the main nonlinearities in the measured curves
descend from the S–c–S contact formed between two
MgB2 grains.
A very rare observation of the larger gap σ∆ is actually
expected and can be explained by the fact that it requires a
strictly defined current direction. Indeed, the total
quasiparticle current across the MgB2-based junction is a
sum of partial contributions from two electronic bands
with a weighing factor 2
pω [6] where pω is the plasma fre-
quency for the corresponding band. Due to the smallness of
p
σω in the c-direction 2( / ) 0.01p p
σ πω ω = [14]), the charge
transport in the c-direction of the MgB2 crystal lattice is
only determined by the π-band. But in the crystallographic
a–b plane direction contributions from the two bands are
comparable since in this case 2( / ) 0.49p p
σ πω ω = . Thus, to
observe the larger gap σ∆ we need contacts oriented
roughly in the a–b plane while the smaller gap π∆ should
be observable for all transport directions. Since the orienta-
tion of superconducting grains in S–c–S junctions was un-
controllable in our experiment, the number of the junctions
which reveal the feature at / eσ∆ was very small.
To estimate correct peak positions, we have differenti-
ated numerically the G(V) curves and found downward-
going zero-crossings which correspond to the real maxima.
After averaging over eight samples, for the smaller gap, we
got (2.78 0.23)π∆ = ± meV whereas, for the larger gap, the
mean value for two junctions clearly exhibiting it was
(7.32 0.09)σ∆ = ± meV.
4. Conductance spectra at the pressure of 1.5 GPa
Soon after the discovery of superconductivity in MgB2,
several groups reported decrease in the critical temperature
under high pressure, but the rate of the decrease varied con-
siderably from –1.6 to –1.9 K/GPa in piston-cylinder studies
with Fluorinert pressure medium and from –1.36 K/GPa
in hydrostatic experiments with a mixture of daphne and
kerosene oils to –0.6 K/GPa in quasi-hydrostatic measure-
ments with solid steatite pressure medium (see related re-
ferences in [9]). Recently, the value dTc/dP =−1.1 K/GPa
was suggested to be the intrinsic value for magnesium di-
boride under hydrostatic pressure [10]. In the preprint [21],
a correlation between Tc and the derivative dTc/dP was
found: for Tc = 39.2 K and 37.5 K dTc/dP ≈ –1.07 K/GPa
and ≈ –1,45 K/GPa, respectively. As was mentioned above,
in our samples the onset temperature as well as a midpoint
one decreased with the pressure at a rate of the order of
1− K/GPa (Fig. 1). It can be considered as an additional
argument proving that the comparatively wide resistive
transition originates from weak links between magnesium
diboride grains each of which has a transition temperature
close to optimum for a given compound.
After applying the hydrostatic pressure P of 1.5 GPa to
the junction formed by a silver tip and a polycrystalline
MgB2 sample, the gap-feature positions in conductance–vs–
voltage curves have changed. It can be clearly seen from
Fig. 4 where we demonstrate how the corrected conduct-
ance spectrum shown in Fig. 3(b), curve 2 is modified un-
der the pressure. To find correct positions of the gap peaks
and the compression effect on them, we should extract the
background in the two curves which was strongly modified
at P = 1.5 GPa. It was represented by broken-line segments
connected the local minimums around corresponding peaks
in the conductance spectra (the dashed lines in the main
panel in Fig. 4). Results of the peaks extraction are shown
as insets in Fig. 4.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 4 347
V. Kononenko, V. Tarenkov, M. Belogolovskii, S. Döring, S. Schmidt, and P. Seidel
Notice that from the theoretical point of view there are
two factors influencing the energy gap values in the two-
band/two-gap model, intraband and interband couplings.
Due to the pressure-induced growth in related phonon fre-
quencies, intraband coupling decreases in each band. At
the same time, interband coupling is expected to increase
when the sample volume is reduced. For the larger gap, the
two factors should act in the same direction and, hence, the
gap σ∆ should decrease at a rate of the order of the critical
temperature. For the smaller gap π∆ , the effect of two coupl-
ings is opposite and the question which of the two factors
is dominant can be solved only by numerical calculations.
Concerning the variation of the critical temperature Tc
with pressure, there is as yet quite a few reports using real-
istic models of magnesium diboride (see, as an example,
atomistic simulations in [22]). Speaking about theoretical
analysis of the pressure effect on the energy-gap structure,
there are up to our knowledge only two publications [10]
and [23]. The calculations in the work [23] were based on
an s-wave, two-band Eliashberg approach reduced to four
coupled integral equations for two gaps and two renormali-
zation functions. The author [23] suggested that, in the first
approximation, the normal density of states at the Fermi
level does not change with pressure. In this way, the varia-
tion of the electron–phonon coupling constant ππλ and that
of the interband scattering is zero and the π∆ value is al-
most constant. The second paper [10] utilized fully aniso-
tropic Eliashberg equations, more suitable for analyzing
the pressure effect on the low-temperature superconducting
characteristics. It was found that the multiple-gap nature of
magnesium diboride persists at high pressures, both aver-
age values of ( )∆ k on σ- and π-Fermi surfaces decrease
substantially, and this effect is especially strong for the
smaller gap.
In contrast to theoretical expectations [10,23], our ex-
periment demonstrates an increase in the smaller gap
whereas the larger gap decreases with the rate of
/ 0.16d dPσ∆ = − meV/GPa which agrees with that of
– (0.13–0.17) meV/GPa predicted in the papers [10,23].
Note that the feature at 2 /V eπ= ∆ is not well resolved due
to the change of the background conductance–vs–voltage
dependence under pressure.
Conclusions
We have performed point-contact measurements on
polycrystalline samples of magnesium diboride which ex-
hibited strongly granular internal structure. Contrary to the
expectations, we have not observed a conventional An-
dreev-reflection spectra for N–c–S contacts with a doubled
zero-bias conductance comparing to the normal one but
rather much higher and steeper peak centered at V = 0. The
finding was interpreted as a formation of two junctions
in series: a contact between the normal-metal Ag tip and
a grain of magnesium diboride and that between this grain
and another MgB2 grain. In contrast to the paper [8], where
a similar explanation was proposed for high-resistance
tunneling-like sandwiches, we were dealing with metallic
MgB2–c–MgB2 contacts. It was proven by comparing their
conductance–vs–voltage characteristics extracted from the
measured curves using an accurate theoretical analysis
with those predicted theoretically for short multiple-mode
S–c–S contacts with a disordered constriction [13]. After
the correction procedure we have usually observed a zero-
bias 1/ V -like singularity of the dc differential conduct-
ance for voltages smaller than the lower superconducting
gap π∆ and two local maxima roughly at /V eπ= ∆
and 2 /V eπ= ∆ . A few samples have exhibited an ad-
ditional feature which after the correction procedure was
located approximately at /V eσ= ∆ corresponding to
the larger gap.
It should be stressed that it is not the first observation of
steep zero-bias peaks with (0) 2 NG G> in point contacts of
a normal counter-electrode with a superconductor. In par-
ticular, they have been observed for iron pnictide single
crystals [24] and thin layers [25] as well as in Fe(Se, Te)
films [26]. It can be that our interpretation of the anoma-
lous zero-bias peaks is valid in these cases as well. Most
probably, the suggested junctions-in-series structure ap-
pears due to strongly degraded and inhomogeneous surfac-
es in Fe-based superconductors [27].
The sample with the most pronounced feature shown
in Fig. 3(b) was used for the study of the pressure effect
on two energy gaps in magnesium diboride, see Fig. 4.
The larger gap, as expected [10,23], was found to decrease
from 7.25 meV to 7.01 meV while the smaller gap was
surprisingly going up from 2.69 meV to 3.07 meV (the gap
Fig. 4. (Color online) Pressure effect on the conductance spectra of
the Ag/MgB2 junction shown in Fig. 3(b) at 4.2 K, both curves are
the result of the correction for ambient pressure and P = 1.5 GPa.
Left and right insets show results of the background (the dashed
lines) extraction at negative and positive voltages, respectively.
The arrows in the insets show voltage positions of π∆ and σ∆
features in the corrected characteristics for P = 0 and P = 1.5 GPa.
348 Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 4
Tracing the evolution of the two energy gaps in magnesium diboride under pressure
values at P = 0 and P = 1.5 GPa were obtained by averag-
ing the positions of the maxima in the corrected curves for
positive and negative voltage biases). In principle, it could
result from the incoherent interband scattering caused by
non-magnetic defects which would increase under com-
pression. But π∆ and σ∆ values extracted from our exper-
imental curves well agree with those expected for pure
MgB2. We may conclude that the incoherent scattering by
inhomogeneities was not important at ambient pressure
and, most probably, remained so under the compression of
1.5 GPa. To our opinion, the contradiction with the theory
[10,23] clearly indicates that the pressure effect of the
interband scattering in clean MgB2 samples has been un-
derestimated. The second conclusion is that, in any case,
the separable anisotropy model discussed in the introduc-
tion is not able to describe the positive derivative /d dPπ∆
since it predicts decrease of all gap values due to increase
in phonon frequencies.
Acknowledgments
This work was performed within the German-Ukrainian
projects SE 664/18-1 supported by Deutsche Forschungs-
gemeinschaft (DFG). S. Schmidt thanks the Landesgra-
duiertenförderung Thüringen for financial support.
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Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 4 349
1. Introduction
2. Experimental
3. Conductance spectra at ambient pressure
4. Conductance spectra at the pressure of 1.5 GPa
Conclusions
Acknowledgments
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