A study of the electric response of He II at the excitation of second sound waves
We report an experimental investigation of the electric response of superfluid helium. Our results confirm the presence of electric potential that appears at the relative oscillatory motion of normal fluid and superfluid components in helium generated by the heater. The resonance of the electric p...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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irk-123456789-1284872018-01-11T03:03:00Z A study of the electric response of He II at the excitation of second sound waves Chagovets, T.V. Квантовые жидкости и квантовые кpисталлы We report an experimental investigation of the electric response of superfluid helium. Our results confirm the presence of electric potential that appears at the relative oscillatory motion of normal fluid and superfluid components in helium generated by the heater. The resonance of the electric potential was observed in the first four harmonics. A suggested method for the detection of the electric response allows the required resonance peak to be distinguished from spurious signals. Our results are in qualitative agreement with the data published by previous researchers. The reasons for the discrepancy in the measured values of the potential difference are discussed. 2016 Article A study of the electric response of He II at the excitation of second sound waves/ T.V. Chagovets // Физика низких температур. — 2016. — Т. 42, № 3. — С. 230–235. — Бібліогр.: 15 назв. — англ. 0132-6414 PACS: 05.70.Ln, 05.70.Jk http://dspace.nbuv.gov.ua/handle/123456789/128487 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Квантовые жидкости и квантовые кpисталлы Квантовые жидкости и квантовые кpисталлы |
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Квантовые жидкости и квантовые кpисталлы Квантовые жидкости и квантовые кpисталлы Chagovets, T.V. A study of the electric response of He II at the excitation of second sound waves Физика низких температур |
| description |
We report an experimental investigation of the electric response of superfluid helium. Our results confirm the
presence of electric potential that appears at the relative oscillatory motion of normal fluid and superfluid components
in helium generated by the heater. The resonance of the electric potential was observed in the first four
harmonics. A suggested method for the detection of the electric response allows the required resonance peak to
be distinguished from spurious signals. Our results are in qualitative agreement with the data published by previous
researchers. The reasons for the discrepancy in the measured values of the potential difference are discussed. |
| format |
Article |
| author |
Chagovets, T.V. |
| author_facet |
Chagovets, T.V. |
| author_sort |
Chagovets, T.V. |
| title |
A study of the electric response of He II at the excitation of second sound waves |
| title_short |
A study of the electric response of He II at the excitation of second sound waves |
| title_full |
A study of the electric response of He II at the excitation of second sound waves |
| title_fullStr |
A study of the electric response of He II at the excitation of second sound waves |
| title_full_unstemmed |
A study of the electric response of He II at the excitation of second sound waves |
| title_sort |
study of the electric response of he ii at the excitation of second sound waves |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2016 |
| topic_facet |
Квантовые жидкости и квантовые кpисталлы |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/128487 |
| citation_txt |
A study of the electric response of He II at the excitation of second sound waves/ T.V. Chagovets // Физика низких температур. — 2016. — Т. 42, № 3. — С. 230–235. — Бібліогр.: 15 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT chagovetstv astudyoftheelectricresponseofheiiattheexcitationofsecondsoundwaves AT chagovetstv studyoftheelectricresponseofheiiattheexcitationofsecondsoundwaves |
| first_indexed |
2025-07-09T09:10:38Z |
| last_indexed |
2025-07-09T09:10:38Z |
| _version_ |
1837159932719267840 |
| fulltext |
Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 3, pp. 230–235
A study of the electric response of He II at the excitation
of second sound waves
Tymofiy V. Chagovets
Institute of Physics ASCR, Na Slovance 2, 182 21 Prague, Czech Republic
E-mail: chagovet@fzu.cz
Received October 7, 2015, revised November 20, 2015, published online January 26, 2016
We report an experimental investigation of the electric response of superfluid helium. Our results confirm the
presence of electric potential that appears at the relative oscillatory motion of normal fluid and superfluid com-
ponents in helium generated by the heater. The resonance of the electric potential was observed in the first four
harmonics. A suggested method for the detection of the electric response allows the required resonance peak to
be distinguished from spurious signals. Our results are in qualitative agreement with the data published by previ-
ous researchers. The reasons for the discrepancy in the measured values of the potential difference are discussed.
PACS: 05.70.Ln Nonequilibrium and irreversible thermodynamics;
05.70.Jk Critical point phenomena.
Keywords: superfluid 4He, second sound, polarization, electric potential.
1. Introduction
Superfluid helium or He II is a macroscopic quantum
fluid that exhibits extraordinary properties. The behavior
of the fluid can be understood using a Landau–Tisza mod-
el, where He II is considered to be a two-component fluid
with independent velocity fields: the inviscid superfluid of
density ,sρ and the normal fluid of density ,nρ where the
total density s nρ = ρ + ρ [1,2]. The superfluid has neither
viscosity nor entropy, and the entire heat content of He II
is carried by the normal component. This simplified picture
is described by two fluid equations of motion. One of the
important outcome of these equations is not only the exist-
ence of density fluctuations relative to ordinary or first
sound, but also a prediction of the second sound, a wave
described by temperature fluctuations.
Recent experiments [3,4] reported another exceptional
property of superfluid 4He, such as electrical activity that
appears at the relative oscillatory motion of the normal
fluid and superfluid components, or second sound wave. A
standing half-wave of second sound was generated by a
heater, which was placed on one end of a dielectric resona-
tor. The AC potential difference between an electrode that
was placed on the opposite end of the resonator and the
ground was recorded. The resonance frequency of the elec-
tric response corresponded to the frequency of the second
sound resonance. It should be noted that experiments with
the first sound in both He I and He II did not show any
electrical signal, even when high power was applied to the
sound emitter [3]. This electrical activity of superfluid he-
lium is rather puzzling. The helium atom is not only chem-
ically inert and electrically neutral and does not have an
electric dipole moment, but it also has the highest ioniza-
tion potential of any element and, correspondingly, an ex-
ceptionally low polarizability.
The experiments of Refs. 3, 4 stimulated a large number
of theoretical studies and suggested various theoretical
explanations for this phenomenon [5–12]. For instance, in
Ref. 6, it was assumed that superfluid helium has an or-
dered electric quadrupole moment that can be polarized by
the nonuniform flow of the superfluid. However, the mi-
croscopic nature of such a quadrupole moment was not
discussed and remains an unanswered question. The author
of Ref. 7 suggested the inertial mechanism of polarization
of 4He atoms based on the large mass difference between
electrons and nuclei. An analog of this polarization occurs
in metals and is called the Stewart–Tolman effect. Howev-
er, this approach supposes the polarization of helium by
first sound, which contradicts the experimental results of
Ref. 3. Moreover, this theoretical model predicts a temper-
ature dependence for the /T U∆ ∆ ratio, which also contra-
dicts the experimental results. In Ref. 5, the electrical ac-
tivity was interpreted based on a similar inertial effect as in
Ref. 7, which arises under the influence of a centrifugal
force causing a nonuniform azimuthal rotational velocity
of the superfluid component around the axis of a quantum
vortex in He II. However, in this case, macroscopic polari-
© Tymofiy V. Chagovets, 2016
A study of the electric response of He II at the excitation of second sound waves
zation requires a relatively high concentration of vortex
lines. Thus, the theoretical models are discussed with re-
gard to the possible explanations and contradictions that
arise in understanding the experimental data, but a satisfac-
tory explanation of this phenomenon has not yet been
found.
Additionally, detailed analysis of the articles [3,4] re-
vealed a number of questions that need to be addressed.
For example, the amplitude of the signals is relatively
small (approximately 100 nV), and measuring such signals
can be difficult due to various sources of noise. In this re-
port, we will demonstrate the existence of a large number
of spurious peaks in a frequency sweep that have ampli-
tudes comparable to that of the signal of interest. These
spurious peaks can potentially be misinterpreted as the
required electric response. In the original experiments, the
authors used a measuring loop with the compensation of
the input capacitance. Such a measuring circuit itself can
be a source of electric pickup or spurious signals with am-
plitudes comparable to the observed electric response. Un-
fortunately, the original papers [3,4] do not include some
rather important information, such as the principal scheme
of the measuring circuit, the capacitance of the connecting
wires and electrodes used in the experiment, and the area
of the resonator's cross-section. Moreover, the analysis of
the experimental data shows some contradictions in exper-
imental data reported in [3] and [4] that reduce confidence
in these results and may give a most misleading impres-
sion. For example, T∆ values, reported in [3] and [4], is
supposed to be related to the same experiment, however
they are approximately one order of magnitude higher.
Therefore, the electric response in He II is require detailed
experimental investigation with confirmation of some pre-
vious results.
The singularity of the phenomenon, the relatively small
amplitude of the measured signal, and the lack of some
important experimental details in the original papers moti-
vated further study of the electric response in He II. The
absence of new experimental data and of an appropriate
theoretical model for the last 10 years makes this issue
even more interesting. The purpose of this work is detailed
verification of correlation between the second sound reso-
nance and the resonance of electric response, test the exist-
ence of the electric response on higher modes of the se-
cond sound. The investigation of this phenomenon is also
requires a test of various measuring circuits without com-
pensation of the input capacitance and develop a reliable
method of detecting the electric response signal in He II.
2. Experimental setup
Our experiments were performed in an open bath cryo-
stat, and a pumping unit was used to maintain the tempera-
ture in the range 1.4–2.2 K. The helium bath temperature
was monitored and stabilized at the chosen value using a
Conductus LTC-21 temperature controller with a calibrat-
ed Cernox sensor and a 50 Ω heater mounted on the bot-
tom of the cryostat. With this system, we were able to sta-
bilize the bath at temperatures of up to ± 100 µK.
The resonator, which was 25-mm long and had an inner
diameter of 7 mm, was machined from a piece of epoxy,
and its inner surface was polished. Both ends of the resona-
tor can be covered by flanges with various attached sen-
sors, for example, a heater with bifilar wire or a thin-film
thermometer, or mounted with electrodes. The resonator
was hung on a support inside a metallic shielded box and
had no electrical contact with the metallic parts of the cry-
ostat. All sensors were connected to the measuring circuit
with low temperature coax cables [13], and the total capac-
ity of the loop was approximately 260 pF.
To excite the second sound wave, we used a manganin
heater with approximately 180 Ω resistance, which was
glued with Varnish glue to the surface of a polished brass
disk with a thickness of 4 mm that was connected to one
end of the resonator. The heater, which had a spiral shape,
was made of two layers bifilar wire that covered the entire
cross-section of the channel.
The initial experiments [3,4] showed low peak values of
the resonance of approximately 10–7 V with a peak width
of approximately 2 Hz. Identifying such small signals is a
rather complicated task due to the relatively high noise
level, which was only 5 times lower than the magnitude of
the signal. The low signal-to-noise ratio and small width of
the resonance peak require measurements with a large time
constant (usually 1 or 3 seconds) for the frequency sweep
with a step of approximately 10 mHz. The increase in the
number of points allows to receive a resonant curve of
more regular shape. These types of measurement occur
over a long period of time, and the identification of the
resonance peak is difficult because of the wide range of
frequencies. Nevertheless, the range of interest can be de-
termined analytically.
As was discovered in Ref. 3, the resonance frequency of
the electric response coincides with the resonance frequen-
cy of the second sound. The resonance frequency, ,rf of
second sound can be calculated as:
21=
4r
nu
f
L
(1)
where 2u is value of the second sound velocity, L is the
actual length of the resonator and n is the number of the
half-wave lengths of the second sound signal for the ob-
served resonance mode. The factor 1/4 is caused by dou-
bling the emission frequency of the heater and because the
first resonance occurs when there is half of a second sound
wavelength between the transmitter and receiver.
The actual length of the resonator was defined using a
set of measurements of the second sound resonance. For
this purpose, the resonator end opposite to the heater was
covered by a polished brass disk with a Ge film thermome-
Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 3 231
Tymofiy V. Chagovets
ter glued to the center of the disk [14]. The low-inertia
thermometer ensured the complete thermal tracking of the
second sound waves. The thermometer was energized with
a 1 µA DC current; to detect the signals, we used a SR 830
dual phase lock-in amplifier. To excite the second sound
wave, we used an Agilent 33250A function generator to
drive the sinusoidal pattern of the heater.
The wave forms of the resonant modes are sinusoidal in
space, the velocity fields have nodes at the ends of the res-
onators, and the temperature oscillations have antinodes
coinciding with the velocity nodes. The observed second
sound resonance peaks have Lorentzian shapes. Our reso-
nator had a quality factor of approximately 60, and the
actual length of the resonator L = 24.3 mm. The relatively
low value of the resonator's actual length, as compared
with its geometrical length, may be attributed to the heater
thickness, which is slightly larger in the resonator. The
non-flat form of the heater is presumably a reason for the
low value of the quality factor.
3. Electric response
To study the electric response of He II in the resonator
generated by a standing half-wave of second sound, the
plate with the thermometer was replaced by a cylindrical
electrode. The electrode, which had a thickness of 3 mm
and a diameter of 7 mm, was glued with Stycast in situ
inside the brass mount.
We considered several measuring circuits depending on
the nature of the phenomenon and the quality of the detect-
ed signal. Measurements of the electric potential between
the plates fixed on both ends of the resonator would be a
relatively reasonable way to study the bulk polarization of
helium atoms. In this case, the electrode and the brass plate
with the heater had a differential voltage connection (A–B)
to the lock-in, whereby coaxial cable (A) was connected to
the electrode and coaxial cable (B) connected to the plate
on the opposite side of the resonator. The observed noise
level in this case was approximately 10–5 V, even for small
drive amplitudes, whereas the amplitude of the required
signal was supposed to be on the order of 10–7 V. As a
result, the high noise level made signal detection complete-
ly impossible. Although there was no electric connection
between the heater and the plate, the proximity of the heat-
er to the plate led to the appearance additional electromag-
netic noise between the electrodes.
Another possible method is to measure the potential dif-
ference between the electrode and the ground. In this cir-
cuit, the noise of the signal was approximately one order of
magnitude lower than in the previous case. It was possible
to observe a resonance peak, but only at higher drive am-
plitudes (∼10·10–3 W/cm2). We assume that the noise that
arises from the coaxial cable's shield is the reason for the
low resolution of the observed signal.
A significant enhancement of the signal-to-noise ratio
was achieved when the electrode and its mount were con-
nected to the lock-in differentially. Figure 1 shows a prin-
cipal scheme of the resonator with the electrical connec-
tions that we used to study electrical activity in He II.
Basically, the lock-in measures the voltage difference be-
tween the center conductor of coaxial cable (A) connected
to the electrode and coaxial cable (B) connected to the
electrode's mount. Noise pickup on the shield has no influ-
ence on the noise in the signal because the shields are ig-
nored. The capacitance between the electrode and the
mount was approximately 20 pF (losses 0.025), and the
total capacitance of the cables was ∼260 pF (losses 0.02).
In some experiments, a low-noise voltage preamplifier
with differential voltage input (SR 560 from Stanford Re-
search Systems) was added to the measuring loop. The use
of a preamplifier with a bandwidth filter helped to reduce
the interfering noise that appears due to mechanical vibra-
tion of the nanovolt level. This scheme allows for the
measurement of charge density only in a thin layer of heli-
um near the electrode. Thereby, it is difficult to determine
the type of charge distribution that takes place in the reso-
nator volume.
The electric response generated by the second sound
wave was observed in the temperature range 1.71–2.04 K.
An example of the electric response resonance is presented
in Fig. 2. The amplitude and shape of the observed reso-
nance peaks were very sensitive to the temperature stabili-
zation of the helium bath. The magnitude of the resonance
dramatically decreases when the temperature fluctuation is
on the order of 500 µK; thus, the signal was barely distin-
guishable from the background noise.
The signal of the electrical activity was observed using
the first four harmonics (see Fig. 3). In most cases, the
highest peak amplitude was observed for the second har-
Fig. 1. Electrical schematic of a typical resonator: epoxy body of
the resonator (1), brass plate with heater (2), brass mount with (3)
brass electrode for detecting the electric response (4), low-noise
voltage preamplifier SR 560 from Stanford Research Systems (5),
and SR 830 lock-in amplifier (6).
232 Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 3
A study of the electric response of He II at the excitation of second sound waves
monic, while for the third and fourth harmonics, the signal
was almost lost in noise. The resonance frequencies of all
four harmonics are in a good agreement with the resonance
frequencies of the second sound that was independently
measured in the same resonator.
It should be noted that a difference between the width
of second sound resonance and the width of electric re-
sponse was not observed in Ref. 3. In our experiment, the
width of second sound resonances was approximately two
times higher than the width of electric response. Moreover,
the values of width could change from measurement to
measurement. As noted in Ref. 15, the reason for this low
accuracy is low quality factor of the resonator.
In addition to the main peak that represented the electric
response, we also detected a number of spurious signals.
For example, there are two sharp peaks in Fig. 3, which are
located at the left and right sides of the first resonance
mode. The magnitudes of these peaks are comparable or
even higher than the required signal. We assume that me-
chanical vibrations from the pumping unit lead to a
microphonic effect in the coaxial cables that appears as
resonance peaks of a certain frequency.
For further study, we choose the second harmonic be-
cause of the higher amplitude of the signal and smaller
number of spurious peaks compared with the first mode.
Nevertheless, a frequency sweep in a range of interest cho-
sen nearby the frequency of the second sound resonance
revealed a number of peaks that might be misinterpreted as
the signal of electrical activity in He II (see the red curve
in Fig. 4, top graph). To exclude the possible influence of
electric pickup on the signal, the frequency was swept with
zero excitation current applied to the heater (see the black
dashed curve in Fig. 4). In this case, the resonance signal
was not observed in the expected frequency range, but it
was also observed that some spurious peaks disappeared
from the frequency sweep.
Taking into account the difficulty in defining the re-
quired signal, the following measuring protocol was im-
plemented. As was shown in Refs. 3, 4, the resonance fre-
quency of the electric response is strongly dependent on
the temperature. Performing measurements at several tem-
peratures that were slightly different (about 10–30 mK)
from the specified temperature revealed a frequency shift
for one of the peak signals. The shift of the resonance fre-
quency was proportional to the change in the second sound
Fig. 2. (Color online) The form of the second mode of the electric
response signal plotted against frequency, showing the absorption
(blue dashed curve) and dispersion (red dotted curve) data meas-
ured at 1.94 K with AC heat flux 0.011 W/cm2. The black curve
corresponds to the signal magnitude.
Fig. 3. (Color online) The resonance peaks of the electric re-
sponse of the first four harmonics (bottom black curves) meas-
ured at 1.73 K. The top red curves represent the experimental
data collected for the second sound resonances using the same
harmonics.
Fig. 4. (Color online) Changing the resonance frequency of the
standing wave by changing the bath temperature. The frequency
range corresponds to the resonance frequency of the second har-
monics in the temperature range 1.97–2 K. The AC power heat
flux was approximately 0.011 W/cm2 at all temperatures. The
black dashed curves correspond to the frequency sweet with zero
excitation current applied to the heater. Black arrows indicate the
frequency of electric induction resonance.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 3 233
Tymofiy V. Chagovets
velocity at the given temperature. Thus, this peak was de-
fined as a resonance of the electric response. Figure 4
shows the frequency sweep for 4 different temperatures.
The resonance that represents the electric response
(marked by black arrows) shifts gradually as the tempera-
ture varies. There are a number of other peaks in this fre-
quency range, but the resonance frequencies of these peaks
is temperature independent. Therefore, we consider them
to be spurious peaks.
4. Discussion
The dependence of the resonance frequency for the se-
cond mode as a function of temperature is presented in
Fig. 5. These data can be compared with the value of the
second sound resonance frequency calculated for our chan-
nel using Eq. (1). A small discrepancy between the calculat-
ed value of the resonance frequency and the value observed
in the experiment can be explained by the slight differences
in the geometry of the resonator. We calculated the resona-
tor length based on the resonance frequency of the second
sound observed in our resonator. The thermometer used in
the second sound experiment had a thickness of approxi-
mately 1 mm and was slightly recessed into the cavity,
which reduced its actual length. As a result the resonance
frequency of the second sound is shifted toward higher fre-
quencies with respect to that of the electric response. For
example, decreasing the resonator length by 1 mm increases
the resonance frequency by approximately 7 Hz. In our ex-
periment, the difference between the experimental and cal-
culated values is about 4 Hz, which is consistent with the
difference in length between the two experiments.
Measurements of second sound resonance can be made
simultaneously with a measurement of the electric re-
sponse. In this case, the thermometer and electrode must be
placed close to each other on one side of the resonator.
However, the periodic oscillation of voltage on the ther-
mometer due to the temperature oscillation in the second
sound wave may induce some pickup signal on the elec-
trode. To avoid potential sources of electric pickup, the
measurements of electric response and second sound reso-
nance were made in two different experiments.
Despite the low quality factor of the resonator in com-
parison with previous research, the absolute values of res-
onance amplitude observed in our experiment are higher
than the one observed previously. The ratio /T U∆ ∆ is on
the order of one hundred, while the value presented in the
original article was two orders of magnitude higher. We
believe that the discrepancy between the two experiments
can be understood as follows. In both experiments, a po-
tential difference, U∆ , was measured on the electrode.
The magnitude of U∆ can be determined as
in= / ,U Q C∆ ∆ where inC is the input capacitance. How-
ever, the parameters of the electrode, such as its capaci-
tance and cross-section, were different in the two experi-
ments. Therefore, the value of U∆ must be reconsidered
in terms of the number of charges per unit area. In our res-
onator, this value is on the order of 1000 for the similar
T∆ values reported in the original papers. The reports
[3,4] do not provide information about the capacitance or
the surface area of the electrode, which makes it difficult to
compare the results. It can be estimated that the discussed
parameters of the electrode were somewhat smaller in the
original experiment.
5. Conclusions
We have presented an experimental study of the electri-
cal activity of superfluid helium that appears at the relative
oscillatory motion of the normal fluid and superfluid com-
ponents. The created apparatus allowed us to register an
AC electric potential of approximately 5·10–7 V. Our data
suggest the presence of an electric potential in superfluid
helium excited by a second sound standing wave. For the
first time, the electric response was observed for the first
four harmonics with resonance frequencies that were simi-
lar to the frequency of second sound resonance. The reso-
nance frequency of the electric response was compatible
with the frequency of second sound resonance in the tem-
perature range 1.72–2.04 K. Despite the weak connection
between the inner space of the resonator and the helium
bath, the amplitude of the resonance peak was very sensi-
tive to thermal fluctuation of the helium bath. We suggest-
ed a reliable method for the detection of the electric re-
sponse that allows the required resonance to be
distinguished from spurious signals. Our results are in
qualitative agreement with the data published by previous
Fig. 5. Temperature dependence of the resonance frequency of the
electric response (open circles). The closed circles correspond to
the resonance frequency the second sound. The solid line represents
the resonance frequency of the second sound calculated for the
resonator based on known data of the second sound velocity.
234 Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 3
A study of the electric response of He II at the excitation of second sound waves
researchers. Nevertheless, the amplitude of the resonance
peak was higher despite the lower quality factor of the res-
onator. The reason for this discrepancy in the absolute val-
ues of the potential difference lies in the parameters of the
electrode, such as the cross-section and capacitance. We
believe that further investigation of this phenomenon could
lead to a more complete understanding of the electric prop-
erties of superfluid helium.
Acknowledgements: The authors appreciate the tech-
nical assistance of F. Soukup and stimulating discussions
with A. Rybalko, E. Rudavskii, L. Skrbek and V. Chagovets.
This work is supported by the Czech Science Foundation
(GACR) under Project No. 13-03806P.
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Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 3 235
1. Introduction
2. Experimental setup
3. Electric response
4. Discussion
5. Conclusions
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