Unusual microwave response and bulk conductivity of very thin FeSe₀.₃Te₀.₇ films as a function of temperature
Results of X-band microwave surface impedance measurements of FeSe₁–xTex very thin film are reported. The effective surface resistance shows appearance of peak at T ≤ Tc when plotted as a function of temperature. The authors suggests that the most well-reasoned explanation can be based on the idea o...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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nasplib_isofts_kiev_ua-123456789-1195222025-02-09T16:59:46Z Unusual microwave response and bulk conductivity of very thin FeSe₀.₃Te₀.₇ films as a function of temperature Barannik, A.A. Cherpak, N.T. Yun Wu Sheng Luo Yusheng He Kharchenko, M.S. Porch, A. Свеpхпpоводимость, в том числе высокотемпеpатуpная Results of X-band microwave surface impedance measurements of FeSe₁–xTex very thin film are reported. The effective surface resistance shows appearance of peak at T ≤ Tc when plotted as a function of temperature. The authors suggests that the most well-reasoned explanation can be based on the idea of the changing orientation of the microwave magnetic field at a S–N phase transition near the surface of a very thin film. The magnetic penetration depth exhibits a power-law behavior of L(T) CTn, with an exponent n ≈ 2.4 at low temperatures, which is noticeably higher than in the published results on FeSe₁–xTex single crystal. However the temperature dependence of the superfluid conductivity remains very different from the behavior described by the BCS theory. Experimental results are fitted very well by a two-gap model with Δ₁/kTc = 0.43 and Δ₂/kTc = 1.22, thus supporting s±-wave symmetry. The rapid increase of the quasiparticle scattering time is obtained from the microwave impedance measurements. 2014 Article Unusual microwave response and bulk conductivity of very thin FeSe₀.₃Te₀.₇ films as a function of temperature / A.A. Barannik, N.T. Cherpak, Yun Wu, Sheng Luo, Yusheng He, M.S. Kharchenko, A. Porch // Физика низких температур. — 2014. — Т. 40, № 6. — С. 636-644. — Бібліогр.: 31 назв. — англ. 0132-6414 PACS 74.20.Rp, 74.25.Ha, 74.25.nn, 74.70.Xa https://nasplib.isofts.kiev.ua/handle/123456789/119522 en Физика низких температур application/pdf Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Свеpхпpоводимость, в том числе высокотемпеpатуpная Свеpхпpоводимость, в том числе высокотемпеpатуpная |
| spellingShingle |
Свеpхпpоводимость, в том числе высокотемпеpатуpная Свеpхпpоводимость, в том числе высокотемпеpатуpная Barannik, A.A. Cherpak, N.T. Yun Wu Sheng Luo Yusheng He Kharchenko, M.S. Porch, A. Unusual microwave response and bulk conductivity of very thin FeSe₀.₃Te₀.₇ films as a function of temperature Физика низких температур |
| description |
Results of X-band microwave surface impedance measurements of FeSe₁–xTex very thin film are reported. The effective surface resistance shows appearance of peak at T ≤ Tc when plotted as a function of temperature. The authors suggests that the most well-reasoned explanation can be based on the idea of the changing orientation of the microwave magnetic field at a S–N phase transition near the surface of a very thin film. The magnetic penetration depth exhibits a power-law behavior of L(T) CTn, with an exponent n ≈ 2.4 at low temperatures, which is noticeably higher than in the published results on FeSe₁–xTex single crystal. However the temperature dependence of the superfluid conductivity remains very different from the behavior described by the BCS theory. Experimental results are fitted very well by a two-gap model with Δ₁/kTc = 0.43 and Δ₂/kTc = 1.22, thus supporting s±-wave symmetry. The rapid increase of the quasiparticle scattering time is obtained from the microwave impedance measurements. |
| format |
Article |
| author |
Barannik, A.A. Cherpak, N.T. Yun Wu Sheng Luo Yusheng He Kharchenko, M.S. Porch, A. |
| author_facet |
Barannik, A.A. Cherpak, N.T. Yun Wu Sheng Luo Yusheng He Kharchenko, M.S. Porch, A. |
| author_sort |
Barannik, A.A. |
| title |
Unusual microwave response and bulk conductivity of very thin FeSe₀.₃Te₀.₇ films as a function of temperature |
| title_short |
Unusual microwave response and bulk conductivity of very thin FeSe₀.₃Te₀.₇ films as a function of temperature |
| title_full |
Unusual microwave response and bulk conductivity of very thin FeSe₀.₃Te₀.₇ films as a function of temperature |
| title_fullStr |
Unusual microwave response and bulk conductivity of very thin FeSe₀.₃Te₀.₇ films as a function of temperature |
| title_full_unstemmed |
Unusual microwave response and bulk conductivity of very thin FeSe₀.₃Te₀.₇ films as a function of temperature |
| title_sort |
unusual microwave response and bulk conductivity of very thin fese₀.₃te₀.₇ films as a function of temperature |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2014 |
| topic_facet |
Свеpхпpоводимость, в том числе высокотемпеpатуpная |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/119522 |
| citation_txt |
Unusual microwave response and bulk conductivity of very thin FeSe₀.₃Te₀.₇ films as a function of temperature / A.A. Barannik, N.T. Cherpak, Yun Wu, Sheng Luo, Yusheng He, M.S. Kharchenko, A. Porch // Физика низких температур. — 2014. — Т. 40, № 6. — С. 636-644. — Бібліогр.: 31 назв. — англ. |
| series |
Физика низких температур |
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© A.A. Barannik, N.T. Cherpak, Yun Wu, Sheng Luo, Yusheng He, M.S. Kharchenko, and A. Porch, 2014
Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 6, pp. 636–644
Unusual microwave response and bulk conductivity
of very thin FeSe0.3Te0.7 films as a function of
temperature
A.A. Barannik
1
, N.T. Cherpak1, Yun Wu
2
, Sheng Luo
2
, Yusheng He
3
,
M.S. Kharchenko
1
, and A. Porch
4
1
O. Ya. Usikov Institute for Radiophysics and Electronics, National Academy of Sciences of Ukraine
Kharkiv 61085, Ukraine
E-mail: a.a.barannik@mail.ru
2
University of Science and Technology, 100083 Beijing, China Institute of Physics, China
3
Chinese Academy of Sciences 100190 Beijing, China
4
Cardiff University, Cardiff CF24 3AA, Wales, UK
Received November 8, 2013, revised December 25, 2013, published online April 21, 2014
Results of X-band microwave surface impedance measurements of FeSe1–xTex very thin film are reported.
The effective surface resistance shows appearance of peak at T ≤ Tc when plotted as a function of temperature.
The authors suggests that the most well-reasoned explanation can be based on the idea of the changing orienta-
tion of the microwave magnetic field at a S–N phase transition near the surface of a very thin film. The magnetic
penetration depth exhibits a power-law behavior of L(T) CT
n
, with an exponent n ≈ 2.4 at low temperatures,
which is noticeably higher than in the published results on FeSe1–xTex single crystal. However the temperature
dependence of the superfluid conductivity remains very different from the behavior described by the BCS theo-
ry. Experimental results are fitted very well by a two-gap model with 1/kTc = 0.43 and 2/kTc = 1.22, thus sup-
porting s±-wave symmetry. The rapid increase of the quasiparticle scattering time is obtained from the micro-
wave impedance measurements.
PACS: 74.20.Rp Pairing symmetries;
74.25.Ha Magnetic properties including vortex structures and related phenomena;
74.25.nn Surface impedance;
74.70.Xa Pnictides and chalcogenides.
Keywords: microwave surface impedance, Fe-chalcogenides, complex conductivity, field penetration depth,
wave symmetry.
1. Introduction
The discovery of superconductivity in the Fe-based
pnictide compound LaFeAsO1–xF (“1111”) has stimulated a
great scientific interest and intense studies of this class of
superconductors [1]. The compounds contain the ferromag-
netic element Fe and so unconventional superconducting
properties were expected because (in general) superconduc-
tivity and ferromagnetism are usually antagonistic. Consid-
erable efforts have been performed in searching for super-
conductivity in structurally simple Fe-based substances. As
a result, the metallic superconductors BaFe2As2 (“122”)
with Co-and Ni- doping were discovered [2–4].
The discovery of superconductivity in pnictides (e.g., in
“1111” and “122”) and chalcogenides (e.g., in “11”) is of
great importance, because it gives additional chance to
study nature of superconductivity in these substances and
cuprates by means of comparison of their properties. Espe-
cially, the discovery of superconductivity in binary As-free
Fe-chalcogenide (“11”) is of great interest, since it only
contains the FeSe-layer, which has an identical structure as
FeAs, and the Se deficiency may be the reason of the su-
perconductivity [5]. By introducing Te, the critical temper-
ature in FeSexTe1–x can be increased. This system is con-
venient because the doping can be well controlled [6].
Unusual microwave response and bulk conductivity of very thin FeSe0.3Te0.7 films as a function of temperature
Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 6 637
For this new family of unconventional superconductors,
the pairing symmetry of their energy gap is a key to under-
standing the mechanism of superconductivity. Extensive
experimental and theoretical works have been done to ad-
dress this important issue for FeAs-based superconductors.
At present, increasing evidence points to multi-gap models
of superconductivity, possibly with an unconventional
pairing mediated by antiferromagnetic fluctuations [7,8].
Thus new experimental works and theoretical approaches
are very important for reliable conclusions.
The measurement of the temperature dependence of the
microwave impedance is a powerful tool for studying not
only the penetration depth [9] but also the whole complex
conductivity of the samples [10]. To date, few works have
been published on the experimental study of microwave
surface impedance of FeSe-based chalcogenides [11,12].
The work [11] reports microwave surface impedance of
FeSe0.4Te0.6 single crystals and the power-law behavior of
penetration depth CT
n
with an exponent n ≈ 2, which is
considered to result from impurity scattering and differs
noticeably from n in other Fe-based superconductors, e.g.,
n = 2.8 in Ba(Fe1–xCox)2As2 [13]. The work [12] is the
study of very thin epitaxial FeSe0.3O0.7 film of thickness df
less than penetration depth λL in the whole temperature
range. In this case some unclear features of the microwave
effective surface impedance were observed, depending on
the temperature. They are: 1) the appearance of a peak in
the effective surface resistance eff
sR at T ≤ Tc; 2) a consid-
erable difference between the effective film surface re-
sistance eff
sR and reactance eff
sX at T > Tc.
This present work is aimed at obtaining bulk (i.e., in-
trinsic) microwave properties Rs(T) and Xs(T) using our
experimental data [12] and thus to obtain temperature de-
pendences of the penetration depth λL(T), the quasiparticle
conductivity σ1(T), the conductivity of the superfluid com-
ponent σ2(T) and the quasiparticle scattering rate τ
–1
(T).
These values are then compared with the results obtained
for our thin epitaxial film and single crystal [11] of the
same compound FeSe1–xTex. Appendix gives an expres-
sion for the effective surface impedance eff
sZ as a function
of film thickness df in terms of the bulk surface impedance
Zs for three configurations of microwave magnetic field
near the surfaces of the sample under study.
2. Experimental data and their peculiarities
Epitaxial FeSe1–xTex (x = 0.7) film deposited on a
LaAlO3 substrate by a pulsed laser deposition method
[14,15] is found to have Tc onset = 14.8 K and a transition
width ΔT = 1.6 K on the levels of resistivity ρ(T)/ρ(Tc onset)=
= 0.1 and 0.9 (inset in Fig.1(a)). The microwave response of
the film was measured using an X-band sapphire dielectric
resonator. It is a close analogy to [16].
The cavity resonator, which has a quality factor of Q0 =
= 45000 at room temperature, is specially designed for the
microwave measurements of small samples using the
TE011-mode, with the sapphire cylinder having a small
hole along its axis. The sample with film thickness df =
= 100 nm and other, lateral dimensions of 1 mm is put in
the center of the hole but isolated from the cylinder, sup-
ported by a very thin sapphire rod. The cavity is sealed in a
vacuum chamber immersed in liquid
4
He and the tempera-
ture of sapphire rod (hence the sample) can be controlled
from 1.6 to 60 K with a stability about ± 1 mK while keep-
ing the cavity at a temperature of 4.2 K. The temperature
dependence of resonance frequency and quality factor of
resonator (Figs. 1(a) and 1(b)) were measured by a vector
network analyzer (Agilent N5230C) for both the thin film
sample and also the bare substrate.
The effective surface resistance (Fig. 2(a)) is deter-
mined by the expression
1 1
eff s ws
s
s
Q Q
R
A
, (1)
where Qs and Qws are the Q-factors of the resonator with
and without the sample under study, respectively. The co-
efficient of inclusion [17] As = 2.9∙10
–4
Ω
–1
was obtained
Fig. 1. (Color online) The temperature dependence of resonance
frequency (a) and quality factor (b) of the resonator for both the
thin film sample and the bare substrate (empty symbols). The
inset shows the temperature dependence of the resistivity.
A.A. Barannik, N.T. Cherpak, Yun Wu, Sheng Luo, Yusheng He, M.S. Kharchenko, and A. Porch
638 Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 6
by modeling using CST 2009. The surface reactance
eff ( )sX T can be written as
eff eff eff(0) ( )s s sX X X T , (2)
where eff (0)sX is the effective reactance at T = 0 and
0
eff 2 ( )
( )s
s
f T
X T
A f
(2a)
here f0 is the center frequency of the resonator and Δf(T) is
the frequency shift relative to the resonator without the
sample. eff ( )sX T is presented in Fig 2(b).
As can be seen in Fig. 2, in the temperature dependence
of the microwave response eff eff eff
s s sZ R iX of the film
there are two features that were not presented in the study
of YBa2Cu3O7–δ single crystals (see, e.g., [18]) and films
(see, e.g., [19,20]), as well as for FeSe0.4Te0.6 single crys-
tal [11]. The most noticeable feature is a peak of eff ( )sR T
at T ≤ Tc near Tc. The second feature of the response is
manifested in the abnormally large change in the resonant
frequency of the resonator and thus in the effective growth
of the reactance when approaching Tc. The possible nature
of these features is discussed below.
3. Finding the bulk surface impedance
The film under study was placed in the resonator so that
its plane was perpendicular to the rotational symmetry axis
of the resonator, i.e., perpendicular to microwave magnetic
field H in a center of the cavity. It is known that when the
film thickness df is comparable to the magnetic penetration
depth λL the measured surface impedance is a function of
the ratio df/λL [10]. At the same time, relations between
eff ( / )s f LZ d and bulk impedance Zs are known for two
cases of configurations of microwave field H at the sur-
face of the film: 1) field is symmetric with respect to two
side surfaces and 2) field has a component on one side of
the film [10]. The first case is typical for placing the film
in the resonator with HE011-mode parallel to the field H ,
the second case occurs when the film is the conducting
endplate of metal or dielectric resonator [17]. In our work
the third case is realized, when the magnetic field at the
planes of the film is in the opposite directions (see Appen-
dix). In this case the above mentioned relation has the form
eff ( / ) cot
2 2
f
s f L s
di
Z d Z k , (3)
where 0 / ,sk Z 2 ,f μ0 = 4π∙10
–7
H/m.
Since the penetration depth at T = 0, λL(0), is not deter-
mined in our work, for the purpose of finding Zs(T) we need
to use the values of λL(0), obtained in other works. These
values are known, e.g., 470 nm (single crystal FeSe0.4Te0.6,
microwave measurement) [11], 560 nm (single crystal
FeTe0.58Se0.42, TDR measurement) [21] and 534 nm (pow-
der sample of FeTe0.5Se0.5, SR) [22]. Obviously, our film
is much thinner than λL(0), and in addition the ratio df/λL(T)
further decreases with increasing temperature.
In the case when Rs << Xs, that is expected in the tem-
perature range from T = 0 to Tc/2, equation (3) reduces to
eff 21
coth cosec
2 2 2
f f f
s s
L L L
d d d
R R ,
eff 1
coth .
2 2
f
s s
L
d
X X (3a)
In the limit of very thin films (df /λL << 1)
eff 2 /s s L fR R d and eff 2 / .s s L fX X d
Expressions (3a) were used to find the bulk (intrinsic)
values of Rs and Xs (Fig. 3). There we used the equality
Rs = Xs at T ≥ Tc and λL(0) = 560 nm [21].
4. Discussion of the results
The approach of finding Rs and Xs in the previous sec-
tion does not explain the nature of the appearance of the
peak eff
sR near Tc. We can consider several explanations
in this respect: 1) the coherence peak; 2) manifestation of
the magnetic component in a superconductor (μ > 1); 3)
Fig. 2. (Color online) The effective surface resistance eff
sR (a)
and change of surface reactance eff
sX (b) of FeSe1-xTex film
depending on temperature.
Unusual microwave response and bulk conductivity of very thin FeSe0.3Te0.7 films as a function of temperature
Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 6 639
the size effect at df ≈ λL (T); 4) the effect of changing the
microwave magnetic field configuration near the film sur-
faces at a S–N transition.
Apparently we should not talk about coherence peak,
because it is not observed in the single crystal [11]. The
appearance of the magnetic component in a superconduc-
tor, when the relative permeability μ > 1, is possible in
principle [23]. However, the effect in [23] was observed at
T > Tc and the peak width is significantly greater than in
the present work.
We observe the peak of eff
sR at T ≤ Tc. The size effect
when df is comparable with λL(T) or normal state skin
depth is excluded completely because df < λL(T) in the
whole temperature interval from T = 0 to Tc.
It seems that the most well-reasoned explanation can be
based on the idea of the changing of the parallel orientation
of the microwave magnetic field near the surface of a super-
conductor at the phase transition from the S-state to an orien-
tation close to perpendicular in the N-state. This occurs when
the field direction near the surface of the very thin film coin-
cides at least partially with the direction of TE011-mode field
near the axis of the resonator (Fig. 9 in Appendix). Here the
correlation between eff
sZ and Zs must change. Evidently,
eff| | | |s sZ Z at T < Tc and, perhaps, eff| | | |s sZ Z at
T ≥ Tc (See Appendix and [10]). We have no mathematical
model describing changing eff ( )sZ T and the relationship of
eff ( )sZ T and Zs(T) near Tc, therefore we found Rs(T) in the
interval of T = 1.6 – 10 K in accordance with (3a) and deter-
mined Rs(T) at T ≥ Tc using 0 /2sR , where ρ is the
measured resistivity. After that we matched up the obtained
values of Rs in a region of T ≤ Tc. The dependence Xs(T) was
found using Xs (0) = ωμ0λL(0) at T = 0, the dependence of
ΔXs(T) taking into account the expression (3a), and using the
equality Rs = Xs at T ≥ Tc and the matching described above.
The correctness of this approach was validated by the mutual
coordination of eff ( ),sR T eff ( ),sX T Rs(T), and Xs(T) within
the framework of equation (3). The obtained values of Rs(T)
and Xs(T) allow us to find the complex conductivity of the
sample, where σ1 is the quasiparticle conductivity
1 0 4
2
| |
s s
s
R X
Z
(4)
and σ2 is the conductivity of the superfluid component
2 2
2 0 4| |
s s
s
X R
Z
, (5)
where 4 2 2 2| | ( ) .s s sZ R X
At low temperature when the condition σ1 << σ2 is true,
we easily obtain from (5) the known expression
2
2 0 / .sX Because 2 2
2 0/ 1/ ,s Le n m it is
easy to obtain the well known relation
0s LX , (6)
which is often used for obtaining information about the
structure of the energy gap in superconductors (see e.g.,
[9]). In general λL(T) is found from equation (5) as
0 2
1
( ) .
( )
L T
T
(7)
The temperature dependence λL(T) is shown in Fig. 4,
where the inset presents the low-temperature part of the da-
ta. The absolute value of λL(0) = 560 nm is taken from [21],
consistent with other published data [11,21]. The penetration
depth is found to obey a power-low behavior, i.e.,
( ) ( ) (0) n
L L LT T CT with the exponent n ≈ 2.4
for temperatures as high as 7 K ≥ Tc/2. The obtained value
of n is higher noticeably than n ≈ 2 in [11,21] and lower than
value of n = 2.8, for example, in crystal Ba(Fe1–xCox)2As2
[13,24] obtained in the radiofrequency and microwave ran-
ges. Generally speaking, a power-law temperature behavior
Fig. 3. (Color online) Surface resistance Rs (T) and surface reac-
tance Xs (T).
Fig. 4. (Color online) Temperature dependence λL(T). The inset
presents the low-temperature part of the dependence L(T) =
= L(T) – L(0), and the solid line corresponds to power-law be-
havior L(T) = CT
n
with n = 2.4.
A.A. Barannik, N.T. Cherpak, Yun Wu, Sheng Luo, Yusheng He, M.S. Kharchenko, and A. Porch
640 Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 6
can be explained by some quantity of low-energy qua-
siparticles, however it depends also on the presence of mag-
netic and nonmagnetic impurities [11,25]. Particularly, in a
superconductor with s -wave symmetry with nonmagnetic
impurities the behavior λL(T) at low temperature has a form
of T2.
Figure 5 displays σ1(T), both with and without subtract-
ing Rs(0) = Rres from the bulk data of Rs before calculating
σ1. Subtracting Rres removes the influence of surface de-
fects and so yields the quasiparticle behavior [11]. We
should note that an error in the estimate of Rres changes
noticeably σ1(T) at low temperatures but relatively much
less so in the higher temperature part of the S-state. It can
be seen in our work with thin films and in [11] with single
crystals of very close composition that a considerable en-
hancement of σ1(T) is observed below Tc. Such an en-
hancement was also observed in cuprate high-Tc supercon-
ductors [20,26,27] and in Fe-based pnictides [28,29] and is
much broader than the coherence peak. It is explained by
suppression of quasiparticle scattering below Tc when
quasiparticle density decreases, giving the appearance of
the broad peak in σ1(T) below Tc.
In this situation it is important to find the quasiparticle
scattering rate τ
–1
in the system under study. On the assump-
tion that all charge carriers condense at T = 0 and ωτ << 1
the following relation is valid [30]
2 2
1
2
0 1
1 (0)/
( ) (0)
L L
L
T
T
, (8)
where λL(T) can be found from (7). To this end we need to
find a conductivity σ2(T), which in turn is determined by
the equation (5).
Figure 6 shows the temperature dependence of σ2 for two
values of residual surface resistance. As one can see, the two
curves are very close. The obtained data allows us to find
[λL(0)/λL(T)]
2
. Figure 7 displays the comparison of experi-
mental results with theoretical models in the low-
temperature part of λL(T) and indicates a very good fit of
experiment data with the two-gap model when 1 =0.43 kTc
(weight coefficient 0.84) and 2 = 1.22 kTc.
These results noticeably differ from ones in [11] ob-
tained by the microwave technique ( 1 = 2 = 0.85 kTc)
and [31] obtained by TDR technique ( 1 =1.93 kTc and
2 = 0.9 kTc), although support s -wave symmetry of the
paired electrons. Obviously, the source of discrepancy can
be established with a further study of the compounds.
The obtained data on σ2(T) and λL(T) allow us to find τ
–1
depending on T. Figure 8 shows apparently a common fea-
ture in the behavior of all known unconventional supercon-
ductors, which consists of a sharp decrease in the qua-
siparticle scattering rate at low temperatures. If we take
Rres < 5m , the rate τ
–1
(T) starts to increase with decreasing
Fig. 5. (Color online) Quasiparticle conductivity σ1(T) obtained
with (empty symbols) and without (filled symbols) subtracting
residual resistance Rres.
Fig. 6. (Color online) Conductivity σ2 of the superfluid compo-
nent depending on temperature, taking into account residual sur-
face resistance.
Fig. 7. (Color online) Ratio [λL(0) /λL(T)]
2
depending on tem-
perature. The solid line corresponds to the two-gap model (Δ1 =
= 0.43 kTc; Δ2 = 1.22 kTc, weight coefficient x is 0.84 for Δ1),
the dashed line corresponds to BCS theory, Δ1 = 0.43 kTc (dash-
dot-dotted) and Δ2 = 1.22 kTc (dash-dotted).
Unusual microwave response and bulk conductivity of very thin FeSe0.3Te0.7 films as a function of temperature
Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 6 641
temperature, which seems to us unphysical.
The energy gaps found in this work differ markedly
from the values shown in other studies (see, e.g.,
[11,21,22,31]). Currently we can not give any convincing
explanation for these discrepancies. Obviously, it is neces-
sary to conduct microwave measurements for the film and
single crystal FeSe1–xTex of the same composition using
the same resonator(s), and measuring for two alternative
orientations of the film in the resonator. It is highly desira-
ble to conduct these measurements not only in the X-band,
but at a higher frequency, for example, in the K-band [29].
It is important to clarify the nature of the unusual response
at T ≤ Tc, as well as to establish the consensus values of the
energy gaps.
5. Conclusion
In conclusion, the microwave surface impedance Zs of
epitaxial FeSe1–xTex (x = 0.7) film of 100 nm thickness
deposited on the LaAlO3 substrate has been measured by
an X-band sapphire cavity operating in the TE011-mode.
The effective surface resistance depending on temperature
shows the appearance of a peak at T ≤ Tc. It can be sug-
gested that the most well-reasoned explanation can be
based on the idea of a changing orientation of microwave
magnetic field near the surface of a very thin film at a S–N
phase transition, when the film thickness is less than L(0).
The penetration depth shows a power-law behavior
( ) ,n
L T CT with an exponent n ≈ 2.4 in the low-tem-
perature interval, which is noticeably higher than in the
published results on FeSe1–xTex single crystal. However
the temperature dependence of the superfluid conductivity
remains very different from behavior described by the BCS
theory. Experimental results indicate very good fit of the
theoretical two-gap model with 1/ 0.43ckT and
2 / 1.22,ckT supporting s±-wave symmetry. A rapid
increase of the quasiparticle scattering time is obtained
from the microwave impedance measurements.
Work is supported partially by IRE NAS of Ukraine
under State Project No. 0106U011978 and by the State
Agency on Science, Innovations and Informatization of
Ukraine under Project No. 01113U004311. Work was per-
formed also within the framework of Agreement of collab-
oration between IRE NASU and IoP CAS.
Appendix
A1.The effects of finite sample thickness on the
measurements of surface impedance
The standard definition of surface impedance assumes
that the superconductor has a thickness much larger than λ
(or, equivalently, the skin depth δ when in the normal
state). This is evidently not valid for thin superconducting
films, where the thickness df is typically of the same order
of magnitude as λ, particularly at temperature close to Tc.
In this case the effective surface impedance eff
sZ measured
for samples of finite thickness differs from the intrinsic
surface impedance Zs (i.e., the surface impedance of a infi-
nitely thick sample), and becomes a function of df/λ; the
exact dependence on thickness depends on the spatial
symmetry of the applied microwave field and the three
configurations shown in Fig. 9 are considered here.
Cases (a) and (b) of Fig. 9 are presented in [10] without
mathematical details. Here mathematical derivation of the
effective surface impedance as a function of df/λ is given
for all three cases.
A2. Effective surface impedance of thin film
For the case shown in Fig. 10 with H applied parallel to
both plane surfaces of film of thickness df (see Fig.1(a)),
from H J we obtain / ,yH z E if ( ,0,0)xHH
and (0, ,0).yEE By analogy from / tE B we
Fig. 8. (Color online) Quasiparticle scattering τ
–1
(T) taking into
account Rres (filled symbols) and at Rres = 0 (empty symbols).
Fig. 9. Three possible configurations of microwave field orienta-
tion relative to a thin superconducting sample that exhibits signif-
icantly different effective surface impedance in the very thin
sample limit; df is comparable to λL
A.A. Barannik, N.T. Cherpak, Yun Wu, Sheng Luo, Yusheng He, M.S. Kharchenko, and A. Porch
642 Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 6
obtain 0/y xE z j H i.e., 2
0/x xH z j H
2 .xk H
For the above geometry, we take the symmetric solution
for Hx, i.e., Hx(z) = Hx (–z) in the form of xH
cos ( ),A kz therefore
1
sin ( )x
y
H Ak
E kz
z
. At
the film surface where z = + df/2
eff
/2
tan
2
f
y f
s
x z d
E kdk
Z
H
(we get the same value for eff
sZ when z = –df/2). But
0/ ( )/ ,sk i k iZ therefore
eff tan
2
f
s
kd
Z iZ (A2.1)
where Zs = Rs + iXs is bulk surface impedance. When,
Rs << Xs, Xs ≈ ωμ0λL
0 0 0
1 22 2
0
1s s
s s Ls L
R R
k i i k ik
Z XX
i.e., 2
1 0 2/ , 1/ .s L Lk R k
We now write 1 2tan ( /2) tan ( ),fkd i where
2
1 0/(2 ),s f LR d 2 /(2 ),f Ld which is trans-
formed into
21 2
1 2 2
1 2
tanh ( )
tan sech tanh .
2 1 tanh ( )
fkd i
i
i
(A2.2).
Thus by application of (A2.2) to (A2.1), eff
sZ can be
expressed in terms of Zs and df/λL:
eff eff eff
s s sZ R iX (A2.3)
where
e 2eff ffRe ( ) tanh sech ,
2 2 2
f f f
s s s
L L L
d d d
R Z R
eff effIm ( ) tanh
2
f
s s s
L
d
X Z X .
For a very thin film df << λL write x = df/λL and
2tanh( /2) ( /2)(1 /12)x x x and 2( /2)sech ( /2)x x
2( /2)(1 /4),x x which then yields the effective surface
impedance
3
eff
312
s f
s
L
R d
R and
eff
2
f
s s
L
d
X X . (A2.4)
This means that the cylindrical resonator technique for
very thin sample lacks sensitivity particularly for meas-
urements of surface resistance when the microwave field is
in the same direction on opposite faces of the crystal.
An alternative configuration is case of Fig. 9(b), which
occurs when a sample replaces the end-wall of an empty
(i.e., air or gas-filled) cylindrical resonator or when a die-
lectric resonator is used. Both of these resonators are ideal
for measuring thin films. The effective surface impedance
when σ1 << σ2 is [31]
eff 2(coth cosech ) i coth .s s sZ R x x x X x (A2.5)
Again defining x = df/λL, we obtain in the film sample limit
(x << 1)
eff eff2 / , /s s s sR R x X X x . (A2.6)
Therefore, for measuring thin samples it is best to have
the microwave field configured as in case (b) of Fig. 9.
Beyond x = df/λ > 3 the effective and intrinsic surface im-
pedance differ little from each other.
A configuration (c) opposite to case (a) in Fig. 9 occurs,
when the microwave field is in opposite directions on op-
posite faces of the film. By analogy with Fig. 9 for the case
(a) we can provide the relative position of H and E vectors,
as shown in Fig. 11.
Here Hx(z) = –Hx (–z). For the given geometry we must
take the asymmetric solution for Hx i.e., sin ,xH B kz
therefore ( ) ( / )cosyE z Bk kz . At the film surface where
z = + df/2
eff cot ,
2
f
s
kdk
Z
therefore
eff cot
2
f
s s
kd
Z iZ (A2.7)
Fig. 10. Orientations of microwave field and density current rela-
tive to a thin superconducting sample for the case in Fig. 9(a).
Fig. 11. Orientations of microwave field and density current rela-
tive to a thin superconducting sample for a case of Fig. 9(c).
Unusual microwave response and bulk conductivity of very thin FeSe0.3Te0.7 films as a function of temperature
Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 6 643
because / sk iZ (see case (a) in Fig. 9). By analogy to
case (a) we obtain when Rs << Xs
1
2
1 1
cot .
2
sh tanh
2 2
f
f f
L L
kd
i
d d
The configuration shown in Fig. 11 is a parallel connection
of two conductors, so we can write
eff eff eff eff1
2
s s s sZ Z R iX (A2.8)
where
eff 21
coth cosech ,
2 2 2 2
f f f
s s
L L L
d d d
R R
eff 1
coth .
2 2
f
s s
d
X X
For thin sample limit (df << λL) eff 2 ( / )s s L fR R d
and eff ( / ),s s L fX X d which coincides with the case of
Fig. 9(b).
Hereinafter the question arises, under what conditions is
the configuration in Fig. 9(c) realized? For this purpose we
consider the cavity in the TE011-mode and with a very thin
superconductor sample located perpendicular to the mi-
crowave field (Fig. 12).
The microwave magnetic field near the sample in su-
perconducting state has a configuration as shown in
Fig. 13(a).
Figure 13 shows that the directions of the magnetic
field lines are opposite at the top and bottom surfaces of
the sample. In this case, the currents have the same orienta-
tion in both planes (see Fig. 13).
A part of the sample between the planes of cross-
sections 1 and 2 with the directions of the magnetic field
and currents looks as shown in Fig. 11.
1. Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono,
J. Am. Chem. Soc. 130, 3296 (2008).
2. P.L. Alireza, Y.T.C. Ko, J. Gillet, C.M. Petrone, J.M. Cole,
G.G. Lonzarich, and S.E. Sebastian, J. Phys.: Condens.
Matter 21, 012208 (2009).
3. A.S. Sefat, R. Jin, M.A. McGuire, B.C. Sales, D.J. Singh,
and D. Mandrus, Phys. Rev. Lett. 101, 117004 (2008).
4. L.J. Li, Q.B. Wang, Y.K. Luo, H. Chen, Q. Tao, Y.K. Li, X.
Lin, M. He, Z.W. Zhu, G.H. Cao, and Z.A. Xu, New J. Phys.
11, 025008 (2009).
Fig. 12. Microwave field configuration in the resonant cavity
with TE011-mode.
Fig. 13. Directions of the magnetic field lines H near a supercon-
ducting film placed in the center of a resonator cavity in itsTE011
–mode (a), (b),(c) and current density J in the top (b) and bottom
(c) surface layers of the film.
A.A. Barannik, N.T. Cherpak, Yun Wu, Sheng Luo, Yusheng He, M.S. Kharchenko, and A. Porch
644 Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 6
5. F.-C. Hsu, J.-Y.Luo, K.-W.Yeh, T.K. Chen, T.-W.Huang,
P.M. Wu, Y.-C. Lee, Y.L. Huang, Y.Y. Chu, D.-C. Yan, and
M.K. Wu, Proc. Nat. Acad. Sci. USA, 105, 14262 (2008).
6. K.-W. Yeh, T.-W. Huang, Y.-L. Huang, T.-K. Chen, F.-C.
Hsu, P.W. Wu, Y.-C. Lee, Y.-Y. Chu, C.-L. Chen, J.-Y. Luo
D.-C. Yan, and M.-K. Wu, Europhys. Lett. 84, 37002 (2008).
7. I.I. Mazin, D.J. Singh, M.D. Johannes, and M.H. Du, Phys.
Rev. Lett. 101, 057003 (2008).
8. H. Kontani and S. Ohari, Phys. Rev. Lett. 104, 157001 (2010).
9. R. Prozorov and V.G. Kogan, Rep. Prog. Phys. 74, 124505
(2011).
10. Handbook of Superconducting Materials: Characterization,
Application and Cryogenics, D.A. Cardwell and D.S. Ginley
(eds.) Institute of Physics (2003).
11. Hideyuki Takahashi, Yoshinori Imai, Seiki Komiya, Ichiro
Tsukada, and Atsutaka Maeda, Phys. Rev. B 84, 132503
(2011).
12. Y. Wu, S.Y. Zhou, X.Y. Wang, L.X. Cao, X.Q. Zhang,
S. Luo, Y.S. He, A.A. Barannik, N.T. Cherpak, and V.N.
Skresanov, IEEE Trans. Appl. Supercond. 21, 599 (2011).
13. A.A. Barannik, N.T. Cherpak, N. Ni, M.A. Tanatar, S.A.
Vitusevich, V.N. Skresanov, P.C. Canfield, R. Prozorov,
V.V. Glamazdin, and K.I. Torokhtii, Fiz. Nizk. Temp. 37,
912 (2011) [Low Temp. Phys. 37, 725 (2011)].
14. Y. Han, W.Y. Li, L.X. Cao, S. Zhang, B. Xu, and B. Zhao, J.
Phys: Condens. Matter 24, 235702 (2009).
15. Y. Han, W.Y. Li, L.X. Cao, X.Y. Wang, B. Xu, B.R. Zhao,
Y.Q. Cuo, and J.L. Yang, arXiv: 0911.5282.
16. J.J. Wingfield, J.R. Powell, C.E. Gough, and A. Porch, IEEE
Trans. Appl. Superconduct. 7, 2009 (1997)
17. N.T. Cherpak, A.A. Barannik, Yu. Filipov, Yu. Prokopenko,
and S. Vitusevich, IEEE Trans. Appl. Supercond. 13, 3570
(2003)
18. D.A. Bonn, Ruixing Liang, T.M. Riseman, D.J. Baar, D.C.
Morgan, Kuan Zhang, P. Dosanjh, T.L. Duty, A. Mac-
Farlane, G.D. Morris, J.H. Brewer, W.N. Hardy, C. Kallin,
and A.J. Berlinsky, Phys. Rev. B 47, 11314 (1993).
19. S. Hensen, G. Muller, C.T. Rieck, and K. Scharnberg, Phys.
Rev. B 56, 6237 (1997).
20. A. Barannik, S. Bunyaev, and N. Cherpak, Fiz. Nizk. Temp.
34, 1239 (2008) [Low Temp.Phys. 34, 977 (2008)].
21. H. Kim, C. Martin, R.T. Gordon, M.A. Tanatar, J. Hu, B. Qian,
Z.Q. Mao, Rongwei Hu, C. Petrovic, N. Salovich, R. Giannetta,
and R. Prozorov, Phys. Rev. B 81, 180503(R) (2010).
22. P.K. Biswas, G. Balakrishnan, D.M. Paul, C.V. Tomy, M.R.
Lees, and A.D. Hillier, Phys. Rev. B 81, 092510 (2010).
23. N.V. Perunov, A.F. Shevchun, N.D. Kushch, and M.R.
Trunin, JETP Lett. 96, 184 (2012)
24. H. Kim, R.T. Gordon, M.A. Tanatar, J. Hua, U. Welp, W.K.
Kwok, N. Ni, S.L. Budko, P.C. Canfield, A.B. Vorontsov,
and R. Prozorov, Phys. Rev. B 82, 060518 (2010).
25. A.B. Vorontsov, M.G. Vavilov, and A.V. Chubukov, Phys.
Rev. B 79, 140507 (2009).
26. D.A. Bonn, P. Dosanjh, R. Liang, and W.N. Hardy, Phys.
Rev. Lett. 68, 2390 (1992).
27. T. Shibauchi, A. Maeda, H. Kitano, T. Honda, and K. Uchi-
nokura, Physica C 203, 305 (1992).
28. K. Hashimoto, T. Shibauchi, S. Kasahara, K. Ikada, S. Tone-
gawa, T. Kato, R. Okazaki, C.J. van der Beek, M. Konc-
zykowski, H. Takeya, K. Hirata, T. Terashima, and Y. Mat-
suda, Phys. Rev. Lett. 102, 207001 (2009).
29. A. Barannik, N.T. Cherpak, M.A. Tanatar, S. Vitusevich,
V. Skresanov, P.C. Canfield, and R. Prozorov, Phys. Rev. B
014506 (2013).
30. E. Schachinger and J.P. Carbotte, Phys. Rev. B 80, 174526
(2009).
31. K. Cho, H. Kim, M.A. Tanatar, J. Hu, B. Qian, Z.Q. Mao,
and R. Prozorov, Phys. Rev. B 84, 174502 (2011).
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