On the determination of the quasiparticle scattering rate in unconventional superconductors by microwave surface impedance
As found from numerous microwave experiments on the unconventional Fe-based superconductors, the temperature dependence of the quasiparticle scattering rate t⁻¹ cannot be accurately described within the framework of standard Drude module in the popular approximation of wt << 1, where w is the...
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Cherpak, N.T. Barannik, A.A. Prozorov, R. Tanatar, M. Velichko, A.V. 2017-06-01T09:54:13Z 2017-06-01T09:54:13Z 2013 On the determination of the quasiparticle scattering rate in unconventional superconductors by microwave surface impedance / N.T. Cherpak, A.A. Barannik, R. Prozorov, M. Tanatar, A.V. Velichko // Физика низких температур. — 2013. — Т. 39, № 12. — С. 1423–1425. — Бібліогр.: 25 назв. — англ. 0132-6414 PACS: 74.25.nn, 74.70.Xa https://nasplib.isofts.kiev.ua/handle/123456789/118928 As found from numerous microwave experiments on the unconventional Fe-based superconductors, the temperature dependence of the quasiparticle scattering rate t⁻¹ cannot be accurately described within the framework of standard Drude module in the popular approximation of wt << 1, where w is the signal frequency. To account for the discrepancy, we have extended the classical Drude model for the case of arbitrary values of wt, and obtained the expression for t⁻¹ as a function of experimentally measurable quantities, namely the real and imaginary parts of the microwave surface impedance. We then show the temperature dependence of t⁻¹ in supercon-ducting Ba(Fe₁–xCox)₂As₂ single crystal pnictide derived from the Ka-band surface impedance measurements within the framework of the modified expression. The measurements indicate the extent to which assumption of wt << 1 gives results different from those obtained without this restriction, i.e., incorrect results. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Краткие сообщения On the determination of the quasiparticle scattering rate in unconventional superconductors by microwave surface impedance Article published earlier |
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On the determination of the quasiparticle scattering rate in unconventional superconductors by microwave surface impedance |
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On the determination of the quasiparticle scattering rate in unconventional superconductors by microwave surface impedance Cherpak, N.T. Barannik, A.A. Prozorov, R. Tanatar, M. Velichko, A.V. Краткие сообщения |
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On the determination of the quasiparticle scattering rate in unconventional superconductors by microwave surface impedance |
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On the determination of the quasiparticle scattering rate in unconventional superconductors by microwave surface impedance |
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On the determination of the quasiparticle scattering rate in unconventional superconductors by microwave surface impedance |
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On the determination of the quasiparticle scattering rate in unconventional superconductors by microwave surface impedance |
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on the determination of the quasiparticle scattering rate in unconventional superconductors by microwave surface impedance |
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Cherpak, N.T. Barannik, A.A. Prozorov, R. Tanatar, M. Velichko, A.V. |
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Cherpak, N.T. Barannik, A.A. Prozorov, R. Tanatar, M. Velichko, A.V. |
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Краткие сообщения |
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Краткие сообщения |
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2013 |
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Физика низких температур |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Article |
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As found from numerous microwave experiments on the unconventional Fe-based superconductors, the temperature dependence of the quasiparticle scattering rate t⁻¹ cannot be accurately described within the framework of standard Drude module in the popular approximation of wt << 1, where w is the signal frequency. To account for the discrepancy, we have extended the classical Drude model for the case of arbitrary values of wt, and obtained the expression for t⁻¹ as a function of experimentally measurable quantities, namely the real and imaginary parts of the microwave surface impedance. We then show the temperature dependence of t⁻¹ in supercon-ducting Ba(Fe₁–xCox)₂As₂ single crystal pnictide derived from the Ka-band surface impedance measurements within the framework of the modified expression. The measurements indicate the extent to which assumption of wt << 1 gives results different from those obtained without this restriction, i.e., incorrect results.
|
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0132-6414 |
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https://nasplib.isofts.kiev.ua/handle/123456789/118928 |
| citation_txt |
On the determination of the quasiparticle scattering rate in unconventional superconductors by microwave surface impedance / N.T. Cherpak, A.A. Barannik, R. Prozorov, M. Tanatar, A.V. Velichko // Физика низких температур. — 2013. — Т. 39, № 12. — С. 1423–1425. — Бібліогр.: 25 назв. — англ. |
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© N.T. Cherpak, A.A. Barannik, R. Prozorov, M. Tanatar, and A.V. Velichko, 2013
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 12, pp. 1423–1425
Краткие сообщения
On the determination of the quasiparticle scattering rate
in unconventional superconductors by microwave surface
impedance
N.T. Cherpak
1
, A.A. Barannik
1
, R. Prozorov
2,3
, M. Tanatar
2
, and A.V. Velichko
1
1
A. Usikov Institute of Radiophysics and Electronics of the National Academy of Sciences of Ukraine
12 Acad. Proskura Str., Kharkiv 61085, Ukraine
E-mail: cherpak@ire.kharkov.ua
2
Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA
3
Ames Laboratory USDOE, Ames, IA 50011, USA
Received July 16, 2013
As found from numerous microwave experiments on the unconventional Fe-based superconductors, the tem-
perature dependence of the quasiparticle scattering rate
–1
cannot be accurately described within the framework
of standard Drude module in the popular approximation of 1, where is the signal frequency. To account
for the discrepancy, we have extended the classical Drude model for the case of arbitrary values of , and ob-
tained the expression for
–1
as a function of experimentally measurable quantities, namely the real and imagi-
nary parts of the microwave surface impedance. We then show the temperature dependence of
–1
in supercon-
ducting Ba(Fe1–xCox)2As2 single crystal pnictide derived from the Ka-band surface impedance measurements
within the framework of the modified expression. The measurements indicate the extent to which assumption of
1 gives results different from those obtained without this restriction, i.e., incorrect results.
PACS: 74.25.nn Surface impedance;
74.70.Xa Pnictides and chalcogenides.
Keywords: quasiparticle conductivity, microwave surface impedance, Fe-pnictide.
Studying the temperature dependence of the quasi-
particle scattering rate
–1
offers a great insight into the
underlying physics of superconductors. Here, the absolute
value and the temperature dependence of
–1
reflect very
important characteristics of the electron system of the ma-
terials [1]. Of particular interest is studying the electron
system in the unconventional superconductors (in particu-
lar the high-Tc cuprates and Fe-based superconductors),
and recently a plethora of various experimental techniques
covering a wide range of signal frequencies have been used
to accomplish this purpose (see, e.g., [2–5]). Supercon-
ducting single crystals and films were measured using dc
signal by, e.g., magnetic-force microscopy and scanning
SQUID [6,7]. Measurements by means of radio-frequency
tunnel-diode resonators [8–10], microwave-range reso-
nance cavities [11–15] as well as THz and optical reflectiv-
ity [16,17] techniques have also been reported.
As far as microwave measurements are concerned, once
can use surface impedance data to extract complex conduc-
tivity of the superconductor which, in case, gives us an
opportunity to extract the temperature-dependent London
penetration depth L and the quasiparticle scattering rate
–1
.
In addition, since the scattering in the normal state is di-
rectly related to the superconducting pairing strength [18],
extension of those measurements into a superconducting
state is of notable interest.
Apparently, microwave and higher frequency meas-
urements are the only kind of experiments that allow one
to determine the complex conductivity in a superconduct-
ing state [19], which in turn can be used to extract
–1
and
the interesting fact is that the values of have been found
to dramatically increase in the unconventional supercon-
ductors (see, e.g., [20]).
The task of finding is usually straightforward in the
case of
<< 1, however in the unconventional super-
conductors where
–1
is strongly temperature-dependent
[11–14], and as the signal frequencies increase towards
the millimeter wave range [15], researches often come
across the difficulty of processing the experimental data
for the case of arbitrary values.
N.T. Cherpak, A.A. Barannik, R. Prozorov, M. Tanatar, and A.V. Velichko
1424 Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 12
In this paper we address the problem of obtaining the
generalized expression for the quasiparticle scattering rate
in terms of microwave surface impedance valid for arbi-
trary values of , and then extract the temperature de-
pendence of in the experimentally measured single
crystal of BaFeCoAs.
Within framework of the local electrodynamics, micro-
wave surface impedance of the conducting materials is
determined as (in SI) [21]
0 ,s s s
i
Z = R iX (1)
where is the frequency of electromagnetic field, which
varies as e
i t
; 0 is the magnetic permeability of vacuum;
is the microwave conductivity, which is a complex value
– ;i sR and sX are surface resistance and reac-
tance of the conductor. Using different techniques of
measurements in the microwave range, one can accurately
determine experimentally values of sR and sX (see, e.g.,
[19,22]), which in turn determine the conductivity .
According to the two-fluid model there are two cur-
rents: a superconducting current, conditioned by superfluid
component, and the normal current attributed to quasi-
particles. Correspondingly, the conductivity in (1) can be
written as [23]
2
,
1
s n
s n
n ne
i
m i i
(2)
where – ,l li nn and sn are electron concentration
of quasiparticle and superfluid components accordingly,
,n sn n n where n is constant; e and m are the charge
and mass of electrons. The conductivity n is written in
the assumption of validity of the Drude model.
We now need to express the conductivity (2) in terms of
( )sR T and ( )sX T because these are the quantities meas-
ured in the experiments:
0 4
2 ,s s
s
X R
Z
2 2
0 4
,s s
s
X R
Z
(3)
where
4 2 2 2( ) .s s sZ X R
It is worth noting that at << 1 the conductivity can
be written in the form
2
1 2 1 2; 0; .s
n s
ne
n i i i
m
(4)
At arbitrary values of , on the other hand, from (2) and
(4) we obtain
1 2
1 2 1 22 2 2 2
; ,
1 1
(5)
where 2 2
0
1
.
( )L T
On the assumption that in the superconducting state at
sufficiently low temperatures (0) 0nn and (0) ,sn n
one can use equations (5) to obtain [23]
2 2
0
1 (0) ( ) 1
; (0) (0) .
( ) ( ) (0)L
T
T T
(6)
Substituting (3) into (6) yields
2 2
2
0 1
1 1
.
2( ) (0)
s s
s sL
X R
X RT
(7)
When << 1 the expression (7) becomes the well known
formula [24]
2 2
2
0 1
1 [ (0)/ ( )]1
.
( ) (0)
L L
L
T
T
(8)
Figure 1 shows the scattering rate in the optimally
doped pnictide single crystal Ba(Fe1–xCox)2As2 [8,9] as a
function of temperature. The data are obtained from Ka-
band microwave impedance measurements by using high
Q-factor quasioptical slotted sapphire resonator (excited in
whispering gallery modes) with YBCO end plates, and the
expressions (7) and (8) are used to process the impedance
measurement data.
It is seen that (7) gives a significant correction in (T)
at low temperatures for exceeding 0.05. In turn, a more
accurate estimate of gives an opportunity to more accu-
rately obtain 2( ),T which is determined by the measured
( )sR T and ( )sX T and offers information about the pene-
tration depth ( )L T and the structure of the superconduct-
ing energy gap [3].
Finally, we should emphasize that the generalized ex-
pression for (Eq. (7)) derived in this work and valid
for arbitrary values of in combination with the novel
Fig. 1. The temperature dependence of the quasiparticle scattering
rate τ
−1
in a single crystal of optimally-doped Ba(Fe1–xCox)2As2
calculated using the generalized expression (7) and expression (8)
valid at << 1. The horizontal dotted line shows τ
−1
for = 0.05.
0 5 10 15 20
10
11
10
12
10
13
10
14
experiment (formula (8))
fitting (formula (8))
experiment (formula (7))
fitting (formula (7))
T, K
On the determination of the quasiparticle scattering rate in unconventional superconductors by microwave surface
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 12 1425
resonator technique with HTS end plates [22,25] enabled
us to study the temperature dependence of the quasiparticle
scattering rate for the whole family of the Fe-based
superconductors including Fe-pnictides [25], Fe-chalco-
genides [14] and others at microwave frequencies.
The authors thank Dr. S.A. Vitusevich, FZ Jülich Peter
Grünberg Institute, Germany, for supporting this research.
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