Superconducting order parameter fluctuations in NbN/NiCu and NbTiN/NiCu bilayer microstripes for photon detection a b Klimov ,
a c Pu¹niak ,
a b Sªysz ,
a b Marek Guziewicz , d Roman Sobolewski
a,* , b Kruszka ,
Bernd Aichner , Florian Jausner , Georg Zechner , Rita Mühlgassner , Wolfgang Lang Andrii
Roman
Wojciech
b
Maciej W¦grzecki , and
Renata
a University of Vienna, Faculty of Physics, AT-1090 Wien, Austria b Institute of Electron Technology, PL-02-668 Warszawa, Poland
c Institute
of Physics, Polish Academy of Sciences, PL-02-668 Warszawa, Poland
d University
of Rochester, Rochester, NY 14627-0231, USA
ABSTRACT Thermodynamic uctuations of the superconducting order parameter in NbN/NiCu and NbTiN/NiCu superconductor/ferromagnet (S/F) thin bilayers patterned to microbridges are investigated. Plain NbN and NbTiN lms served as reference materials for the analyses.
The samples were grown using dc-magnetron sputtering
on chemically cleaned sapphire single-crystal substrates. After rapid thermal annealing at high temperatures, the superconducting lms were coated with NiCu overlays, using co-sputtering. The positive magnetoresistance of the superconducting single layers is very small in the normal state but with a sharp upturn close to the superconducting transition, a familiar signature of superconducting uctuations. The uctuation-enhanced conductivity (paraconductivity) of the NbN and NbTiN single layer lms is slightly larger than the prediction of the parameter-free Aslamazov-Larkin theory for order-parameter uctuations in two-dimensional superconductors. The addition of a ferromagnetic top layer, however, changes the magnetotransport properties signi cantly. The S/F bilayers show a negative magnetoresistance up to almost room temperature, while the signature of uctuations is similar to that in the plain lms, demonstrating the relevance of both ferromagnetic and superconducting eects in the S/F bilayers. The paraconductivity is reduced below theoretical predictions, in particular in the NbTiN/NiCu bilayers. Such suppression of the uctuation amplitude in S/F bilayers could be favorable to reduce dark counts in superconducting photon detectors and lead the way to enhance their performance.
Keywords:
superconducting order-parameter uctuations, paraconductivity, NbN/NiCu, NbTiN/NiCu, super-
conductor/ferromagnet bilayers, superconducting photon detectors
1. INTRODUCTION A key performance gure of superconducting single-photon detectors (SSPDs) is a low dark count rate, i.e., the spurious output signals without absorption of optical photons. The functional principle of these detectors requires that they are operated very close to the critical current to allow for the formation of a resistive hotspot
1, 2
after incidence of a photon.
In general, operation of a superconductor near the phase transition into the normal state is in uenced by
3 Strong uctuations can locally suppress
thermodynamic uctuations of the superconducting order parameter.
superconductivity and, thus, trigger unwanted output signals. Even though analysis of uctuations is impracticable below the critical temperature
Tc ,
because the superconducting condensate shields them in electrical
transport measurements, they can be probed conveniently above
46
Tc
by various measurement techniques and in
particular with electrical transport measurements.
In fact, superconducting order parameter uctuations have been identi ed
7 as the primary origin of dark
counts in SSPDs when they are operated near their critical current, i.e., at a bias current
* Further author information: (Send correspondence to W.L.) W.L.: E-mail:
[email protected], Telephone: +43 1 4277 51424
Ib > 0.95 Ic .
At
lower
Ib
the thermally activated unbinding of vortex-antivortex pairs originating from the Berezinskii-Kosterlitz-
Thouless (BKT) mechanism appears to dominate. Additional eects, like nucleation of vortices at the edges of the superconducting stripe and their mobilization might be also important.
8
Recently, it was found that an ultrathin, weak-ferromagnetic cap layer on the top of a superconducting lm can enhance the structure's
Ic
due to additional ux pinning and also improves the dark-count rate.
9 Proximity
10 and results obtained on S/F bilayers indicate eects in superconductor/ferromagnet (S/F) heterostructures 11, 12 many interesting interactions between these two macroscopic quantum phenomena. In this paper, we present an investigation of superconducting order parameter uctuations above
Tc
via an
analysis of the paraconductivity the excess conductivity caused by the ickering superconducting bubbles that are created by thermodynamic uctuations in the normal state.
Comparing the results of S/F bilayers
with reference data in plain S layers allows us to demonstrate an in uence of the F overlay on the uctuation amplitude in the S layer.
2. THEORETICAL BACKGROUND: SUPERCONDUCTING ORDER PARAMETER FLUCTUATIONS The order parameter in the Ginzburg-Landau theory is subject to thermodynamic uctuations, leading to the socalled superconducting uctuations. They manifest themselves in an intrinsic broadening of the superconducting transition due to appearance of short-lived superconducting regions above and normal-conducting ones below the critical temperature of
Tc
Tc .
Superconducting uctuations in uence virtually all physical quantities in the vicinity
and are commonly investigated via an additional contribution to the electric conductivity, the so-called
paraconductivity or an enhanced magnetic susceptibility above
Tc .
The amplitude of such uctuations increases
with smaller zero-temperature Ginzburg-Landau coherence length
ξ(0)
and with reduced dimensionality and
is, thus, almost negligible in bulk metallic superconductors. Conversely, in cuprate superconductors with their small and anisotropic
ξ(0)
and in ultrathin, 2-dimensional (2D) superconducting metallic lms or 1D whiskers,
uctuations can be remarkably strong.
For these reasons, superconducting uctuations provide a convenient
3
route to investigate the coherence length and the dimensionality of a superconductor. In our thin lms, the typical length scales are stripe with a length
l
larger than
w.
w > ξ(0) & d, where w is the width ∆σ is determined by
∆σ = where
ρ
and
d
the thickness of a
The paraconductivity
is the measured resistivity and
ρN
1 1 − N , ρ ρ
(1)
the resistivity in the normal state. In most cases the latter cannot
be determined experimentally and, thus, is commonly inferred by extrapolation from resistivity values measured at
T > 2Tc ,
where superconducting uctuations should be negligible. Evidently, this procedure introduces some
uncertainty into the analysis. The dominant uctuation mechanism contributing to paraconductivity in the vicinity of Aslamazov and Larkin
Tc
was derived by
13 (AL) and depends on the geometric constrictions of the sample with respect to the
temperature-dependent coherence length
ξ(T ) = ξ(0)(1 − T /Tc )−1/2 .
The 1D expression of the paraconductivity
πe2 ξ(0) , 16~dw3/2
(2)
e2 , 16~d
(3)
e2 , 32~ξ(0)1/2
(4)
is then given by
∆σ AL(1D) = the 2D expression by
∆σ AL(2D) = and the 3D one by
∆σ AL(3D) = where
e
is the elementary charge,
~
is the reduced Planck constant, and
temperature. Note that the 2D-AL expression (Eq. 3) is
universal
= ln(T /Tc ) ≈ (T − Tc )/Tc
a reduced
(independent of the material) and, thus, can
serve as a direct test of the applicability of the classic uctuation theory.
A magnetic eld
B
leads to a reduction of the uctuation amplitude by several processes, giving rise to a
magnetoresistance eect. The most prominent is an orbital interaction with the Aslamazov-Larkin mechanism (ALO) that is operative for Abrahams
et al.14
B
oriented perpendicular to the lm surface and dominates near
Tc .
According to
the paraconductivity in the 2D case is reduced to
ALO(2D)
∆σB
=
1 h e2 [ψ( + ) − ψ(1 + )+ ] 8~d h2 2 2h 2h
2eξ(0)2 B is a reduced magnetic eld and ψ is the ~ is the only adjustable material-dependent parameter. Other contributions to the
in the presence of a perpendicular magnetic eld, where digamma-function. Here,
ξ(0)
(5)
h=
MR, like a Zeeman interaction, are much smaller in the vicinity of
Tc .15
In clean superconductors with a long mean free path of the charge carriers, the lifetime of superconducting uctuations is enhanced over the AL mechanism, giving rise to additional uctuation contributions derived by
16 and Thompson17 (MT). The 2D paraconductivity is given by
Maki
∆σ M T (2D) = where
δ
e2 , ln 8~d( − δ) δ
(6)
is a pair-breaking parameter that re ects the limitation of the phase relaxation time of the quasiparticles
involved in the MT process.
3. EXPERIMENTAL METHODS Superconducting NbN lms were grown on chemically cleaned sapphire single-crystal substrates by high-temperature, reactive RF magnetron sputtering from Nb targets in N2 -Ar gas mixture at a temperature of
850◦ C.
The
NbTiN lms were deposited from metallic Nb and Ti targets by co-sputtering. In order to improve their superconducting properties all samples were, subsequently, annealed at
≈ 1000◦ C,
using a rapid thermal annealing
(RTA) process. The superconductor/ferromagnet (S/F) bilayers were produced by an additional deposition process on top of the pre-fabricated metallic lms. First, the surfaces of the NbN or NbTiN lms were cleaned using ion-beam etching and then coated with NiCu overlays by co-sputtering. The composition of the deposited F layers was analysed by EDX spectroscopy and reference NiCu lms showed a Curie temperature of
≈ 30
K indicating
weak ferromagnetism. Preparation and characterization of our samples is described in more detail in previous
1820 Finally, the lms (thicknesses are subsequently given in parentheses) were lithographically
publications.
patterned to various microbridges with dimensions ranging from 0.7 to
12 µm
width and
33 µm
to 2.77 mm
length. Separated current and voltage contact pads were established on top of the lms, i.e., for the S/F bilayers on top of the F layer and connected using Au wires and Ag paste. The electrical transport measurements were conducted either in a dipstick inserted in a helium dewar, or in a closed-cycle refrigerator equipped with a LakeShore 340 temperature controller and Rhodium-Iron and Cernox thermometers.
21
an electromagnet and oriented perpendicular to the sample surface.
The four-probe DC measurements were
The magnetic eld was supplied by
performed employing a Keithley 6221 current source and a Keithley 2182A nanovoltmeter, reversing the current for every data point to exclude spurious thermoelectric voltages. In magnetoresistance measurements the polarity of the magnetic eld was reversed. The entire setup was computer-controlled and allowed for the collection of multiple data to enhance the signal to noise ratio.
4. RESULTS AND DISCUSSION First, we demonstrate, how the addition of the F top layer changes the transport properties in the normal state.
In fact, the magnetoresistance (MR)
∆ρ/ρ0 = [ρ(B) − ρ(B = 0)]/ρ(B = 0)
is signi cantly dierent
in the S (NbN and NbTiN) lms and the S/F (NbN/NiCu and NbTiN/NiCu) bilayers, as is illustrated in Fig. 1. All MR curves show a similar sharp upturn in the vicinity of
Tc
due to the magnetic- eld suppression
of superconducting uctuations. In the normal state, however, the S lms have vanishing MR, while the S/F
1 x 1 0
-3
N b N N b N /N iC u
(a ) -4
1 x 1 0
-3
5 x 1 0
-4
N b T iN N b T iN /N iC u
∆ /
2 x 1 0
-3
0
0
∆ /
-3
(b )
0
5 x 1 0
2 x 1 0
-5 x 1 0
-4
-1 x 1 0
-3
0
-5 x 1 0 0
5 0
1 0 0
1 5 0
2 0 0
2 5 0
3 0 0
-4
0
5 0
1 0 0
T e m p e ra tu re (K )
1 5 0
2 0 0
2 5 0
3 0 0
T e m p e ra tu re (K )
Figure 1. (a) Comparison of the magnetoresistance of a plain NbN(4.8 nm) lm and a NbN(6 nm)/NiCu(6 nm) bilayer in a magnetic eld B = 0.9 T. (b) Corresponding data for NbTiN(3.9 nm) and a NbTiN(7 nm)/NiCu(6 nm) bilayer. bilayers exhibit a negative MR over a wide temperature range that increases towards lower temperatures. The particular characteristics of the negative MR appears compatible with a Curie temperature of approximately
20 but its temperature dependence follows the theoretical predictions22 for
30 K found in reference NiCu lms,
spin- uctuation induced negative MR only qualitatively. In the normal state, the S/F bilayers can be regarded as a system with two parallel-shunted conduction channels (the S and the F layers) and, hence, it is expected that the negative MR results from conduction along the F channel. Conversely, the sharp upturn of MR and its change to positive values indicates that the S channel starts to dominate the transport properties already at
T & Tc .
At
T < Tc ,
the F layer is dominated
by the superconducting proximity eect. After all, a signi cant in uence of the F top layer on superconducting uctuations can be envisaged.
40 K > T > 2Tc ρN (38 K) = 1.215 µΩm.
The resistivity of the plain NbN lm is almost temperature independent at paraconductivity was calculated according to Eq. 1 using a constant
5
1 0
4
in the
6
1 0
5
1 0
4
(b )
1 0
-1
∆σ ( Ω- 1 m
-1
∆σ ( Ω- 1 m
Tc
) 1 0
)
6
(a )
1 0
and, thus, the The
N b N
N b N /N iC u
P a r a c o n d u c tiv ity 2 D -A L th e o ry
0 .0 1
0 .1
ln ( T /T c )
P a r a c o n d u c tiv ity 2 D -A L th e o ry
0 .0 1
0 .1
ln ( T /T c )
Figure 2. (a) Experimentally determined paraconductivity of the NbN(4.2 nm) plain lm as a function of the reduced temperature (symbols). The line indicates the prediction of the 2D AL theory (Eq. 3) without adjustable parameter. (b) Paraconductivity of the NbN(4.2 nm)/NiCu(3.5 nm) bilayer sample as a function of the reduced temperature.
uctuation theory is a mean- eld value that has no obvious signature in the transition curve.
According to
common practice, we have used the in ection point of the superconducting transition curve to obtain the value for
Tc
to determine the reduced temperature
.
The purpose of this strategy is to exclude any ambiguity in the
evaluation of the experimental data. This is crucial for our comparison, since the 2D AL expression (Eq. 3) has no adjustable parameter. The data are compared to the theoretical prediction in Fig. 2(a). The critical exponents (the slopes in the log-log plot) are in excellent agreement, con rming the 2D nature of the superconducting uctuations. decline of
∆σ
> 0.4 can be caused by our choice of ρN that = 1.0 (T = 38 K) and has no bearing on our analysis.
below theoretical predictions for
leads to an apparent cut-o
∆σ = 0
at
the experimental paraconductivity is about 1.8 times larger than theoretically predicted. parameter that possibly has a relevant uncertainty, is the thickness of our lms.
The
inherently However,
Note that the only
But it enters the same way
in the calculation of the paraconductivity and in Eq. 3, so that in fact our conclusion is unaected by the lm thickness. Paraconductivity in excess over AL theory has been observed in clean superconductors and is attributed to the MT process (Eq. 6). With an added thin F top layer,
3, 6
Tc
of the NbN(4.2 nm)/NiCu(3.5 nm) bilayer lm is reduced by about 0.6 K,
but the paraconductivity remains essentially unchanged, as displayed in Fig. 2(b). Note that for determining
∆σ ,
the conductivity of the NiCu top layer had to be subtracted, introducing some uncertainty of the absolute
values of
∆σ .
Nevertheless, the critical exponent is well-de ned and again
∆σ ∝ −1 ,
in agreement with the 2D
AL theory. On the other hand, in a sample with a thicker F layer, NbN(6 nm)/NiCu(6 nm), the paraconductivity is suppressed (see Fig. 3). For lm,
∆σ
> 0.02
the data t well to the 2D AL theory, but note that in the plain NbN
was in excess over the theoretical curve what is not seen here. At lower temperatures
paraconductivity drops below the 2D-AL prediction.
< 0.02,
the
As a possible explanation, we propose the in uence of
ferromagnetic domains in the NiCu top layer. Such domain patterns of 100 nm average size have been observed
23
in weakly ferromagnetic Cu0.47 Ni0.53 thin lms.
Then, it follows from Eq. 5 that the paraconductivity is
reduced in a magnetic eld. Since the orientation of the magnetic eld plays no role, every magnetic domain can contribute to the suppression of
∆σ ,
t, according to Eq. 5 and assuming
even if the overall magnetization of the F layer is zero. A corresponding
|BF M | = 0.2
T and
ξ(0) = 4.7
nm is shown as a full line in Fig. 3 and ts
the data quite well.
5
1 0
4
∆σ ( Ω- 1 m
-1
)
1 0
N b N /N iC u P a r a c o n d u c tiv ity 2 D -A L O th e o ry 2 D -A L th e o ry
1 0
3
0 .0 1
0 .1
ln ( T /T c ) Figure 3. Experimental paraconductivity of the NbN(6 nm)/NiCu(6 nm) bilayer sample as a function of the reduced temperature (symbols). The broken line represents the parameter-free 2D AL theory, the full line the 2D-ALO theory (Eq. 5) with ξ(0) = 4.7 nm and |BF M | = 0.2 T.
)
6
1 0
5
1 0
4
∆σ ( Ω- 1 m
-1
1 0
N b T iN P a r a c o n d u c tiv ity 2 D -A L th e o ry
1 0
3
0 .0 1
0 .1
ln ( T /T c ) Figure 4. Experimental paraconductivity of the NbTiN(3.9 nm) plain lm as a function of the reduced temperature (symbols). The line represents the 2D AL theory (Eq. 3) without adjustable parameter. The paraconductivity of the NbTiN(3.9 nm) sample is shown in Fig. 4 and is essentially similar to that of NbN. Again, we observe a critical exponent
∆σ ∝ −1
over a wide range of the reduced temperature, but here
the paraconductivity exceeds the theoretical prediction by a factor of 1.2 only. The NbTiN sample has a higher normal state resistance
ρN (38 K) = 2.53 µΩm as compared to the NbN lm,
which indicates a shorter mean free
carrier path and would lead to a reduced MT uctuation contribution. In a S/F bilayer sample,
Tc
is reduced by about 0.7 K and the paraconductivity, as seen in Fig. 5, is
substantially altered. Here, the data indicate a smaller uctuation contribution in the major parts of the reduced temperature range and no straightforward critical exponent can be identi ed. The experimental paraconductivity reaches the predicted value only in a narrow temperature range around We have to distinguish two temperature regions. is
∆σ ∝ −3/2
≈ 0.05.
At high temperatures
> 0.07,
the critical exponent
equivalent to the 1D AL theory of Eq. 2 and shown as a dotted line in Fig. 5.
A tentative
explanation of this behavior could be provided by the observation of maze-like ferromagnetic domains mentioned above.
23 Since a magnetic eld suppresses paraconductivity, one can speculate that 1-D uctuation channels
might survive below the magnetic grain boundaries, where the stray eld is smallest. At lower temperatures
< 0.05,
the paraconductivity drops dramatically below both 2D-AL and 1D-AL
predictions. Again, we invoke the in uence of ferromagnetic domains in the NiCu top layer and t to Eq. 5, assuming
|BF M | = 0.5
T and
ξ(0) = 4.7
nm, shown as a full line in Fig. 5. The
|BF M |
used in this t appears to
be larger than previous magnetization measurements on 6-nm-thick NiCu lms and NbTiN(6 nm)/NiCu(6 nm) bilayers.
20 However, they probed the overall magnetization with the magnetic eld oriented parallel to the lms
and, thus, the local magnitization of individual domains might be larger. In addition, a slight hump that can be noticed in the paraconductivity of the NbN/NiCu bilayer around (see Fig. 3) and in that of the NbTiN/NiCu bilayer around
≈ 0.4
≈ 0.2
(see Fig. 5) points to a another deviation
from a plain critical-exponent behavior due to minor inhomogeneities in the samples causing a distribution of
Tc 's.24
Similar, but more pronounced structures, have been observed in cuprate superconductors.
5
5. CONCLUSIONS We have investigated the paraconductivity above
Tc in NbN and NbTiN thin lms and found that its temperature
dependence follows the parameter-free AL theory for 2D superconductors well. The paraconductivity was slightly above predictions, indicating a contribution from MT type uctuations.
5
1 0
4
∆σ ( Ω- 1 m
-1
)
1 0
N b T iN /N iC u P a 2 D 2 D 1 D
1 0
ra c -A L -A L -A L
o n O th th
d u c tiv ity th e o ry e o ry e o ry
3
0 .0 1
0 .1
ln ( T /T c ) Figure 5. Experimental paraconductivity of the NbTiN(7 nm)/NiCu(6 nm) bilayer lm as a function of the reduced temperature (symbols). The broken and dotted lines indicate the critical exponents of the 2D and 1D Al theory, respectively. The full line is a r to the 2D-ALO theory (Eq. 5) with ξ(0) = 4.7 nm and |BF M | = 0.5 T. These results served as reference for investigating the paraconductivity of S/F-bilayer samples, NbN and NbTiN with a NiCu overlay. Whereas paraconductivity of NbN(4.2 nm)/NiCu(3.5 nm) samples indicated almost no in uence of the NiCu top layer on the uctuation amplitude, a reduction of paraconductivity near found in NbN(6 nm)/NiCu(6 nm) samples with a roughly twice as thick NiCu overlay.
Tc
was
The suppression of
paraconductivity is even more pronounced in NbTiN(7 nm)/NiCu(6 nm) bilayers, indicating a strong in uence of the F layer on the superconductor. Also, the temperature dependence of magnetoresistance demonstrates this interaction.
An unusual negative magnetoresistance in the S/F bilayers extends almost to room temperature
and is not present in the S single layers. Finally, reduced thermodynamic order-parameter uctuations might be favorable for a lower dark-count rate in SSPDs biased close to the critical current and, hence, NbTiN/NiCu bilayers might be a good candidate for the fabrication of SSPDs with enhanced performance.
ACKNOWLEDGMENTS We appreciate elucidating correspondence with A. I. Buzdin and A. A. Varlamov.
The authors acknowledge
the European Union COST Action MP1201. This work was partly supported by the European Union within the European Regional Development Fund, through the Innovative Economy Grant (POIG.01.01.02-00-108/09, "MIME"). Research in Rochester has been supported in part by the grant from the HYPRES Co., and by the New York State Advanced Technology Centers for Innovative and Enabling Technologies (University of Rochester) and Advanced Sensor Technologies (Stony Brook University).
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