Boundary effect on superconductivity in long single-crystal superconducting nanowires

Article abstract of DOI:10.1016/j.physc.2007.08.029

We fabricate single-crystal Pb, Sn, and Zn nanowires, of length 6 or 60 μm and diameter 30-250 nm, using an in situ template-based electrochemical method. In this approach, a single nanowire is formed in contact with a pair of bulk film electrodes of Au, Sn, or Pb. We observe that, with superconducting electrodes having a higher critical temperature T_c, superconductivity is induced in Sn and Zn nanowires at the T_c of the electrodes for nanowires as long as 60 μm. With Au electrodes, superconductivity is suppressed completely in 6 μm-long nanowires and partially in 60 μm-long nanowires. Based on transmission electron microscopy studies, the nanowires are single crystalline. Analysis of the temperature dependence of the normalized resistance suggests that the residual-resistance-ratio plays an important role in the observed anomalous long-range proximity effect.

Full text of DOI:10.1016/j.physc.2007.08.029

Available online at www.sciencedirect.com
Physica C 468 (2008) 304–309
www.elsevier.com/locate/physc
Boundary effect on superconductivity in long
single-crystal superconducting nanowires
Haidong Liu a, Zuxin Ye a, Zhiping Luo b, K.D.D. Rathnayaka a, Wenhao Wu a,*
a Department of Physics, Texas A&M University, College Station, Texas 77843, USA
b Microscopy and Imaging Center, Texas A&M University, College Station, Texas 77843, USA
Accepted 16 August 2007
Available online 13 November 2007
Abstract
We fabricate single-crystal Pb, Sn, and Zn nanowires, of length 6 or 60 lm and diameter 30–250 nm, using an in situ template-based
electrochemical method. In this approach, a single nanowire is formed in contact with a pair of bulk film electrodes of Au, Sn, or Pb. We
observe that, with superconducting electrodes having a higher critical temperature Tc, superconductivity is induced in Sn and Zn
nanowires at the Tc of the electrodes for nanowires as long as 60 lm. With Au electrodes, superconductivity is suppressed completely
in 6 lm-long nanowires and partially in 60 lm-long nanowires. Based on transmission electron microscopy studies, the nanowires are
single crystalline. Analysis of the temperature dependence of the normalized resistance suggests that the residual-resistance-ratio plays
an important role in the observed anomalous long-range proximity effect.
Ó 2007 Elsevier B.V. All rights reserved.
PACS: 74.45.+c; 74.78.Na; 81.07.ꢀb; 82.45.Yz
Keywords: Proximity effect; Nanowires; Porous membrane; Electroplating; Microscopy analysis
1. Introduction
0.5 lm when they are in good contact with superconduc-
ting electrodes. It has been shown that this induced super-
conductivity is often a subtle effect, depending sensitively
on the transparency of the interfaces. These observations
can be understood in terms of Andreev reflection [13–15]
at the S–N interface, which describes the leakage of Cooper
pairs from a superconductor into a normal metal. In this
process, electrons above the Fermi level in the normal side
are converted into holes below the Fermi level and Cooper
pairs are formed inside the superconducting side. The elec-
trons and the holes in the normal side form phase-conju-
gated pairs. Coherence is lost at a certain distance from
the interface due to dephasing processes in the normal
metal. This length [16] is given by the coherence length in
the normal metal L/ and the thermal length LT which is
The proximity effect at a superconductor (S) and nor-
mal-metal (N) interface has been studied for decades [1–
4]. For example, for a bilayer of a low Tcl superconductor,
such as Al, and a higher Tch superconductor, such as Pb,
the critical temperature Tc of the bilayer increases gradu-
ally from Tcl to Tch with increasing thickness of the Pb film
on the Al film. One can also consider similar experiments in
which fully normal metals such as Ag can be covered by a
superconductor such as Pb. Recently, the proximity effect
has been studied in sub-micron to nano-sized interfaces.
Of particular interest is the induced superconductivity
observed in carbon nanotubes [5–8], semiconductor nano-
wires [9–11], and graphene sheets [12] of length 0.1–
1=2
2pꢀhvF =kBT in the clean limit and ðꢀhD=kBT Þ in the dirty
limit, where ꢀh is Planck’s constant, kB is the Boltzmann
constant, vF is the Fermi velocity, and D is the electron
diffusivity.
*
Corresponding author. Tel.: +1 979 845 7737; fax: +1 979 845 2590.
E-mail address: wwu@physics.tamu.edu (W. Wu).
0921-4534/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.physc.2007.08.029

H. Liu et al. / Physica C 468 (2008) 304–309
305
In this paper, we describe an induced superconducting
effect in single-crystal Sn and Zn nanowires (NWs) of
length up to 60 lm that are in contact with pairs of super-
conducting electrodes having a higher critical temperature,
Tc. The length of our NWs is much longer than the length
of the samples used in earlier studies of induced supercon-
ductivity in carbon nanotubes [5–8], semiconducting NWs
[9–11], and graphene sheets [12]. It is also much longer than
the thermal lengths discussed above. For example, the ther-
mal length is about 2 lm at 7 K and 3.8 lm at 3.5 K for Sn
in the clean limit. Therefore, the long-range proximity
effect we have observed can not be explained by the picture
discussed above. Our results provide new evidence that a
new mechanism is needed to explain the long-range prox-
imity effect observed in this work as well as in previous
experiments [17–19].
a smaller pore diameter (ꢁ100 nm) can be easily distin-
guished from the rest of the membrane with a pore diame-
ter 200–250 nm. In this paper, we use the typical NW
diameters we observed in microscopy analyses to label
the diameters of NWs fabricated using the same batch of
membranes.
We followed a standard electrodeposition procedure,
except for an in situ contact method which will be discussed
below. For depositing Pb NWs, the electrolyte was a
200 ml solution with 16.2 g Pb(BF4)2 50 wt% solution in
water, 6.72 g HBF4, and 3.0 g HBO3. For depositing Sn
NWs, the electrolyte was prepared by mixing 16.72 g of a
Sn(BF4)2 solution at 50 wt% with 200 ml of water. For
depositing Zn NWs, the electrolyte was prepared by dis-
solving 4.7 g ZnCl2 into 200 ml water. A Pt anode was used
with the reducing potentials relative to an Ag/AgCl refer-
ence electrode being 0.4–0.5 V for Pb, 0.4–0.5 V for Sn,
and 1.1–1.2 V for Zn.
2. Sample fabrication
For carrying out transport measurements on single
NWs, we applied an in situ method to form electric con-
tacts on single NWs. We first evaporated a thick (ꢁ300
nm) Au, Sn, or Pb back electrode on the filter side (see
Fig. 1) of a membrane at a tilted angle. It blocked all the
pores to form the cathode for electroplating. The anode
was placed in the electrochemical cell, facing the other sur-
face of the membrane. Typically, electroplating is initiated
at the cathode and the pores are filled to form NWs as posi-
tive ions drift into the pores. Various groups [20–29] have
used a number of methods to form electric contacts on
NWs for transport studies. We applied an in situ method
[25–27], which allowed us to contact single NWs with a vir-
tually zero contact resistance. In this approach, in addition
to the thick back electrode evaporated on the filter side of a
membrane, we evaporated a relatively thinner (50–200 nm)
front electrode of Au, Sn, or Pb, also at a tilted angle, on
the other surface of the membrane. It blocked most of
the pores and left only a small number of pores open for
electroplating, as illustrated by the left frame in Fig. 2.
We used a voltmeter to monitor the potential difference
V between the two electrodes. During electroplating, V ini-
tially decreased gradually as the open pores were being
filled. When the fastest growing NW made a contact with
the front electrode, a sudden drop in V was observed.
The Pb, Sn, and Zn NWs used for this study were elec-
troplated into porous membranes. Two types of mem-
branes were used: relatively thinner (6 lm) polycarbonate
(PC) membranes with random pore sites and thicker
(60 lm) anodic aluminum oxide (AAO) membranes with
a honeycomb pore arrangement. The PC membranes pro-
duced NWs of length 6 lm and diameters 30–200 nm.
The AAO membranes produced NWs of length 60 lm
and diameters 100–250 nm. The membranes were pur-
chased from Whatman Co. and SPI Supplies Inc. The com-
panies provided the nominal pore diameters for their
membranes. These membranes are typically used as filters.
As such, the labeled nominal pore diameter reflects the
pore diameter in a thin filter layer (ꢁ0.4 lm for PC mem-
branes and ꢁ1.5 lm for AAO membranes). For the thicker
part of a membrane, the pore diameter is larger. Fig. 1
shows a transmission electron microscopy (TEM) cross-
section image of a slice of an AAO membrane prepared
by ultramicrotomy. The nominal diameter of the pores
was 100 nm. In the TEM image, the thinner filter layer with
Fig. 1. Cross-section TEM image of a slice of an AAO membrane. The
dashed line separates the thinner filter layer having a smaller pore
diameter from the rest of the membrane. NWs remaining in their original
channels appear as dark contrast. The dark layer at the top is a portion of
a Pb back electrode.
Fig. 2. Left frame illustrates our in situ technique for contacting single
NWs. Right frame shows the voltage between the front and the back
electrode during electroplating.

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H. Liu et al. / Physica C 468 (2008) 304–309
Electrodeposition was then terminated to obtain a sample
having a single NW whose ends were in contact with the
back and the front electrodes. Resistance measurements
were done with each electrode connected to two measuring
wires in a pseudo four-probe configuration to eliminate the
resistance of the measuring wires. The results were typically
in good agreement [27] with the expected resistance values
for single NWs calculated using the dimensions of the NWs
and the bulk resistivity of the materials. We believe this
in situ method produces virtually ideal contacts between a
NW and the electrodes with a nearly perfect transparency
at the interfaces, probably due to an atomic-scale inter-dif-
fusion layer at the interface. We note that the contact
formed between a NW and the back electrode is far more
stable then the contact formed between a NW and the front
electrode. Thus, we used the filter side of the membrane for
the back electrode and the other side with a larger pore
diameter for the front electrode.
3. Structure and composition analysis
Fig. 3. Top: TEM image of a Zn NW with selected area electron
diffraction. Bottom: EDS taken from the Zn NW. The C and Cu peaks
were from the TEM sample grid. The O peak was likely from an oxide
layer on the NW. Peaks for Pb at 10.5 keV and 12.7 keV are absent.
Our in situ contact method can be carried out only if the
NW material electroplated into the pores has a higher reac-
tivity than that of the electrodes. Otherwise, the front elec-
trode became reactive and would peel off during
electroplating. When the reactivity of the NW material is
higher than that of the electrode material, it is impossible
for electrode materials to be mixed into the NWs. To con-
firm this and to investigate the structure of the NWs, we
have carried out extensive transmission electron micros-
copy (TEM) and scanning electron microscopy (SEM)
analyses.
have not found any sign of mixing of materials from the
electrodes into the NWs. Imaging of NWs was also carried
out for NWs remaining in their original pore channel, in
thin slices of membranes produced by ultramicrotomy, as
shown in Fig. 1.
For TEM investigation of extracted NWs, the back and
the front electrodes were first gently polished off a mem-
brane, which was then dissolved (in 1 M NaOH solution
for AAO membranes or in dichloromethane for PC mem-
branes). NWs were extracted using a centrifuge. Free
standing NWs in ethanol or water can be placed on a Cu
grid for TEM and SEM studies. The top frame in Fig. 3
is a typical TEM image of a Zn NW grown with Pb elec-
trodes. Selected-area electron diffraction (SAED) patterns,
shown in the inset to the top frame and taken on different
spots along the NW, revealed the same geometry without
rotation, indicating that the NWs were single crystalline.
Plane indexes and growth direction are marked on the
SAED pattern, from which the Zn NWs were found to
have a hexagonal structure, as that of the superconducting
bulk phase. Sn and Pb NWs grown on various back elec-
trodes were also found to be single crystalline. The lower
frame in Fig. 3 shows an energy dispersion spectroscopy
(EDS) taken on the Zn NW in the top frame. Besides C
and Cu, associated with the TEM sample grid, and O, asso-
ciated with an oxide layer on the NW, peaks associated
with Pb near 10.5 keV and 12.7 keV were clearly absent.
Therefore, the possibility of mixing of Pb from the elec-
trode into the Zn NW can be excluded. Similar EDS stud-
ies performed on many NWs grown with various electrodes
4. Long-range proximity effect
We measured the resistance R of single NWs of Pb, Sn,
and Zn down to 1.8 K using a Quantum Design physical
properties measurement system (PPMS) with a 9-T super-
conducting magnet. We note that the critical temperatures
for bulk Pb, Sn, and Zn are, respectively, Tc(Pb) = 7.2 K,
Tc(Sn) = 3.7 K, and Tc(Zn) = 0.88 K. In Fig. 4, we plot
R vs. T for a number of Sn (left frames) and Zn (right
frames) NWs of various diameters that were in contact
with pairs of electrodes of either Au, Sn, or Pb. These
NWs were 6 lm in length, fabricated using PC membranes.
We observe in Fig. 4a that Sn NWs did not show any sig-
nature of superconductivity down to 1.8 K when they were
in contact with Au electrodes. While Tc(Zn) was outside
the accessible temperature range of the PPMS, similar mea-
surements with Pb NWs in contact with Au electrode also
observed complete suppression of superconductivity down
to 1.8 K. In Fig. 4b and e, we observe that both Sn and Zn
NWs were superconducting at Tc(Sn) when they were in
contact with Sn electrodes. In Fig. 4c and f, we observe that
both Sn and Zn NWs were superconducting at Tc(Pb)
when they were in contact with Pb electrodes. Thus, we
conclude that superconductivity is completely suppressed
in 6 lm-long Sn NWs by Au electrodes. When in contact

H. Liu et al. / Physica C 468 (2008) 304–309
307
Fig. 6. (a): R vs T for 60 lm-long Pb NWs in contact with Au electrodes,
showing a partial transition with a significant residual resistance at low T.
(b): With Pb electrodes, Pb NWs show transition without a residual
resistance.
Fig. 4. R vs T for Sn (left frames) and Zn (right frames) NWs in contact
with pairs of Au (top), Sn (middle), or Pb (lower) electrodes. The
diameters of the NWs are indicated.
with electrodes having a higher Tc, superconductivity is
induced in these NWs at the Tc of the electrodes.
In Fig. 5 we plot R vs T for 60 lm-long Sn and Zn NWs
in contact with Pb electrodes. The induced superconductiv-
ity in these long NWs at Tc(Pb) was as robust as the
induced superconductivity observed in 6 lm-long NWs.
In Fig. 6, we plot R vs T measured on 60 lm-long Pb
NWs. The Pb NWs were superconducting at Tc(Pb) with
a zero residual resistance when in contact with Pb elec-
trodes. When in contact with Au electrodes, there was still
a superconducting transition at Tc(Pb), but there was a sig-
nificant residual resistance well below Tc(Pb). Therefore,
the suppression of superconductivity by Au electrodes in
these long nanowires was only partial. This was also
observed in 60 lm-long Sn NWs.
We also applied a magnetic field to suppress supercon-
ductivity in both the NWs and the electrodes. This provided
another means to investigate how superconductivity in the
NWs depended on the superconductivity in the electrodes.
We measured simultaneously the resistive transitions of
NWs and the electrodes. In Fig. 7, we plot R vs. T for a
Sn NW at various magnetic fields applied transverse to
Fig. 7. R vs T for a 60 lm-long Sn NW in contact with Pb electrodes, at
transverse fields of 0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, and 3.0 kOe for
curves from left to right showing the field suppression of superconduc-
tivity in the Sn NW.
the NW, showing a shift of the transition toward lower tem-
peratures with increasing field. This Sn NW was 60 lm in
length and 200 nm in diameter, and in contact with a pair
of Pb electrodes. In Fig. 8b, we plot resistance vs field at
three temperatures measured on one Pb electrode in contact
with the Sn NW, with the field aligned in parallel with the
plane of the Pb electrode (transversed to the Sn NW). We
obtained the critical temperatures and the critical fields at
the mid point of the resistive transitions. The dependence
of the critical temperatures on magnetic field is shown by
Fig. 8a for data obtained from curves in Figs. 7 and 8b.
Fig. 8a shows that the transition of the Sn NW followed
Fig. 8. (a): Open squares show the critical temperature vs transverse field
for the Sn NW in Fig. 7. Solid circles show the critical field vs temperature
for one Pb electrode in contact with the same Sn NW, obtained from
curves in (b). (b): Resistive transitions for this Pb electrode measured at
7 K, 5 K, and 2 K, for curves from left to right.
Fig. 5. The left frame shows R vs T up to 300 K for one Zn and one Sn
NWs in contact with Pb electrodes. The right frame shows transitions at
the critical temperature of Pb for the Zn and Sn NWs in contact with Pb
electrodes.

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H. Liu et al. / Physica C 468 (2008) 304–309
length 6 or 60 lm and diameter 30–250 nm, which were
in contact with a pair of bulk film electrodes of Au, Sn,
or Pb. We observed that, with superconducting electrodes
having a higher critical temperature Tc, superconductivity
was induced in Sn and Zn NWs at the Tc of the electrodes
for NWs as long as 60 lm. With Au electrodes, supercon-
ductivity was suppressed completely in 6 lm-long NWs
and partially in 60 lm-long NWs. TEM studies demon-
strated that the NWs were single crystalline. These studies
also ruled out the possibility of mixing of electrode materi-
als into the NWs. Analysis of the temperature dependence
of the normalized resistance suggests that the value of
RRR plays an important role in the observed anomalous
long-range proximity effect.
Fig. 9. Normalized R vs T for a number of Zn NWs in contact with Sn
electrodes, showing a sharp drop of residual resistance below Tc with
increasing RRR values.
Acknowledgements
precisely the transition of the Pb electrode, providing direct
evidence for a long-range proximity effect in the NWs.
The long-range proximity effect described above have
been observed consistently in virtually all the samples
(ꢁ120) of various NW/electrode combinations we have
measured so far. These NWs were single crystalline with
residual-resistance-ratio (RRR) values in the range of 1.4
to 50. We are not sure exactly how to control growth to
produce NWs of desirable RRR values. In Fig. 9, we plot
the normalized resistance versus temperature curves for Zn
NWs grown in PC membranes with Sn electrodes. We note
that the inverse of the normalized resistance value in the
flat region right above the critical temperature gives the
value of RRR. This figure shows clearly that the critical
temperature of the Zn NWs is shifted to Tc(Sn) with Sn
electrode and this observation did not seem to depend on
the value of RRR. However, the residual resistance below
the critical temperature was sensitively dependent upon the
value of RRR. The induced superconductivity was partial
for NWs having small RRR values of less than 2.5. For
RRR larger than 2.5, the residual resistance dropped to
zero quickly. We estimate the upper limit of the coherence
length using the thermal length in the clean limit for NWs
with large values of RRR, LT ¼ 2pꢀhvF=kBT. It is about
1.9 lm at 7.2 K and 3.7 lm at 3.7 K for Zn. This is compa-
rable to one-half of the length of 6 lm-long NWs. The
leakage of normal currents from both ends into a supercon-
ducting NW over this length could explain the suppression
of superconductivity completely in 6 lm-long NWs and
partially in 60 lm-long by Au electrodes. However, it is
much too short to account for the induced superconductiv-
ity in 60 lm-long NWs. Therefore, the observed long-range
proximity effect is not understood based on existing theo-
ries. Fig. 9 suggests that the value of RRR plays an impor-
tant role in this anomalous long-range proximity effect.
We thank V. Pokrovsky, D. G. Naugle, and J. Ross for
useful discussions. This work was supported by NSF under
Grant Nos. DMR-0551813 and DMR-0606529. The PPMS
was funded by NSF under Grant No. DMR-0315476.
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