Measurement of a Sign-Changing Two-Gap Superconducting Phase in Electron-Doped
Ba
ð
Fe
1
x
Co
x
Þ
2
As
2
Single Crystals Using Scanning Tunneling Spectroscopy
M. L. Teague,
1
G. K. Drayna,
1
G. P. Lockhart,
1
P. Cheng,
2
B. Shen,
2
H.-H. Wen,
2
and N.-C. Yeh
1
1
Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
2
Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, China
(Received 13 July 2010; published 24 February 2011)
Scanning tunneling spectroscopic studies of
Ba
ð
Fe
1
x
Co
x
Þ
2
As
2
(
x
¼
0
:
06
, 0.12) single crystals reveal
direct evidence for predominantly two-gap superconductivity. These gaps decrease with increasing
temperature and vanish above the superconducting transition
T
c
. The two-gap nature and the slightly
doping- and energy-dependent quasiparticle scattering interferences near the wave vectors (
, 0) and
(0,
) are consistent with sign-changing
s
-wave superconductivity. The excess zero-bias conductance
and the large gap-to-
T
c
ratios suggest dominant unitary impurity scattering.
DOI:
10.1103/PhysRevLett.106.087004
PACS numbers: 74.20.Rp, 74.25.Jb, 74.55.+v, 74.70.Xa
The recent discovery of iron-based superconductors
[
1
–
10
] has renewed intense research activities in super-
conductivity. Comparison of the similarities and contrasts
between the iron-based compounds and the cuprates can
provide useful insights into the microscopic mechanism
for high-temperature superconductivity [
11
]. In particular,
antiferromagnetic spin fluctuations appear to influence the
physical properties of both cuprate and iron-based super-
conductors [
11
–
16
]. On the other hand, theoretical calcu-
lations [
8
,
15
–
17
] and angle resolved photoemission
spectroscopy (ARPES) [
18
–
20
] suggest that multibands
and inter-Fermi surface interactions are crucial to super-
conductivity in the iron-based compounds.
While substantial experimental results from ARPES
studies [
18
–
20
] and phase sensitive measurements of
various iron-based compounds [
21
,
22
] are supportive
of the scenario of two-gap superconductivity with sign-
changing
s
-wave (
s
) order parameters for the hole and
electron Fermi pockets, tunneling and point-contact spec-
troscopic studies of the iron pnictides appear to be incon-
clusive [
23
–
28
]. For instance, reports of point-contact
spectroscopy and scanning tunneling spectroscopy (STS)
have suggested either BCS-like
s
-wave superconductivity
[
23
] or nodes in the superconducting order parameter
[
24
,
28
] of the ‘‘1111’’ iron-arsenides
LnFeAsO
1
x
F
x
(Ln:
trivalent rare-earth elements). On the other hand, STS
studies of the electron and hole-doped ‘‘122’’ iron arsenides
Ba
ð
Fe
1
x
Co
x
Þ
2
As
2
and
ð
Ba
1
x
K
x
Þ
Fe
2
As
2
have revealed
findings ranging from strong spatial variations in the tun-
neling spectra with occasional observation of a large super-
conducting gap [
25
] to moderate spatial variations with
predominantly a small superconducting gap [
26
]. In the
nonsuperconducting limit, nematic surface reconstructions
have been observed [
27
].
In this Letter we report direct STS evidence for two-
gap superconductivity in the electron-doped 122 system
Ba
ð
Fe
1
x
Co
x
Þ
2
As
2
of two different doping levels. For each
doping level, two different energy gaps can be clearly
resolved at
T
T
c
. Both gaps decrease monotonically
with increasing temperature and then completely vanish
above
T
c
. The gap values agree favorably with those
obtained from ARPES so that the larger gap
may be
associated with the holelike Fermi pockets and the smaller
gap
M
with the electronlike Fermi pockets. Moreover,
Fourier transformation (FT) of the tunneling conductance
reveals energy and doping dependent quasiparticle
scattering interferences (QPI) near the nesting wave vec-
tors (
, 0) and (0,
) between the Fermi pockets
at
and
M
, which is consistent with the sign-changing
order parameters for the hole and electron pockets [
17
].
Finally, excess zero-bias tunneling conductance and the
large
2
;M
=
ð
k
B
T
c
Þ
ratios for both doping levels may be
attributed to strong unitary impurity scattering [
29
].
The
Ba
ð
Fe
1
x
Co
x
Þ
2
As
2
samples investigated in this work
are single crystals with
x
¼
0
:
06
(underdoped) and 0.12
(overdoped), and the corresponding superconducting tran-
sition temperatures are
T
c
¼
14
and 20 K, respectively. The
single crystals were grown from the flux method [
30
], and
details of the synthesis and characterization of the samples
have been described elsewhere [
30
–
32
]. Given the reactive
nature of
Ba
ð
Fe
1
x
Co
x
Þ
2
As
2
, freshly cleaved surfaces were
essential for the STS studies. To date all reported STS
studies were carried out on samples that were mechanically
cleaved under ultrahigh vacuum (UHV) conditions and at
cryogenic temperatures [
25
–
27
], and the resulting sample
surfaces all exhibited significant (
2
1
) reconstructions of
the Fe(Co) layer. We chose to perform mechanical cleavage
of the single crystals in pure argon atmosphere at room
temperature, well above the tetragonal-to-orthorhombic
structural phase transition. The cleaved samples were
loaded
in situ
onto the cryogenic probe of our homemade
scanning tunneling microscope (STM) in argon. The sealed
STM assembly was subsequently evacuated and cooled to
6 K in UHV with a base pressure at
10
10
Torr
.
Both spatially resolved topography and tunneling con-
ductance (
dI=dV
) versus energy (
E
¼
eV
) spectroscopy
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were acquired pixel-by-pixel over an extended area of each
sample simultaneously, with tunneling currents along the
crystalline
c
axis. The typical junction resistance was kept
at
1G
. To remove slight variations in the tunnel junc-
tion resistance from pixel to pixel, the differential conduc-
tance at each pixel is normalized to the polynomial fit to its
high-energy conductance background from
j
E
j¼
max
þ
1
:
5 meV
to
j
E
j¼
max
þ
6
:
5 meV
. A detailed survey
of the surface topography and tunneling conductance spec-
tra was carried out over typically
ð
5
:
4
5
:
4
Þ
nm
2
and
ð
6
:
0
6
:
0
Þ
nm
2
areas, and each area was subdivided into
(
128
128
) pixels. Generally the tunneling spectra ap-
peared to be relatively consistent throughout each scanned
area, with representative point spectra shown in the left
panels of Figs.
1(a)
and
1(b)
for doping levels
x
¼
0
:
06
and
0.12, respectively. Two predominant tunneling gap features
are apparent for both doping levels. In comparison with
the ARPES data [
18
–
20
], we may assign the larger gap to
the superconducting gap of the hole Fermi surface at the
point of the Brillouin zone
and the smaller gap to that
of the electron Fermi surface at the
M
point
M
. However,
upon closer inspection, we note that the larger gap features
often exhibit broadening or even slight splitting, as exem-
plified in Figs.
1(a)
,
1(b)
, and
3(c)
. The physical origin
of this splitting or broadening is unknown.
Next, we employ a phenomenological fitting generalized
from the Dynes formula [
33
] to analyze the spectra and
we restrict to two-gap superconductivity in our analysis.
Specifically, the normalized tunneling conductance
G
for a
metal-insulator-superconductor junction in the case of a
two-gap superconductor may be given by
G
¼
A
þ
X
i
¼
;M
B
i
Z
Re
ð
E
i
i
Þð
df=dE
Þj
E
eV
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð
E
i
i
Þ
2
2
i
q
dE:
(1)
Here
A
and
B
i
are positive constants,
i
denotes the
quasiparticle scattering rate associated with the supercon-
ducting gap
i
, and
f
ð
E
Þ
is the Fermi function. Hence, by
applying Eq. (
1
) to the temperature dependent tunneling
conductance in the left panels of Figs.
1(a)
and
1(b)
,
we obtain temperature dependent values for
and
M
, which are illustrated in the right panels of Figs.
1(a)
and
1(b)
. Both gaps are particle-hole symmetric (see
Fig.
2
) and vanish immediately above
T
c
for both doping
levels, implying that
and
M
are indeed superconduct-
ing gaps. Further, the quasiparticle scattering rates derived
from Eq. (
1
) are very large even at
T
¼
6K
, showing
ð
=
Þ¼
0
:
4
and 0.5 for
x
¼
0
:
06
and 0.12, and
ð
M
=
M
Þ¼
0
:
1
for both
x
¼
0
:
06
and 0.12.
It is apparent from Fig.
1
that the two-gap fitting is not
ideal, which may be attributed to the following. First, the
generalized Dynes formula does not explicitly consider
the possibility of a sign-changing
s
-wave order parameter,
the latter is theoretically shown to be very sensitive to
unitary impurities so that the zero-bias conductance may
be strongly enhanced without requiring a large (
=
) ratio
[
29
]. Second, there may be different gaps associated with
the two hole pockets, so that Eq. (
1
) is not consistent with
the detailed electronic structures.
FIG. 1 (color online). Direct spectroscopic evidence for two-
gap superconductivity in
Ba
ð
Fe
1
x
Co
x
Þ
2
As
2
: (a) left panel:
normalized tunneling conductance (
dI=dV
) vs bias voltage (
V
)
spectra taken at
T
¼
6
, 10, and 15 K for the sample with
x
¼
0
:
06
and
T
c
¼
14 K
. The solid lines represent theoretical fittings
to spectra using the Dynes formula in Eq. (
1
) modified for two-
gap BCS superconductors. Two distinct tunneling gaps
and
M
can be identified from the spectrum at
T
¼
6K
. Right panel:
the tunneling gaps
and
M
as a function of the reduced
temperature (
T=T
c
) are shown by the symbols and solid lines.
The error bars indicate the widths of the gap distributions
obtained from the fitting using Eq. (
1
). (b) Left panel: (
dI=dV
)
vs (
V
) spectra taken at
T
¼
6
, 14, and 21 K for the sample with
x
¼
0
:
12
and
T
c
¼
20 K
. Right panel:
;M
-
vs
:
-
ð
T=T
c
Þ
.
FIG. 2 (color online). Superconducting gap maps and histo-
grams at
T
¼
6K
: (a) left to right: the first two panels correspond
to the
M
and
maps for the underdoped sample (
x
¼
0
:
06
), and
the right two panels represent the corresponding histograms for
both the quasiparticle (solid bars) and quasihole (shaded bars)
branches, showing particle-hole symmetry and the meanvalues of
hj
M
ji ¼
4 meV
and
hj
ji ¼
8 meV
. (b) The left two panels
are, respectively, the
M
and
maps for the sample with
x
¼
0
:
12
. The right two panels are histograms of
M
and
, showing
particle-hole symmetry and
hj
M
ji ¼
5 meV
,
hj
ji ¼
10 meV
.
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The results shown in Figs.
1(a)
and
1(b)
are representa-
tive of the spectral characteristics of both samples, as
manifested by the gap spatial maps and the corresponding
histograms for both samples in Figs.
2(a)
and
2(b)
, where
the gap values are empirically determined as one-half
of the peak-to-peak values. Overall
h
i¼
10
:
0 meV
and
h
M
i¼
5
:
0 meV
for
x
¼
0
:
12
and
h
i¼
8
:
0 meV
and
h
M
i¼
4
:
0 meV
for
x
¼
0
:
06
.
Our findings of the two-gap spectra differ from previous
STS studies [
25
,
26
], which may be the result of differences
in the surface preparation. Specifically, we show in
Fig.
3(a)
an example of the atomically resolved surface
topography of the overdoped sample over a
ð
5
:
4
5
:
4
Þ
nm
2
area. We find that cleaving the samples under
argon gas at room temperature generally resulted in frag-
mented surfaces, as exemplified by the height histogram in
Fig.
3(b)
for the same
ð
5
:
4
5
:
4
Þ
nm
2
area. In particular,
we note that the topography in Fig.
3(a)
exhibited no
apparently reconstructed (
1
2
) surfaces, and the overall
height variations were limited to within one
c
-axis lattice
constant
c
0
¼
1
:
239 nm
. This finding is in contrast to the
mostly flat and reconstructed surfaces reported by other
groups for cold-cleaved samples [
25
–
27
]. Despite the
fragmented surfaces, consistent two-gap spectral features
were found throughout the scanned area, as exemplified in
Fig.
3(c)
for the tunneling spectra taken near the middle
of Fig.
3(a)
.
Next, we examine the spatial variations in the tunneling
conductance at constant bias voltages. In Figs.
4(a)
and
4(b)
,
we illustrate the tunneling conductance maps of two
samples and under three different bias voltages of
V
¼
0
,
(
h
M
i
=e
) and (
h
i
=e
). The Fourier transformed (FT)
tunneling conductance at
V
¼ðh
M
i
=e
Þ
and (
h
i
=e
)is
shown in Fig.
4(c)
for
x
¼
0
:
06
and in Fig.
4(d)
for
x
¼
0
:
12
. We find that dominant QPI occur at three
wave vectors [
22
]:
q
1
between two electron pockets across
the first Brillouin zone,
q
1
ð
2
;
0
Þ
=
ð
0
;
2
Þ
;
q
2
be-
tween the hole- and electron pockets at
and
M
points,
q
2
ð
;
0
Þ
=
ð
0
;
Þ
; and
q
3
between two adjacent elec-
tron pockets,
q
3
ð
;;
Þ
. For the underdoped sam-
ple, strong QPI at
q
2
and the absence of QPI at
q
3
is
consistent with the five-orbital theoretical calculations
[
15
,
16
,
34
] for two possible scenarios: one is scalar-
impurity QPI between sign-reversing order parameters
associated with the hole- and electron pockets, and the
other is magnetic impurity QPI between order parameters
of the same sign. Given that scalar scatterers are generally
more common than magnetic impurities, we suggest that
the prevailing QPI wave vectors at
q
2
are the result of
sign-reversing order parameters. In this context, the ap-
pearance of
q
3
wave vectors in the overdoped sample
FIG. 3 (color online). Correlation of atomically resolved sur-
face topography with tunneling conductance spectra: (a) Surface
topography of the overdoped sample (
x
¼
0
:
12
) over a
ð
5
:
4
5
:
4
Þ
nm
2
area. (b) The height histogram of the area in (a), showing
height variations within one lattice constant along the
c
axis.
(c) Spatial evolution of the normalized
ð
dI=dV
Þ
-
vs
-
V
spectra
across a horizontal line slightly below the middle of the topogra-
phy image in (a), which reveals consistent two-gap features.
FIG. 4 (color online). Tunneling conductance maps of
Ba
ð
Fe
1
x
Co
x
Þ
2
As
2
samples at three constant bias voltages
V
¼
0
,(
h
M
i
=e
), (
h
i
=e
), and for
T
¼
6K
: (a)
x
¼
0
:
06
and
(b)
x
¼
0
:
12
. (c) Fourier transformed (FT) tunneling conduc-
tance maps at
V
¼ðh
M
i
=e
Þ¼
4 meV
(left panel) and
V
¼
ðh
i
=e
Þ¼
8 meV
(right panel) for
x
¼
0
:
06
. (d) FT conduc-
tance maps at
V
¼ðh
M
i
=e
Þ¼
5 meV
(left panel) and
V
¼
ðh
i
=e
Þ¼
10 meV
(right panel) for
x
¼
0
:
12
. The thin white
lines define the first and second Brillouin zones, and we have
used the lattice constant
a
¼
0
:
53 nm
for the length of the first
Brillouin zone (
2
=a
). All three QPI wave vectors
q
1
,
q
2
, and
q
3
are slightly energy and doping dependent.
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might be due to a larger density of Co atoms in the surface
Fe
=
Co
layers: unlike those in the bulk, the charge transfer
from the surface Co atoms is incomplete so that they may
behave like magnetic impurities [
15
,
16
,
34
,
35
].
It is worth noting that for both samples the
q
2
wave
vectors appear to exhibit one preferential direction. In
addition, energy-dependent features at small wave vectors
(
j
q
j
<=
2
) are observed along the same direction. These
findings may be related to the nematic-order wave vectors
found in the parent state of these compounds [
27
], although
our limited momentum resolution cannot provide detailed
comparison. Overall, we attribute
q
1
,
q
2
, and
q
3
to the QPI
scattering wave vectors because they are not only slightly
energy dependent but also doping dependent, and so they
cannot be simply attributed to Bragg diffractions of the
lattices. The relatively weak energy dependence of the QPI
wave vectors is the result of small and nearly isotropic
Fermi pockets in the iron arsenides, which differs from the
highly energy-dependent QPI wave vectors in the cuprate
superconductors [
36
–
39
].
Finally, we note that the relatively high zero-bias con-
ductance in all tunneling spectra at
T
T
c
is suggestive of
dominant unitary impurity scattering [
29
]. Further, unitary
impurity effects on the suppression of
T
c
for the sign-
changing
s
-wave superconductors are found to be as sig-
nificant as those on the
d
-wave superconductors [
29
]. On
the other hand, unitary impurity effects on suppressing
the sign-changing
s
-wave order parameters involve sign-
dependent components that are partially canceled, and
are therefore weakened [
29
]. Hence, the large ratios
of
ð
2
h
;M
iÞ
=
ð
k
B
T
c
Þ
for the 122 system, with
ð
2
h
M
iÞ
=
ð
k
B
T
c
Þ
6
:
6
(5.8) and
ð
2
h
iÞ
=
ð
k
B
T
c
Þ
13
:
2
(11.6) for
x
¼
0
:
06
(0.12), may be attributed to significant unitary
impurity scattering in these sign-changing
s
-wave super-
conductors. A possible source for the unitary impurity
scattering may be associated with disorder in the Co dop-
ing into the Fe planes, which is in contrast to the situation
in the 1111 iron arsenides where doping takes place in the
charge reservoir [
5
] so that the disorder effect is weaker
and the
ð
2
Þ
=
ð
k
B
T
c
Þ
ratio is small (
3
)[
23
,
28
], whereas
the
T
c
values are generally higher.
In summary, we have demonstrated direct STS evi-
dence for two-gap superconductivity in electron-doped
Ba
ð
Fe
1
x
Co
x
Þ
2
As
2
single crystals of two doping levels.
The Fourier transformed tunneling conductance reveals
strong quasiparticle scattering interferences near the nest-
ing wave vector between the hole Fermi pockets at
and
the electron Fermi pockets at
M
, consistent with sign-
changing order parameters of the two Fermi pockets. The
excess zero-bias conductance and the large
2
;M
=
ð
k
B
T
c
Þ
ratios for both doping levels may be attributed to signifi-
cant unitary impurity scattering in a sign-changing
s
-wave
superconducting system.
The work at Caltech was jointly supported by NSF Grant
No. DMR-0907251, and the Kavli and Moore Foundations.
The work in China was supported by the NSFC, the
Ministry of Science and Technology of China, and the
Chinese Academy of Sciences within the knowledge in-
novation program. We thank Patrick A. Lee, Igor Mazin,
and Yunkyu Bang for valuable discussions.
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