Reprinted fromLETTER
Anomalous Superconducting-Gap Structureof Slightly Overdoped Ba(Fe1¹xCox)2As2
Tetsuya Hajiri, Takahiro Ito, Masaharu Matsunami, Byeong Hun Min,
Yong Seung Kwon, and Shin-ichi Kimura
J. Phys. Soc. Jpn. 83, 093703 (2014)© 2014 The Physical Society of Japan

Person-to-person distribution by the author only. Not permitted for publication for institutional repositories or on personal Web sites.

Letters

Journal of the Physical Society of Japan 83, 093703 (2014)
http://dx.doi.org/10.7566/JPSJ.83.093703

Anomalous Superconducting-Gap Structureof Slightly Overdoped Ba(Fe1¹xCox)2As2
Tetsuya Hajiri1,2+, Takahiro Ito1,3, Masaharu Matsunami2,4, Byeong Hun Min5,
Yong Seung Kwon5, and Shin-ichi Kimura2,4†
1
Graduate School of Engineering, Nagoya University, Nagoya 464-8603, JapanUVSOR Facility, Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan
3
Nagoya University Synchrotron Radiation Research Center, Nagoya University, Nagoya 464-8603, Japan
4
School of Physical Sciences, The Graduate University for Advanced Studies (SOKENDAI), Okazaki, Aichi 444-8585, Japan
5
Department of Emerging Materials Science, DGIST, Daegu 711-873, Republic of Korea
2(Received May 9, 2014; accepted July 14, 2014; published online August 18, 2014)

We observed the anisotropic superconducting-gap (SC-gap) structure of a slightly overdoped superconductor,
Ba(Fe1¹xCox)2As2 (x = 0.1), using three-dimensional (3D) angle-resolved photoemission spectroscopy. Two hole Fermi
surfaces (FSs) observed at the Brillouin zone center and an inner electron FS at the zone corner showed a nearly
isotropic SC gap in 3D momentum space. However, the outer electron FS showed an anisotropic SC gap with nodes or
gap minima around the M and A points. The different anisotropies obtained the SC gap between the outer and innerelectron FSs cannot be expected from all theoretical predictions with spin ﬂuctuation, orbital ﬂuctuation, and bothcompetition. Our results provide a new insight into the SC mechanisms of iron pnictide superconductors.

Iron pnictide superconductors1) have the second-highest
superconducting transition temperature (Tc ) and a wide
variety of superconducting (SC) states, particularly as SCgap structure owing to multiple Fermi surfaces (FSs) andorbital characters.2,3) Focusing on the SC state of the 122type iron pnictides, the Ba1x KxFe2As2 system shows a fully
opened SC gap and a nodal SC gap around optimally doped4)
and a hole-end KFe2As2,5) respectively, observed by angleresolved photoemission spectroscopy (ARPES).6–9) On theother hand, the BaFe2(As1x Px)2 system has nodes in thewhole SC region.10,11) There are different ARPES results forthis system: one reports nodes at the hole FS of the dz2 orbitalaround the Z point,12) and the other around the longer axisof the ellipsoid-shaped electron FS despite the lack of nodein the hole FSs.13) The former can be explained by spin
ﬂuctuation alone,14) while the latter requires an additional
orbital ﬂuctuation.15)
The Ba(Fe1x Cox)2As2 system shows an antiferromagnetic
spin ﬂuctuation in the whole of SC region.16) The antiferromagnetic scattering vector QAF is from a hole FS to anelectron FS,17) which is similar to those in other ironpnictides. Hence, spin ﬂuctuation that induces a fully openeds -wave18,19) in this system has been proposed. On the other
hand, both the softening of the C66 mode20) and the orbitalpolarized electronic structure21) suggest the presence oforbital ﬂuctuation. It is therefore important to elucidate theeffects of spin and orbital ﬂuctuations on the electronic
structure. With respect to the SC state, a fully opened SC
gap has been observed in the underdoped region ofx  0:075,22,23) although some experiments have shown
evidence of nodal behavior.24,25) In the overdoped region ofx > 0:075, on the other hand, a nodal SC gap with either
nodes or gap minima on at least one FS has beensuggested.23–26) To clarify the SC state of this unique system,
it is necessary to elucidate the position of nodes in theoverdoped region. In this system, only one ARPES study of
the SC-gap structure of optimally doped Ba(Fe1x Cox)2As2
has been reported,27) while no ARPES studies of the SC gap
or nodes of overdoped Ba(Fe1x Cox)2As2 have been reported.
Since a three-dimensional (3D) SC-gap structure can be

expected, it is important for ARPES in 3D momentum space
using tunable incident photons.
In this Letter, we report our investigation of the 3D SC-gap
structure of slightly overdoped Ba(Fe1x Cox)2As2 (x ¼ 0:1),
using synchrotron radiation ARPES. The two hole FSs
obtained at the zone center and the inner electron FS obtainedat the zone corner were found to have nearly isotropic SC
gaps in 3D momentum space. In the outer electron FS,
however, we observed an anisotropic SC gap with nodes or
gap minima. The different anisotropies obtained the SC gap
between the outer and inner electron FSs is not consistent
with previous theories.
The 3D-ARPES experiments were performed on in-situ
cleaved single crystals of slightly overdoped Ba(Fe1x Cox)2As2 (x ¼ 0:1) with Tc  22:5 K. The ARPES measurements were carried out at the SAMRAI end-station of theundulator beamline BL7U of UVSOR-III at the Institute for
Molecular Science, using an MBS A-1 analyzer.28) The
energy resolution was about 5 meV for the SC-gap measurement and in-plane FS mapping, and about 10 meV for the
band-dispersion mapping and out-of-plane FS mapping. The
angular resolution was about 0.17°. The Fermi level (EF ) was
calibrated using an evaporated gold ﬁlm.
Figure 1(a) shows the out-of-plane FSs. The open circles
in Fig. 1(a) denote the peak position of the momentumdistribution curves (MDCs) determined by the ﬁtting using a
Lorentzian with a constant background, as shown in the inset
of Fig. 1(c) and in Fig. 1(d1). Hereafter, we use open circles
on FS images of each ﬁgure in the same manner. We examine
the band character of each FS (¥, Z, and M points) from the
ARPES data, as shown in Figs. 1(b)–1(d) along each line cut
in Fig. 1(a). The solid circles in Figs. 1(b) and 1(c) denotethe band dispersions determined by the peak and shoulder
structure positions of the ARPES spectra; there are two holebands near EF at both the ¥ and Z points. At the ¥ point, onehole band crosses EF , while the other has a top at about
20 meV without crossing EF , as shown in the inset of
Fig. 1(b). At the Z point, both hole bands cross EF , as shownin the inset of Fig. 1(c), which is the MDC ﬁtting at EF . At
the M point of the zone corner, we conﬁrm the existence of093703-1©2014 The Physical Society of Japan

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Letters

3.6

kz (Å-1)

3.4

T = 12 K

35 eV

hν =
30 eV

Z

A

1

3.2
24 eV
3.0

20 eV

2.8

19 eV

2.6
-1.0

-0.5

Γ

M

Γ

0
-1

0.5

0.0

1.0

1.5

2.0

(d)

M

hν =
24 eV

80 40

0

80 40

Binding energy (meV)

Binding energy (meV)Z(b)

hν = 19 eV

0.2

θ

θ

-0.2

kx 2

1

-0.2

40
80
0 (d3)
4080|θ | = 54.3°

h ν = 9 eV(g)hν = 21 eV
19 eV
15 eV
14 eV
11 eV
9 eV

124.6°

Outer|θ | = 72.7°
105.5°
131.1°

Inner

61.7°
104.6°
178.5°

157.6°(d)two electron bands with bottoms at about 40 and 80 meVfrom the MDC ﬁtting at EF , from the ARPES image, andfrom the MDC’s second-derivative image, as shown in
Figs. 1(d1)–1(d3), respectively.
Figures 2(a) and 2(b) show a schematic FS image at kz ¼ 0
and the in-plane FS at h ¼ 19 eV around the ¥ point,respectively. Figure 2(c) shows the symmetrized ARPES
spectra with the selected FS angle (ª) around the ¥ point.
Each spectrum is normalized to the integrated intensity
between 18 and 22 meV. Hereafter, all the spectra arenormalized in the same manner. Each spectrum has ashoulder structure due to the SC gap at about 5–7 meV, asmarked by arrows,29) and its ª dependence is summarized inFig. 2(d). Figures 2(e) and 2(f ) show the h (kz )-dependent
symmetrized ARPES spectra and the SC-gap size at the outerhole FS at  ¼ 90°, respectively. Figures 2(g) and 2(h) show
the ª-dependent symmetrized ARPES spectra and the SC-gap
size of the two (inner and outer) hole FSs around the Z point,respectively. Consequently, by combination of the results
obtained along the ¥-Z line, we found that the SC gaps of thetwo hole FSs are nearly isotropic without any nodes in 3D
momentum space.
We now turn our attention to the SC-gap structure of
the ellipsoid-shaped electron FSs at the zone corner.
Figure 3(a) shows the in-plane FSs at h ¼ 14 eV aroundthe A point [Fig. 3(b)]. There are two FSs similar to thosein Fig. 1, but the matrix element is different. This is because
the experimental conﬁguration and photon energy used are
different from those used in Fig. 1, which were measured at
kx ¼ 0 with h ¼ 20{40 eV. The temperature (T)-dependent
ARPES spectra at 35 K (> Tc ) and 12 K (< Tc ) at the outerelectron FS are shown in Fig. 3(c). At jj ¼ 168:4° on the|θ | = 90°

90°

-20

Fig. 1. (Color online) (a) Out-of-plane FS images. The open circles denote
the FSs determined by the peak position of the MDCs. See text for details.
(b, c) ARPES spectra near the ¥ and Z points. The insets are the ARPES
spectra at ky ¼ 0 at the ¥ point and the MDC ﬁtting at EF around the Z point.
(d) ARPES results at the M point. (d1) MDC ﬁtting at the EF , (d2) ARPES
image and (d3) the MDC’s second-derivative image of (d2).

(e)

77.8°

0

ky (Å-1)

0.0

kx (Å-1)hν = 19 eV

(c)

θ

Γ

0.0

ka (π/a)0 (d2)ΓZ

0

Gap (meV)

Intensity (arb. units)

ky = 0(d1)

θIntensity (arb. units)hν = 30 eV

Intensity(arb. units)hν = 20 eV (c)kz = 0ky

M/Aky (Å-1)
(b)

M/A

(a)

kb (π/a)(a)T. Hajiri et al.

ky (Å-1)

J. Phys. Soc. Jpn. 83, 093703 (2014)

0

20

-20
0
20
Energy relative to EF (meV)Γ point

8

(f)
8

Z

Γ

(h)
8

4

4

4

0

0

0

0

90
180
FS angle (deg.)

1020hν (eV)

-20

0

20

Z point

Outer
Inner
0

90
180
FS angle (deg.)

Fig. 2. (Color online) 3D SC-gap structures at hole FSs. (a) Schematic FS
image at kz ¼ 0. (b) In-plane FS image at h ¼ 19 eV around the ¥ point.
(c) Symmetrized ARPES spectra with various ª around the ¥ point. (d) ªdependence of the SC-gap size around the ¥ point. (e) Symmetrized ARPES
spectra with various h at the outer hole FS denoted by the solid circle inpanel (b). (f ) h dependence (kz dependence) of the SC-gap size inh ¼ 8{22 eV in 1 eV steps. (g) Symmetrized ARPES spectra of the outerand inner hole FSs at h ¼ 9 eV around the Z point. (h) ª dependence of the
SC-gap size around the Z point.

shorter axis, the crossing point of the T-dependent spectra islocated in the occupied states, thus suggesting the opening of
the SC gap. At jj ¼ 137:4°, the crossing point shifts toward
EF , and then, at jj ¼ 97:5° on the longer axis, the crossing
point is exactly at EF , thus suggesting the closing of the
SC gap. The T-dependent symmetrized ARPES spectra withvarious ª of the outer electron FS are shown in Fig. 3(d).
Around the shorter axis (jj ¼ 180°), the spectra at T ¼ 12 K(< Tc ) have shoulder structures marked by arrows, indicating the opening of the SC gap. Toward the longer axis(jj ¼ 90°), the energy of the shoulder decreases and ﬁnally
vanishes at jj ¼ 97:5°. The symmetrized ARPES spectrum
at jj ¼ 92:3° shows a small dip at about 3 meV, which may
be caused by loop-like nodes, as will be discussed later. In thesame manner, we show the T-dependent and symmetrized
ARPES spectra at the inner electron FS in Figs. 3(e) and3(f ), respectively. In contrast with those of the outer electron
FS, the crossing point and SC-gap size of the inner FS are
almost unchanged. A similar ª dependence of the SC gap isalso observed at h ¼ 24 eV around the M point, as shown in
Figs. 3(g) and 3(h).
For a more detailed determination of the 3D SC-gap
structure in the electron FSs, we investigate the electron FSs
at the middle of the M and A points taken at h ¼ 19 eV, as
shown in Fig. 3(b). In the same manner as that for the A

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Letters

J. Phys. Soc. Jpn. 83, 093703 (2014)

(c)

A

0.0
-0.1

θ
-1.2

-1.0

kx (Å-1)kz (Å-1)

(b)
3.4

A

3.0

M

2.6
A

hν = 14 eV

Outer

0.1

Intensity (arb. units)ky (Å-1)hν = 14 eVhν = 14 eV

(a)

35 K
12 K

(e)

4.7°

137.4°

46.8°

97.5°

86.3°

168.4°

4.7°

137.4°
115.9°

33.8°
46.8°

24 eV

97.5°

73.2°

19 eV

92.3°

86.3°

hν =
35 eV

0.0

ky (Å-1)

125.6°(i)

177.9°

84.5°

157.5°

39.7°

98.6°

Outer

21.9°

(f)

hν = 19 eV

(g)

Inner

(h)

Outer

82.6°

(j)

176.6°

81.4°

128.0°

63.4°

101.6°

14 eV

Outer
2.2
-0.4

hν = 24 eV|θ | =
168.4°

177.2°(d)T. Hajiri et al.

0.4

-20

0

20

Inner
-20

Inner

Inner

0
20
-20
0
Energy relative to EF (meV)

20

-20

0

20

Fig. 3. (Color online) 3D SC-gap structures at electron FSs. (a) In-plane FS image at h ¼ 14 eV around the A point. (b) kz position of each SC-gap
measurement around the electron FSs as a function of ky . (c–f ) T-dependent and symmetrized ARPES spectra at T ¼ 35 K (> Tc ) and 12 K (< Tc ) of the outer(c, d) and inner (e, f ) electron FSs at h ¼ 14 eV. (g–j) T-dependent symmetrized ARPES spectra at the outer (g, i) and inner (h, j) electron FSs at h ¼ 24 and
19 eV.

appearance of superconductivity; that is, interband scattering
seems to be more important for the appearance of superconductivity. Moreover, the softening of the C66 mode20) andthe orbital-polarized electronic structure21) also suggest theexistence of orbital ﬂuctuation. Hence, not only spin
ﬂuctuation but also orbital ﬂuctuation might be involved in
the appearance of superconductivity in this system.
According to the theory of the 3D SC gap of the
BaFe2(As1x Px)2 system, if a dxy hole FS exists, the fully
opened anisotropic SC gap on both electron FSs should
appear owing to the spin ﬂuctuation.15) Actually, our recent
polarization-dependent ARPES study of the Ba(Fe1x Cox)2As2 system suggests the existence of a dxy hole FS.31)
On the other hand, owing to orbital ﬂuctuation, both electron
FSs have a nearly isotropic SC gap.15) If spin and orbital
ﬂuctuations compete, both electron FSs have an anisotropic
nodal SC gap (with loop-like nodes) depending on the degree(a) hν = 14, 24 eV8(b) hν = 19 eV

Outer

Outer

Inner

Inner

4
Gap (meV)point, the T-dependent symmetrized ARPES spectra of theouter and inner electron FSs are shown in Figs. 3(i) and 3(j),respectively. In contrast with the A and M points, the SC-gap
size of both electron FSs are almost constant.
We summarize the ª dependences of the SC-gap sizesof the outer and inner electron FSs around both the A(h ¼ 14 eV) and M (h ¼ 24 eV) points and around the
middle of the M and A points (h ¼ 19 eV) in Figs. 4(a) and
4(b), respectively. The SC-gap size of the outer electron FS
around the A and M points has a maximum of about 8 meValong the shorter axis (jj ¼ 0, 180°). Toward the longer axis(jj ¼ 90°), the SC-gap size becomes smaller and a node or a
gap minimum exists. On the other hand, at the inner electron
FS, the SC gap is nearly isotropic at about 5–7 meV. Aroundthe middle of the M and A points (h ¼ 19 eV); however,both electron FSs have an SC gap at 4–7 meV without nodes,
while the outer electron FS has a possible fourfold symmetry
within experimental resolution. Our observations therefore
suggest that nodes or gap minima exist only around thelonger axis of the ellipsoid-shaped outer electron FS aroundthe M and A points. The reproducibility of the SC gap aroundthe hole FSs was checked by repeated experiments. For theelectron FSs, it was checked by comparing the spectra of thesample cleaved at T ¼ 12 K with those at T ¼ 12 K aftercleaving at T ¼ 35 K. Moreover, it was conﬁrmed from thesimilarity of the ª dependences of the SC gaps at the A(h ¼ 14 eV) and M (h ¼ 24 eV) points.
On the basis of the obtained 3D SC-gap structure, we now
discuss the mechanism of the appearance of the superconductivity of this system. In the Ba(Fe1x Cox)2As2 system,
both spin ﬂuctuation16) and the antiferromagnetic scatteringvector QAF between the hole and electron FSs17) in the SC
region have been reported. In the heavily overdoped non-SC
region, there is no interband scattering owing to the absenceof a hole FS.30) These results imply that interband scattering
between the hole and electron FSs is important for the

0
8
4
0

14 eV
24 eV
0

90

180
0
FS angle (deg.)

90

180

Fig. 4. (Color online) ª dependences of the SC-gap sizes of the outer andinner electron FSs at h ¼ 14 and 24 eV (a) and at h ¼ 19 eV (b).

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J. Phys. Soc. Jpn. 83, 093703 (2014)

Lettersof competition.15) Our present ARPES results of the Ba(Fe1x Cox)2As2 system suggest different anisotropies between the outer and inner electron FSs around the M and A
points, while the above theories predict the same anisotropy
between both electron FSs. Since the different anisotropes
obtained are considered to be related to the appearance ofsuperconductivity, further theoretical and also experimental
studies are needed.
In summary, we performed 3D-ARPES measurements ofslightly overdoped Ba(Fe1x Cox)2As2 (x ¼ 0:1) to clarify the
3D SC-gap structure. We observed that two hole FSs and an
inner electron FS have a nearly isotropic SC gap, and that theouter electron FS has an anisotropic SC gap with nodes or
gap minima. These results provide a new insight into theappearance of the superconductivity of iron pnictide superconductors.
Acknowledgments The authors gratefully acknowledge M. Sakai for his
technical assistance during the experiments. Part of this work was supported by
the Use-of-UVSOR Facility Program (BL7U, 2012) of the Institute for Molecular
Science. The work at DGIST was partially supported by the Leading Foreign
Research Institute Recruitment Program (Grant No. 2012K1A4A3053565) and
Basic Science Research Program (NRF-2013R1A1A2009778) through the
National Research Foundation of Korea funded by MEST. T.H. was supported
by a Grant-in-Aid for JSPS Fellows.

+

hajiri.tetsuya@f.mbox.nagoya-u.ac.jp
Present address: Graduate School of Frontier Biosciences, Osaka University,
Suita, Osaka 565-0871, Japan.
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