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Pairing symmetry of the multiorbital pnictide superconductor BaFe1.84Co0.16As2
from Raman scattering
S. Sugai,1,2,3 Y. Mizuno,1,3 K. Kiho,3,4 M. Nakajima,3,5 C. H. Lee,3,4 A. Iyo,3,4 H. Eisaki,3,4 and S. Uchida3,5
1
Department of Physics, Faculty of Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan
2
Venture Business Laboratory, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan
3TRIP, Japan Science and Technology Agency (JST), Chiyoda, Tokyo 102-0075, Japan
4National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japan
5
Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
共Received 23 March 2010; published 18 October 2010兲
The pairing symmetry of BaFe2−xCoxAs2 was investigated by Raman scattering. The gap structure appears
only in the B2g symmetry inconsistent with Muschler et al. 关Phys. Rev. B 80, 180510共R兲 共2009兲兴. They
concluded that the gap symmetry is the extended s with the argument that the B2g spectra probe the electron
pocket. Our calculation using the realistic band parameter, however, shows that the B2g spectra are derived
from mainly the hole pocket. The calculated intensity is much stronger in A1g than in B2g but the observed A1g
spectra have no gap structure. This inconsistency is removed, if the orbital combination is introduced in the
pairing symmetry. That is, the symmetry of orbital combination is B2g and that of momentum space is A1g. The
energy of the gap peak is smaller than the gap energy of the hole pocket, indicating the observed peak is the
resonant peak created in the gap of the s⫾ superconductor.
DOI: 10.1103/PhysRevB.82.140504
PACS number共s兲: 74.70.Xa, 74.25.nd, 74.20.Rp, 74.25.Ha
Symmetry of the superconducting gap is a key of the superconductivity mechanism. Spin-fluctuation-mediated pairing mechanism arising from the nesting between the hole
pocket at the ⌫ point and the electron pocket at the M point
was proposed because the superconducting phase of the iron
pnictide is adjacent to the spin-density wave phase. The s⫾
pairing model in which the gap changes the sign between
hole and electron pockets but has no node on Fermi surfaces
共FSs兲 was proposed.1–3 With increasing electron density the
extended s 共nodal s⫾: nodes in the electron pocket兲 or d
共nodes in the hole pocket兲 pairing becomes stable. Functional
renormalization study presented the extended s pairing with
the nearly isotropic gap in the hole pocket and anisotropic
gap in the electron pocket.4,5 A time-reversal symmetry
breaking s + id pairing model was proposed.6 A s++ pairing
model was also proposed to explain the robust superconductivity to impurities.7
Angle-resolved photoemission spectroscopy 共ARPES兲
disclosed that the gap energies are nearly isotropic in each of
the hole and electron pockets and the gap energy changes
from the ⌫ to M point consistent with the s⫾ symmetry.8–11
Maier and Scalapino12 proposed that the imaginary part of
the dynamical spin susceptibility has a resonant peak below
the gap 2⌬, if the gap symmetry is s⫾. Neutron scattering
disclosed the magnetic resonant peaks.13–15
Recently Chubukov et al.16 proposed that the s⫾ gap can
be distinguished from the pure s, extended s, and d wave
gaps by using Raman scattering because a resonant peak develops inside the gap only in the s⫾ pairing. In other symmetry a pair-breaking peak develops at the gap energy. Very
recently Muschler et al.17 reported that the gap structure in
the Raman spectra of BaFe2−xCoxAs2 can be understood by
the extended s symmetry18 on the assignment that the gap
structure in the B2g spectra are derived from the electron
pocket. Our calculation, however, shows that the hole pocket
always gives the dominant intensity in all polarization con1098-0121/2010/82共14兲/140504共4兲
figurations. The calculated A1g intensity is much larger than
the B2g spectra even if the screening effect is introduced but
the A1g spectra have no gap structure. The inconsistency is
removed by introducing the symmetry of the orbital combination which is the characteristic property of the multiorbital
superconductor.19,20
Single crystals of BaFe1.84Co0.16As2 were synthesized by
a self-flux method. The superconducting transition temperature is 25 K. Raman spectra were obtained on the fresh
cleaved surface in the quasi-back-scattering configuration using 5145 Å Ar-ion laser. The polarization configuration
c共ab兲c̄ denotes that the polarized light with the electric field
parallel to the a axis is illuminated along the c axis and the
backward scattered light with the electric field parallel to the
b axis is measured, where a, b, and c are the crystallographic
axes of the tetragonal structure. The a and b axes are parallel
to the Fe-As-Fe directions. The bisecting directions of the a
and b axes are named x and y. The A1g and B1g modes are
allowed in the 共aa兲 spectra, B2g in 共ab兲, A1g and B2g in 共xx兲,
and B1g in 共xy兲. The Raman system was calibrated so that the
2
S
intensity is proportional to
⍀.
Figure 1共a兲 shows the polarized Raman spectra in the superconducting state at 5 K and the normal state at 25 K. All
the spectra are plotted in the same intensity scale with the
common zero level. Any background subtraction was not
done to determine the zero level. The intensity around
75 cm−1 is largest in the 共aa兲 spectra and then 共xx兲, 共ab兲 and
to 共xy兲 in decreasing order. The 75 cm−1 peaks in the 共ab兲
and 共xx兲 spectra at 5 K are the superconducting gap peaks.
The gap symmetry is B2g in the same way as Muschler et
al.17 In the 共aa兲 and 共xy兲 spectra the low-energy intensity
below 100 cm−1 decreases as temperature decreases from 25
to 5 K but the superconducting peak does not emerge. The
sharp peak at 214 cm−1 is the B1g phonon peak and the
broad peak at 184 cm−1 is the A1g phonon peak which broadens below 100 K as discussed later.
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SUGAI et al.
(b)
(arb. units)
(a)
β
γ
Fe
ky
As
α
δ
b
y
a
kb
ka
x
kx
(c)
FIG. 1. 共Color online兲 共a兲 Polarized Raman spectra below and at
Tc. The intensity scales and the zero levels are the same for all four
spectra. 共b兲 Differential Raman spectra between 5 and 25 K and the
resonant peak observed by neutron scattering 共Refs. 14 and 15兲. The
Raman peak energy is shown by the red or leftmost solid line. The
solid black lines are gap energies of electron and hole pockets obtained by ARPES 共Ref. 11兲. The dashed line is the gap energy
obtained by tunnel spectroscopy 共Ref. 21兲.
The differential Raman spectra between the superconducting phase and the normal phase are plotted in Fig. 1共b兲 together with the resonant peaks observed in neutron scattering. The top two spectra are the differential neutronscattering spectra between 10 and 30 K in BaFe1.84Co0.16As2
by Lumsden et al.14 and the differential spectra between 4
and 60 K at 共1/2, 1/2, 1兲 in BaFe1.85Co0.15As2 by Inosov et
al.15 The average gap energies of the hole pocket 共2⌬
= 13.2 meV兲 and the electron pocket 共10.0 meV兲 obtained by
ARPES 共Ref. 11兲 are shown by solid lines. The observed
anisotropy is small. The gap energy obtained by tunnel spectroscopy is also shown.21 The A1g Raman spectra were obtained from 关I共aa兲 + I共xx兲 − I共ab兲 − I共xy兲兴 / 2. The peak energies in the A1g, B2g, and 共xx兲 spectra are the same 75 cm−1
共red or leftmost solid line兲 as the resonant peak energies in
neutron scattering. The energy is close to the gap energy of
the electron pocket but smaller than that of the hole pocket.
If the Raman peak is produced from the hole pocket, it is the
resonant peak of the s⫾ pairing but if the peak is produced
from the electron pocket, it is the pair-breaking peak.
Individual charge fluctuation is screened by the longrange Coulomb interaction, if the charge fluctuation averaged
on the Fermi surface is nonzero.22–24 The screened Raman
efficiency without the final-state interaction is given by23
冋
2
具−1F典FS
2S
បe4
= 4 Im 具−2F典FS −
⍀ c
具F典FS
册
2⑀
1
e
兺 S,i ki k j eL,j ,
ប2 i,j
F is the Tsuneto function whose imaginary part is
(kaka)
(kakb)
(kakb)
ka
(kxkx)
(kxkx)
(kxky)
(kxky)
ky
kx
0
1
FIG. 2. 共Color online兲 共a兲 The structure of an FeAs layer. As
atoms with 共without兲 black edge are above 共below兲 the Fe atomic
sheet. 共b兲 Hole FSs ␣ and  and the electron FSs ␥ and ␦. The ac
and bc orbitals are shown by red and green, respectively. The dotted
square is the folded Brillouin zone. 共c兲 兩2⑀ / ki k j兩2 of the hole and
electron bands in the two-orbital model. The intensity on the FS
gives the Raman intensity.
共1兲
Im F共,k兲 = NF
共2兲
Electron band
(kaka)
kb
at zero temperature, where is the mass tensor,
−1 =
Hole band
4兩⌬k兩2
冑2 − 4兩⌬k兩2
,
共3兲
具 典FS represents the average along the Fermi surface, eL and
eS are the polarizations of the laser and scattered light, NF is
the density of states at the Fermi level, and ⌬共k兲 is the gap
energy. The first and the second terms of Eq. 共1兲 represent
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PHYSICAL REVIEW B 82, 140504共R兲 共2010兲
TABLE I. Raman intensity from the hole pocket  at 共 , 兲 and
the sum of the electron pockets ␥ + ␦ at 共0 , 兲 and 共 , 0兲.
tron pocket and vice versa. The maximum screening is ob2
tained by calculating 具−1典FS
within each pocket. The maxi2
is listed in Table I.
mally screened intensity 具−2典FS − 具−1典FS
The largest screened intensity comes from the  hole pocket
in the 共aa兲 spectra. The intensity from the electron pocket is
small. The decreasing order of scattering intensity from
共aa兲 : A1g + B1g and 共xx兲 : A1g + B2g, 共ab兲 : B2g to 共xy兲 : B1g is
consistent with the experimental result. In the cuprate with a
single a2 − b2 orbital the strength of the gap peak in the superconducting state is proportional to the intensity in the
normal state. In contrast, in the iron pnictide the 共aa兲 spectra
of Fig. 1共a兲 do not show the gap structure in spite of the large
intensity. Instead the 共ab兲 共B2g兲 spectra have strong gap
structure.
Raman scattering in multiorbital electronic states is little
different from single-orbital states in the normal phase because the electronic transition is mainly to the neighboring
intraorbital state across the FS by the momentum conservation with light. On the other hand in the superconducting
phase the paired states are composed of two orbitals ac and
bc.19,20 The orbital combination is expressed by †, where
= 共ac , bc兲, and 0, 1 − 3 are the unit and Pauli matrices.
†0 = a2c2 + b2c2, †1 = 2acbc, and †3 = a2c2 − b2c2
transform as a2 + b2 共A1g兲, ab 共B2g兲, a2 − b2 共B1g兲 in the D4h
point group, respectively. If the symmetry of the orbital combination is B2g, the observed gap symmetry B2g is derived
from the A1g pairing symmetry in the momentum space because B2g = A1g 丢 B2g. The hole pocket gives the dominant
part of the A1g intensity in the momentum space. The Raman
peak energy of the gap structure is smaller than the gap energy of the hole pocket observed in ARPES as shown in Fig.
1共b兲. The A1g symmetry does not change under the final-state
interaction.16 Therefore the observed peak is the resonant
peak of the s⫾ gap which has the A1g symmetry.
Precursor phenomena are observed above the superconducting transition. Figure 3 shows the temperature dependence of the low-energy Raman spectra. The intensity below
60 cm−1 increases in the 共xx兲 and 共ab兲 spectra as tempera-
共aa兲
Hole
Electron
共xx兲
Bare
Screened
Bare
Screened
100
18
28
1
100
16
11
5
共ab兲
共xy兲
9
3
7
3
(arb. units)
the bare and the screening intensities, respectively. This
screening term is finite for the A1g mode but zero for other
modes because of the cancellation of the plus and minus
mass along the FS. Equation 共2兲 gives the polarization dependence and Eq. 共3兲 does the pair-breaking peak at 2⌬.
Figure 2共a兲 shows the FeAs layer viewed from the c axis.
Figure 2共b兲 is the FS of hole pockets ␣ and  and electron
pockets ␥ and ␦ in the two-orbital tight-binding model of
BaFe2As2.25 The ac and bc orbitals are shown by red and
green, respectively.26 The dotted lines show the folded Brillouin zone 共BZ兲 for the crystallographic unit cell including
two iron atoms. We use the symmetry of the folded Brillouin
zone. The hole pocket  is folded into ⌫ in the folded BZ.
Figure 2共c兲 shows the contour maps of 兩2⑀ / ki k j兩2 for the
electron band and the hole band in the two-orbital model. A
set of ki and k j is denoted by 共kik j兲, which gives the scattering intensity in the 共ij兲 polarization configuration. In the
electron-doped Ba2Fe1.85Co0.15As2 the ␣ hole pocket
disappears11 and the  and ␥共␦兲 pockets are in the good
nesting condition. In the 共aa兲 and 共xx兲 polarization configurations the 兩2⑀ / ki k j兩2 has large intensity near the ␣ and 
hole FSs while small near the ␥ and ␦ electron FSs. In the
共ab兲 polarization configuration the intensity of 兩2⑀ / ki k j兩2
is small near the ␣ and  hole FSs and much smaller near the
␥ and ␦ electron FSs. In the 共xy兲 polarization configuration
the 兩2⑀ / ki k j兩2 is small both in hole pockets and electron
pockets.
For the hole pocket the screening is reduced by the elec-
FIG. 3. 共Color online兲 Temperature dependence of polarized Raman spectra. The 20 K spectra are superimposed on the 5 K spectra.
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ture decreases below 70 K while the change is not observed
in the 共aa兲 and 共xy兲 spectra. The change is induced by the
increase in the electronic states near the Fermi energy. The
polarization configurations with the precursor phenomena
are the same as those of the resonant peaks. The 182 cm−1
共at 300 K兲 A1g phonon is active in the 共aa兲 and 共xx兲 spectra
and the 207 cm−1 共at 300 K兲 B1g phonon is active in the 共aa兲
and 共xy兲 spectra.27,28 The sharp A1g phonon peak heavily
broadens from the width 8 cm−1 at 300 K to 20 cm−1 at 5 K
in the 共aa兲 spectra and from 8 cm−1 at 300 K to 32 cm−1 at
5 K in the 共xx兲 spectra. The broadening is related to the
superconductivity because the broadening is not observed in
BaFe2As2. This mode is the vibration of As atoms along the
c direction. It is known that the height of the As atom from
the Fe layer is sensitive to the pairing symmetry.29
In order to ensure the presence of spin excitations, the
high-energy spin excitation spectra are shown in Fig. 4. The
spectra are almost the same as those in the normal state of
BaFe2As2.30 The energy range of large scattering intensity
extends far above the two-magnon peak energy 2200 cm−1
in the spin-density wave phase of BaFe2As2. The present
high-energy spectra indicate that the short-range magnetic
correlation remains in the superconducting state.
In conclusion, the present Raman scattering disclosed that
the pairing symmetry of the multiorbital BaFe1.84Co0.16As2 is
expressed by A1g in the momentum space and B2g in orbitals.
The 75 cm−1 superconducting peak is the resonant peak of
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FIG. 4. 共Color online兲 Wide-energy Raman spectra presenting
magnetic excitations. The normal phase spectra of BaFe2As2 共Ref.
30兲 are also shown. The scale is on the right side.
the hole pocket created inside the gap of the s⫾ superconductor. The existence of the high-energy spin excitations as
in the cuprate superconductors suggests the spin-fluctuationmediated superconductivity
This work was supported by Transformative Research
Project on Iron Pnictides 共TRIP兲, Japan Science and Technology Agency 共JST兲.
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