Orbital-driven two-dome superconducting phases in iron-based superconductors

2.5 MB·

by  Da-Yong Liu

Orbital-driven two-dome superconducting phases in iron-based superconductors
Da-Yong Liu1, Feng Lu2, Wei-Hua Wang2, Hai-Qing Lin3, and Liang-Jian Zou1,4∗
1 Key Laboratory of Materials Physics, Institute of Solid State Physics,
Chinese Academy of Sciences, P. O. Box 1129, Hefei, Anhui 230031, China
2 Department of Electronics and Tianjin Key Laboratory of Photo-Electronic
Thin Film Device and Technology, Nankai University, Tianjin 300071, China
3 Beijing Computational Science Research Center, Beijing 100193, China
4 Department of Physics, University of Science and Technology of China, Hefei, 230026, China
7
(Dated: January 11, 2017)
1
0 Recentseveralexperimentsrevealedthatnovelbipartitemagnetic/superconductingphaseswidely
2
exist in iron pnictides and chalcogenides. Nevertheless, the origin of the two-dome superconduct-

n ing phases in iron-based compounds still remains unclear. Here we theoretically investigated the
a electronic structures, magnetic and superconducting properties of three representative iron-based
J systems, i.e. LaFeAsO1−xHx, LaFeAs1−xPxO and KFe2As2. We found that in addition to the de-

0 generate in-plane anisotropic xz/yz orbitals, the quasi-degenerate in-plane isotropic orbitals drive
1 these systems entering into the second parent phase. Moreover, the second superconducting phase
iscontributedbytheisotropicorbitalsratherthantheanisotropiconesinthefirstsuperconducting

] phase, indicating an orbital-selective pairing state. These results imply an orbital-driven mecha-
n
nism and shed light on the understanding of the two-dome magnetic/superconducting phases in
o
iron-based compounds.
c
-
r PACSnumbers: 74.70.Xa,74.20.Pq,74.25.Dw
p
u
s Iron-based superconductors display rich phase dia- ∼0.63µ inLaFeAsO.Moreover,itpossessesanunusual
. B
t grams with spin-density wave (SDW) [1, 2], orbital or- orthorhombic lattice distortion accompanied by the in-
a
m der [3, 4], nematicity [5–7] and superconductivity [8–10]. stability of As atoms which are away from the center of
These competing or coexisting phases arise from the in- theFesquarelatticeinthelow-temperaturephase. These
-
d terplay among charge, spin, orbital and lattice degrees unusualphenomenademonstratethattheorbitalphysics
n
of freedom of iron-based compounds. In the early stage inLaFeAsO H couldbedifferentfromLaFeAsO.One
1−x x
o
it had already realized that the multi-orbital characters naturally arisesa questionwhether the two SC domes in
c
[ ofbandstructuresandorbitalorderinginmanydifferent LaFeAsO1−xHx isparticular? Detailedanalysistorecent

families of iron pnictides and chalcogenides [11–19], and experimentaldatashowsthatsomeotheriron-basedcom-
1
the orbital selective Mott physics was also suggested in pounds also have two distinct AFM/SC phases, demon-
v
0 some iron-based compounds [16, 18], however, our un- strating that such two SC domes may be a general phe-
0 derstand to the roles of orbital degree of freedom seem nomenon in various iron-based SC families.
5 to be no more than that. The key roles of orbitaldegree
More recently, several experiments revealed that
2
offreedomonsuperconducting(SC)pairinginteractions,
0 LaFeAs1−xPxO exists a different AF1-SC1-AF2-SC2
pairing symmetry, and phase diagrams in these different
1. iron-based superconductors seem to be far from under- phase diagram [22–24]. Also in K1−xFe2−ySe2, a sec-
ond SC phase re-emerges under high pressure [25]. In
0
stood or revealed.
7 KFe2As2, a second SC phase is also found accompanied
1 with a collapsed tetragonal phase under high pressure
The parentcompoundLaFeAsO possessesa stripe an-
: [26]. In addition, two SC domes are also observed in
v tiferromagnetic (SAFM) ground state associated with a
i weakxz orbitalorderin the low-temperaturephase, and theK-dopedFeSethinfilmsgrownonSiCsubstrate[27].
X
And in the intercalated FeSe [28], the high pressure also
exhibits an orthorhombic to tetragonal structural phase
r could lead to two SC domes, similar to K Fe Se .
a transition upon doping or increasing temperature. Once 1−x 2−y 2
On the other hand, the pressure can induce a new AFM
substituting O with F, such an SAFM is gradually sup-
parent phase in pure FeSe [29]. The more recent nu-
pressed and an SC dome emerges in LaFeAsO F [8].
1−x x
clearmagneticresonance(NMR)experimentshowedthat
While for hydrogen doping, recent experiments demon-
therealsoexisttwoSCdomesandasecondorthorhombic
strated that the phase diagram shows two SC domes
phase in LaFeAsO F [30]. More and more bipartite
accompanied with bipartite magnetic parent phases in 1−x x
AFM/SC phases have been found in various iron-based
LaFeAsO H , as seen the AF1-SC1-SC2-AF2 phase
1−x x
compounds, however,the nature of the secondAFM/SC
diagram in Refs. [20, 21]. The neutron diffraction ex-
phase still remains unclear.
periment showed that the second magnetic parent phase
lies around x=0.5 in LaFeAsO H . This novel parent InthisLetter,weaimtoclarifytheoriginofthebipar-
1−x x
phase also shows SAFM order except that Fe spin has a titeAFM/SCphasesinLaFeAsO H ,LaFeAs P O,
1−x x 1−x x
largemagneticmomentof∼1.21µ ,incomparisonwith and KFe As compounds. For this purpose, we first
B 2 2
2
study the electronic, magnetic and SC properties of i.e. on-site energies of Fe-3d orbitals in two compounds
LaFeAsO H using the first-principles method, pro- can be seen in Supplemental Material[32] and Ref. [33].
1−x x
jected Wannier functions, the random phase approxima- The most obvious multi-orbital feature of
tion (RPA) and mean-field approximationbased on five- LaFeAsO H at x=0.5 is that the three t orbitals,
1−x x 2g
orbital Hubbard models. We find that quasi-degenerate xz/yz and xy, have nearly identical on-site energies,
xy/xz/yz orbitals drive the emergence of the second thus are almost degenerate. We call these three orbitals
magnetic parent phase, and the in-plane isotropic xy- quasi-degeneracy, since the bandwidths of these three
orbital dominates an orbital-selective SC pairing state orbitals in LaFeAsO H are clearly distinguished
0.5 0.5
in LaFeAsO1−xHx. While in LaFeAs1−xPxO, one of the with Wxz/yz >Wxy. The anion-height instability, which
quasi-degenerateorbitlas,i.e. in-planeisotropic3z2−r2 was recently suggested to be responsible for the AF2
orbital, is responsible for the second magnetic parent phase [34], is in fact a naturalconsequenceof the orbital
phase. InKFe As , a quasi-degeneratexz/yz/xy orbital quasi-degeneracy; according to the Jahn-Teller effect,
2 2
instability leads to a structural phase transition from a these quasi-degenerateorbitals are unstable, resulting in
tetragonal phase into a collapsed tetragonal (CT) phase the lattice distortion at low temperatures. On the other
under pressure. Therefore we propose that the quasi- hand, due to different orbital components and weights
degenerateorbitalsplaykeyrolesintheemergenceofthe in the two parent phases with x=0 and 0.5, a single
second AFM phase and the active isotropic orbital con- rigid-band tight-binding model could not describe the
trols the second SC phase, leading to the two SC domes entireT-xphasediagram. Thustodepictthelow-energy
inthe phasediagramsoftheseironpnictides andchalco- physics in LaFeAsO H , we have to adopt two sets
1−x x
genides. of different tight-binding parameters at x=0 for AF1
Fig. 1 schematically displays the phase diagram of and SC1 phases, and at x=0.5 for AF2 and SC2 phases,
LaFeAsO1−xHx according to the recent experiments respectively.
[20, 21, 31] and our numerical calculations and analysis.
Wefindthatthedegeneratexz/yz orbitalsdominatethe 3 3
(a) (b) xz/yz
xy
AF1 phase at x∼0 and the SC1 phase, while the quasi- 2 2 x2-y2
3z2-r2
degenerate xy/xz/yz orbitals dominate the AF2 phase 1 1
at x∼0.5 and the SC2 phase, respectively. In unveil- Energy(eV) −01 Energy(eV) −10
−2 −2
−3Γ Χ Μ Γ −3Γ X M Γ
3 3
(c) (d)
2 2
1 1
Energy(eV) −01 Energy(eV) −01
−2 −2
−3Γ Χ Μ Γ −3Γ Χ Μ Γ
FIG. 2. (Color online) Orbital-resolved band structures of
the five-orbital tight-binding model for (a) LaFeAsO, (b)
LaFeAsO0.5H0.5, (c) LaFeAs0.5P0.5O and (d) LaFePO.
FIG. 1. (Color online) Schematic phase diagram of InordertoexploretheroleofFermisurfacenestingand
LaFeAsO1−xHx. Different orbital configurations are dis- the possible magnetic instability in LaFeAsO H at
1−x x
played in thefirst and second AFM/SC phases.
x=0.5,westudythedynamicalspinsusceptibilitywithin
RPA.Thebarespinsusceptibilityisgivenbytheformula
ing the different orbital physics in LaFeAsO H , we
1−x x [35–37]
first study the electronic structures of two parentphases
LhealFpeAofsOth1−expHrxojaecttxed=0Waanndni0e.r5,furnescptieocntivteelcyh.nWiquiteh, tthhee χl01l2l3l4(q,iω)=−N1 X alν4(kω)a+lν2,ε∗((k~k)a+lµ1~q()k−+εq)(a~klµ)3,+∗(kiη+q)
five-orbital tight-binding model H0 is constructed. The ~k,µν µ ν
orbital-resolved band structures are displayed in Fig. 2 ×[f(ε (~k+~q))−f(ε (~k))] (1)
µ ν
(a) and (b). It is clearly showed that besides the xz/yz
orbitals, the xy orbital also contributes considerable The RPA susceptibility is expressed as
weight near Fermi level (E ) at x=0.5, different from
F
that at x=0. For comparison,the crystalfield splittings, χRPA(q,iω)=χ (q,iω)[I±Γ χ (q,iω)]−1, (2)
c(s) 0 c(s) 0
3
where χ is the bare susceptibility defined in Eq. 1, a slight polarization n = n −n (n < n ) but a
0 o1 xz yz xz yz
and the nonzero components of the matrices Γ and very large one n =n −(n +n )/2. The large n
c o2 xy xz yz o2
Γ are given as (Γ ) = U, (Γ ) = 2U′ − J , indicates a strong xy ferro-orbital order compared with
s c aa,aa c aa,bb H
(Γ ) =−U′+2J ,(Γ ) =J and(Γ ) =U, the weak xz-orbital order, as seen the inset of Fig. 1.
c ab,ab H c ab,ba H s aa,aa
(Γ ) = J , (Γ ) = U′, (Γ ) = J with or- The strong xy ferro-orbital order thus leads to a very
s aa,bb H s ab,ab s ab,ba H
bitals a 6= b. It is found that the peaks of the dynam- large N.N. spin exchange parameter J , which explains
2
ical spin susceptibility appear at Q ∼(π, π/3), rather the strong anisotropy between J and J [41]. There-
1 2
than (π, 0), implying that the nesting scenario fails in fore,theorbitalorderscenarioinvolvedwiththreequasi-
LaFeAsO H . This is due to the absence of the hole degenerate orbitals in LaFeAsO H (x=0.5) is signifi-
0.5 0.5 1−x x
pocket at Γ point like K Fe Se [38], in contrast to cantlydifferentfromthe weakorbitalorderinLaFeAsO.
1−x 2−y 2
that in LaFeAsO [32, 39, 40].
To further understand the AF2 parent phase, we
also investigate the magnetic ground state properties of
LaFeAsO H by the first-principles electronic struc-
0.5 0.5
turescalculations. Wefindthatastablemagneticground
state is SAFM, in agreement with the neutron diffrac-
tion experiment [21]. Based on the total energy differ-
s
ences among different magnetic configurations and fit- nt
e
m
ting by the J -J -J Heisenberg model, we estimate
1a 1b 2 o
thespinexchangeparameters: J1a=7.8meV/s2,J1b=4.7 c m
meV/s2, and J2=31.4 meV/s2 in LaFeAsO0.5H0.5. The neti
next nearest-nearest-neighbor (N.N.N.) coupling J2 is mag
much larger than the N.N. spin couplings J1a and J1b, d （a）
n
very different from other iron-based compounds. This a
s
strong magnetic anisotropy indicates the possible exis- cie
n
tence of strong orbital order, which we will show in the a
p
following. cu
c
To explore the interplays among the charge, spin and al o
orbitaldegrees offreedom including the electronic corre- bit
lation in AF1 and AF2 parent phases, we consider the Or
five-orbital Hubbard models H = H +H for x=0 and
0 I
for x=0.5, respectively, to investigate the electronic and
magnetic properties. Within the mean-filed approxima-
tion, we define the order parameters n and m with
α α
（b）
α=xz, yz, xy, x2−y2 and 3z2−r2 as
nα =Xhc†k,α,σck,α,σi,mα =Xσhc†k+Q,α,σck,α,σi(3)
k,σ k,σ
where Q is magnetic vector and σ=±1. Then we can FIG. 3. (Color online) Orbital occupancies and mag-
neticmoments dependenceon Coulomb interaction U within
obtainthe magneticmomentm= m andtotalpar-
Pα α the five-orbital Hubbard model for (a) LaFeAsO and (b)
ticle number n = n through the self-consistently
Pα α LaFeAsO0.5H0.5 with parameter JH=0.1U.
calculations.
We determine the magnetic groundstate atthe mean-
field level through considering the following magnetic From Fig. 3 (b), one notices that in LaFeAsO0.5H0.5,
vectors Q including (0, 0), (π, 0), (π, π), (π, π/3) and when U > Uc∼1.6 eV, nxy=nxy↑ + nxy↓∼1 and
(2π/3,0). TheconsequenceisthattheSAFMphasewith mxy=nxy↑ −nxy↓∼1, indicating nxy↑ ∼1 and nxy↓ ∼0,
Q=(π, 0) is the most stable, in consistent with our pre- i.e. the spin-up channel of xy orbital is almost fulfilled.
ceding LDA data and the experimental results [21]. The This demonstrates that an orbital-selective Mott phase
dependence ofthe orbitaloccupanciesandmagnetic mo- (OSMP) occurs with the insulating xy orbital and the
ments on Coulombinteraction U are shown in Fig. 3 (a) metallic xz and yz orbitals, as seen the sketch of the
forx=0andFig.3(b)forx=0.5,respectively. Itisobvi- OSMP [32]. The insulating xy orbital exhibits strong
ously found that in LaFeAsO H at x=0.5 the orbital ordering with respect to xz/yz orbitals, similar to man-
1−x x
polarizationoccursinthreeorbitalswhenthesystemen- ganites and other transition-metal oxides. This OSMP
tersinto the secondmagneticparentphase. The original accompaniedby astrongorbitalordercontributesto the
quasi-degeneratethreeorbitalswithalmostequalparticle second AFM parent phase at x=0.5.
numberundergoasignificantreconstruction,resultingin To look into the emergence of the second SC phase
4
SC2, we investigate the dependence of orbital order pa- the AF2 and SC2 phases, which is consistent with the
rameters on doping x within the five-orbital Hubbard experimental observations [23]. The orbital-resolved
model of LaFeAsO H at 0.5 [32]. These two orbital
1−x x
orderingparametersshowacompetingbehavior: thexz-
orbital weight increases while the xy-orbital weight de-
creaseswhenxvariesfrom0.5to0.35,favoringaparam-
agnetic metallic phase andthe emergenceofSC2 around
x<0.5 end. Out of expectation, when x>0.5, the xy-
orbital weight becomes more large, consistent with the
experimental observation [21, 31]. These results explain
why the SC2 phase appears at the left end of AF2 phase
in the phase diagram of LaFeAsO H .
1−x x
In analyzing the SC pairing properties of the SC2
phase, we calculate the pairing vertex arising from the
exchangeofspinandorbitalfluctuationsusingRPA.The
singlet orbital vertex function Γ is given by
αβµν
3 1
Γαβµν(k,k′,ω)=[2UsχRsPA(k−k′,ω)Us+ 2Us FIG.5. (Coloronline)Schematicorbitalconfigurationsinthe
1 1 phase diagram of LaFeAs1−xPxO.
− UcχRPA(k−k′,ω)Uc+ Uc] .(4)
2 c 2 αβµν
band structures are shown in Fig. 2 (c) and (d) for
The dominant orbital pairing vertices for LaFeAs P Oatx=0and0.5,respectively. FromFig.2
1−x x
(d) it is clearly found that in the AF2 phase, in addition
(a) (b) to the degenerate xz/yz orbitals, there also exist quasi-
degenerate3z2−r2/x2−y2orbitalsatx∼0.5,whichcould
be seen from the crystal field splittings, i.e. the on-site
energy differences, of Fe-3d orbitals [32]).
Finally, we also perform similar analysis for KFe As
2 2
with n=5.5 under pressure, and find that the quasi-
degenerate character of orbitals occurs when the SC1 or
SC2 phase disappears, as seen from the schematic phase
diagram in Fig. 6 according to the experimental result
FIG. 4. (Color online) Orbital pairing vertices along high
symmetricdirectionsfor(a)LaFeAsO1−xHx atx=0.125with in Ref. [26]. For comparison, the on-site energies of Fe-
U=1.4andJH=0.1U,and(b)LaFeAsO1−xHxatx=0.35with 3d orbitals are givenin Supplemental Material[32]. The
U=0.8 and JH=0.1U. Orbital index 1 refers to xz, 2 to yz, instability of the quasi-degenerate xz/yz/xy orbitals at
and 3 to xy orbital, respectively. about10GPadrivesastructuralphasetransitionfroma
tetragonalphasetoaCTphaseunderhighpressureupto
LaFeAsO H at x=0.125 and x=0.35 are shown 15 GPa. The dominant xy-orbitalcharacter is presented
1−x x
in Fig. 4. It is found that in SC1 phase, the yz-orbital at 10 GPa, but absent at 20 GPa, which is also veri-
dominates the pairing vertex around (π, 0), while the fied by a recent DFT and dynamical mean-field-theory
xy-orbital in SC2 phase, implying an orbital-selective (DMFT) calculations [43]. In addition, we predict that
pairing state observed by a recent ARPES experiment another quasi-degenerate xz/yz-xy/3z2−r2 orbital in-
in iron chalcogenides [42]. It reveals that the in-plane stability emerges above 30 GPa.
anisotropic xz/yz orbitals in Fe square plane are domi- Throughtheanalysisoftheabovethreerepresentative
nant in SC1 phase, but the in-plane isotropic xy orbital systems, we conclude that the active quasi-degenerate
is in SC2 phase. Therefore the orbital fluctuations orbitals drive the emergence of the second AFM or
due to the three quasi-degenerate orbitals also strongly SC phase [32]. Meanwhile, the orbital physics of the
contribute to the SC2 phase. fully degenerate xz/yz orbitals is the dominant sce-
Foranothertwo-domecompoundLaFeAs P Owith nario in the AF1/SC1 phase [32]. Actually, the dop-
1−x x
the isovalent substitution of phosphorus for arsenic, ing/substitution (chemical internal pressure) or hydro-
we briefly discuss its origin of two AFM/SC domes. static pressure pushes the in-plane anisotropic xz/yz or-
Fig. 5 shows a sketch of the LaFeAs P O phase di- bitals with C2 symmetry awayfromE , but it activates
1−x x F
agram according to the experiments [22–24]. Similar to the in-planeisotropicxy, x2−y2 or3z2−r2 orbitalwith
LaFeAsO H , we propose that the degenerate xz/yz- C4 symmetry in the planar square Fe lattice. There-
1−x x
orbitals are dominant in the AF1 and SC1 phases, while fore, it is readily understood that the isotropic orbitals
an active in-plane isotropic 3z2 −r2 orbital dominates emerge around E . The in-plane isotropic orbital would
F
5
(2008).
[2] J. Dong,H. J. Zhang, G.Xu,Z. Li, G. Li, W. Z.Hu,D.
Wu, G. F. Chen, X. Dai, J. L. Luo, Z. Fang, and N. L.
Wang, Europhys. Lett.83, 27006 (2008).
[3] C.C.Lee,W.G.Yin,andW.Ku,Phys.Rev.Lett.103,
267001 (2009).
[4] D. Y. Liu, Y. M. Quan, D. M. Chen, L. J. Zou, and H.
Q. Lin, Phys. Rev.B 84, 064435 (2011).
[5] J.H.Chu,J.G.Analytis,K.DeGreve,P.L.McMahon,
Z. Islam, Y. Yamamoto, and I. R. Fisher, Science 329,
824 (2010).
[6] F. Wang, S. A. Kivelson, D. H. Lee, Nat. Phys. 11, 959
(2015).
[7] X.J.Zheng,Z.B.Huang,D.Y.Liu,andL.J.Zou,Phys.
Rev. B 92, 085109 (2015).
[8] Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono,
FIG.6. (Coloronline)Schematicorbitalconfigurationsinthe J. Am.Chem. Soc. 130, 3296 (2008).
phase diagram of KFe2As2 underpressure. [9] X. H. Chen, T. Wu, G. Wu,R. H. Liu, H. Chen, and D.
F. Fang, Nature453, 761 (2008).
[10] K. Seo, B. A. Bernevig, and J. P. Hu Phys. Rev. Lett.
101, 206404 (2008).
suppress (π, 0) spin fluctuations, but enhance the (π, π)
[11] Z. P. Yin, K. Haule, and G. Kotliar, Nat. Mat. 10, 932
spin fluctuations and orbital fluctuations. Consequently,
(2011).
the orbital fluctuations in the second AF/SC phase play [12] E. Dagotto, Rev.Mod. Phys. 85, 849 (2013).
a dominant role, which is supported by a quite recent [13] D.J.Singh,andM.H.Du,Phys.Rev.Lett.100,237003
NMR experiment [44]. (2008).
In summary, we have shown that in addition to [14] W.Bao,Y.Qiu,Q.Huang,M.A.Green,P.Zajdel,M.R.
conventional magnetic and superconducting phases in Fitzsimmons, M. Zhernenkov,S. Chang, M. H. Fang, B.
Qian,E.K.Vehstedt,J.H.Yang,H.M.Pham,L.Spinu,
LaFeAsO H , LaFeAs P O and KFe As , the
1−x x 1−x x 2 2 and Z. Q.Mao, Phys. Rev.Lett. 102, 247001 (2009).
quasi-degenerateorbitals drive the emergence of the sec- [15] K. Haule, and G. Kotliar, New J. Phys. 11, 025021
ond AFM/SC phases, lead to universal two-dome SC
(2009).
phase in iron pnictides. Due to the orbital modulation, [16] L.de´Medici,S.R.Hassan,M.Capone,andX.Dai,Phys.
thereexisttwodistincttypesofSCphases,oneisin-plane Rev. Lett.102, 126401 (2009).
anisotropicorbitaldominantSC1 phase with low T , the [17] J. X.Zhu,R.Yu,H.D. Wang,L. L.Zhao, M. D.Jones,
c
other is in-plane isotropic orbital dominant SC2 phase J. H. Dai, E. Abrahams, E. Morosan, M. H. Fang, and
Q. M. Si, Phys. Rev.Lett. 104, 216405 (2010).
with high T . Actually, our scenario could be generally
c [18] R.Yu,andQ.M.Si,Phys.Rev.Lett.110,146402(2013).
extended to the similar two-dome SC phases observed
[19] S. Kong, D. Y. Liu, S. T. Cui, S. L. Ju, A. F. Wang, X.
experimentally in iron chalcogenides, such as the FeSe-
G.Luo,L.J.Zou,X.H.Chen,G.B.Zhang,andZ.Sun,
based compounds under pressure, as well as the heavy Phys. Rev.B 92, 184512 (2015).
fermion superconductors. The understanding of novel [20] S. Iimura, S. Matuishi, H. Sato, T. Hanna, Y. Muraba,
orbital-selectivemagnetic/SC state definitely sheds light S. W. Kim, J. E. Kim, M. Takata, and H. Hosono, Nat.
on the origin of the two-dome phases in iron-based ma- Commun. 3, 943 (2012).
[21] M. Hiraishi, S. Iimura, K. M. Kojima, J. Yamaura, H.
terials. This suggests that, to search for much higher
Hiraka, K. Ikeda, P. Miao, Y. Ishikawa, S. Torii, M.
T iron-based SC materials, the presence of the active
c Miyazaki,I.Yamauchi,A.Koda,K.Ishii,M.Yoshida,J.
isotropic orbital near E is an important factor.
F Mizuki,R.Kadono,R.Kumai,T.Kamiyama,T.Otomo,
This work was supported by the National Sciences Y. Murakami, S. Matsuishi, and H. Hosono, Nat. Phys.
Foundation of China under Grant Nos. 11574315, 10, 300 (2014).
11274310, 11474287 and 11404172. H. Q. Lin acknowl- [22] S. Kitagawa, T. Iye, Y. Nakai, K. Ishida, C. Wang, G.
edges financial support from NSAF U1530401. Numeri- Cao, and Z. Xu,J. Phys. Soc. Jpn. 83, 023707 (2014).
[23] H. Mukuda, F. Engetsu, T. Shiota, K. T. Lai, M.
cal calculations were performed at the Center for Com-
Yashima, Y. Kitaoka, S. Miyasaka, and S. Tajima, J.
putationalScience of CASHIPS and the Beijing Compu- Phys. Soc. Jpn. 83, 083702 (2014).
tational Science Research Center.
[24] K. T. Lai, A. Takemori, S. Miyasaka, F. Engetsu, H.
Mukuda,andS.Tajima,Phys.Rev.B90,064504(2014).
[25] L. L.Sun,X.J.Chen, J. Guo, P.W.Gao, Q.Z.Huang,
H. D. Wang, M. H. Fang, X. L. Chen, G. F. Chen, Q.
Wu,C.Zhang,D.C.Gu,X.L.Dong,L.Wang,K.Yang,
∗ Correspondingauthor;[email protected]; [email protected]. Li, X. Dai, H. K. Mao, and Z. X. Zhao, Nature
[1] C. de la Cruz, Q. Huang, J. W. Lynn, Jiying Li, W. 483, 67 (2012).
RatcliffII,J.L.Zarestky,H.A.Mook,G.F.Chen,J.L. [26] Y. Nakajima, R.Wang, T. Metz, X. Wang,L. Wang, H.
Luo, N. L. Wang, and Pengcheng Dai, Nature 453, 899 Cynn, S. T. Wier, J. R. Jeffries, and J. Paglione, Phys.
6
Rev.B 91, 060508(R) (2015). [35] S.Graser, T.A.Maier, P.J.Hirschfeld, D.J.Scalapino,
[27] C. L. Song, H. M. Zhang, Y. Zhong, X. P. Hu, S. H. Ji, New J. Phys.11, 025016 (2009).
L.L.Wang,K.He,X.C.Ma,andQ.K.Xue,Phys.Rev. [36] P.J.Hirschfeld,M.M.Korshunov,andI.I.Mazin,Rep.
Lett.116, 157001 (2016). Prog. Phys. 74, 124508 (2011).
[28] M. Izumi, L. Zheng, Y. Sakai, H. Goto, M. Sakata, Y. [37] D. J. Scalapino, Rev.Mod. Phys. 84, 1383 (2012).
Nakamoto, H. L. T. Nguyen,T. Kagayama, K. Shimizu, [38] T. Qian, X. P. Wang, W. C. Jin, P. Zhang, P. Richard,
S.Araki,T.C.Kobayashi,T.Kambe,D.Gu,J.Guo, J. G. Xu, X. Dai, Z. Fang, J. G. Guo, X. L. Chen, and H.
Liu, Y. Li, L. Sun, K. Prassides, and Y. Kubozono, Sci. Ding, Phys. Rev.Lett. 106, 187001 (2011).
Rep.5, 9477 (2015). [39] S. Onari, Y. Yamakawa, and H. Kontani, Phys. Rev. B
[29] T. Terashima, N. Kikugawa, A.Kiswandhi, D. Graf, E.- 88, 041106 (R) (2013).
S. Choi, J. S. Brooks, S. Kasahara, T. Watashige, Y. [40] Y. N. Huang, D. Y. Liu, L. J. Zou, and W. E. Pickett,
Matsuda,T.Shibauchi,T.Wolf,A.E.Bo¨hmer,F.Hardy, Phys. Rev.B 93, 195148 (2016).
C. Meingast, H. v. Lo¨hneysen, and S. Uji, Phys. Rev. B [41] K. Suzuki,H. Usui, S. Iimura, Y. Sato, S. Matsuishi, H.
93, 094505 (2016). Hosono, and K. Kuroki, Phys. Rev. Lett. 113, 027002
[30] J.Yang,R.Zhou,L.L. Wei,H.X.Yang,J. Q.Li,Z.X. (2014).
Zhao, G. Q.ZhengChin. Phys.Lett. 32, 107401 (2015). [42] Z. K. Liu, Y. Zhang, R. Yu, J. X. Zhu, J. J. Lee, R. G.
[31] R.Sakurai,N.Fujiwara,N.Kawaguchi,Y.Yamakawa,H. Moore, F. T. Schmitt,W. Li, S. C. Riggs, J. H. Chu,B.
Kontani, S. Iimura, S. Matsuishi, and H. Hosono, Phys. Lv, J. Hu, M. Hashimoto, S. K. Mo, Z. Hussain, Z. Q.
Rev.B 91, 064509 (2015). Mao, C.W.Chu,I.R.Fisher,Q.M.Si,Z.X.Shen,and
[32] SeeSupplementalMaterial. D. H. Lu,Nat. Comms. 6, 7777 (2015).
[33] K. Kuroki, S. Onari, R. Arita, H. Usui, Y. Tanaka, H. [43] D. Guterding, S. Backes, H. O. Jeschke, and R. Valent´ı,
Kontani, and H. Aoki, Phys. Rev. Lett. 101, 087004 Phys. Rev.B 91, 140503 (R) (2015).
(2008). [44] N.Kawaguchi,N.Fujiwara, S.Iimura,S.Matsuishi,and
[34] S.Onari,Y.Yamakawa,andH.Kontani,Phys.Rev.Lett. H. Hosono, arXiv: 1609.04957.
112, 187001 (2014).