PHYSICAL REVIEW B 93, 024503 (2016)

Orbital-dependent electron correlation in LiFeAs revealed by angle-resolved
photoemission spectroscopy
T. Hajiri,1,2,* T. Ito,1,3 M. Matsunami,2,4,† B. H. Min,5 Y. S. Kwon,5,6 K. Kuroki,7 and S. Kimura2,7,8
1

Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan
2
UVSOR Facility, Institute for Molecular Science, Okazaki 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 444-8585, Japan
5
DGIST-LBNL Joint Research Center, DGIST, Daegu 711-873, Republic of Korea
6
Department of Emerging Materials Science, DGIST, Daegu 711-873, Republic of Korea
7
Department of Physics, Graduate School of Science, Osaka University, Osaka 565-0043, Japan
8
Graduate School of Frontier Biosciences, Osaka University, Suita 565-0871, Japan(Received 12 February 2015; revised manuscript received 4 September 2015; published 6 January 2016)
We report on the electronic structure of the 111-type iron pnictide superconductor LiFeAs as a function oftemperature using angle-resolved photoemission spectroscopy. Below approximately 50 K, both the dyz holeband at the Z point and the dxz/yz electron band at the A point shift to a higher binding energy side. However,at the high-symmetry points Z, A, , and M, the remaining bands are almost independent of temperature. Oneof the possible scenarios for these observations is that a strong, three-dimensional orbital-dependent correlation
exists in the normal state of LiFeAs in relation to short-range spin fluctuations.
DOI: 10.1103/PhysRevB.93.024503
I. INTRODUCTION

Iron pnictide superconductors [1], especially from thefamily of BaFe2 As2 (namely, 122 type), exhibit a characteristic change in electronic structure even above Tc . For
instance, BaFe2 (As1−x Px )2 and Ba(Fe1−x Cox )2 As2 systems
have a fourfold rotational symmetry-broken phase (namely,
the nematic phase) [2,3] above the temperature T of the spindensity-wave (SDW)/antiferromagnetic (AFM) and structuraltransitions [4–6]. The nematic phase is considered to be at
the origin of anomalous physical properties, such as in-planeanisotropic resistivity [7], the softening of the C66 mode [8],the orbital-polarized electronic structure between dxz anddyz orbitals [9], and the pseudogap [10]. In addition, in
Ba(Fe1−x Cox )2 As2 systems, all bands shift with decreasing
temperature due to thermally excited carriers in the narrow
bands near the Fermi level EF . It is considered that the band
shift of Ba(Fe1−x Cox )2 As2 systems is related to the temperature evolution of interband charge or spin fluctuations [11].
Because the electronic structure and physical properties above
Tc are considered to be closely related to superconductivity,
the electronic structure above Tc should be investigated toelucidate the origin of superconductivity in iron pnictides.
The 111-type iron pnictide superconductor LiFeAs is an
ideal system for investigating the electronic structure aboveand below Tc , because stoichiometric LiFeAs shows superconductivity without SDW/AFM and structural transitions,which distinguishes it from other iron pnictides such as the 122
type. Previously, a spin-fluctuation scenario has been proposed
for the superconductivity of LiFeAs [12–17]. However, no*
Present address: Department of Crystalline Materials
science, Nagoya University, Nagoya 464-8603, Japan;
t.hajiri@numse.nagoya-u.ac.jp†
Present address: Toyota Technological Institute, Nagoya 468-8511,
Japan.

2469-9950/2016/93(2)/024503(5)orbital order/fluctuation behavior is observed in LiFeAs, incontrast to the case for the 122 type. The importance oforbital fluctuation for superconductivity is highlighted by arecent angle-resolved photoemission spectroscopy (ARPES)
study [18] and by theoretical studies [19,20]. On the other
hand, a possible new superconductivity mechanism has beenreported for KFe2 As2 , in which different effective interactions
occur in the individual Fermi surfaces (FSs) [21]. In LiFeAs,
the effective interactions in each FS are not yet clarified. Therefore, understanding the origin of superconductivity in ironpnictides requires elucidating the FS-dependent interactions
and electronic structure above Tc in these materials.
In this paper, we thus report on the temperature-dependent
electronic structure of LiFeAs. We found that the binding
energies of both the dyz hole band at the Z point and thedxz/yz electron band at the A point increase below T ∼ 50 K,
which is the temperature of the appearance of a spin fluctuationand is greater than Tc . The remaining bands are almost
temperature independent. These results possibly suggest thata strong orbital-dependent correlation exists in the normal
state in LiFeAs, which may be related to short-range spin
fluctuations.

II. EXPERIMENT

Three-dimensional (3D) ARPES experiments were performed on single crystals of stoichiometric LiFeAs withapproximately Tc,onset = 19.7 K [22]. ARPES measurements
were performed at the SAMRAI end station of the undulator
beamline 7U of UVSOR-III at the Institute for Molecular
Science, Japan, using an MBS A-1 analyzer [23]. The energy
and angular resolutions were approximately 8 meV and 0.17◦ ,respectively. All measurements were performed on in situ
cleaved samples in an ultrahigh vacuum under 1 × 10−8 Pa.
We use the same inner potential (15.4 eV) and photon energies(which correspond to the high-symmetry points) as in our

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T. HAJIRI et al.

PHYSICAL REVIEW B 93, 024503 (2016)previous study [12]. EF of the samples was determined withrespect to that of an evaporated gold film.
III. RESULTS AND DISCUSSION

Figures 1(a)–1(d) show ARPES images at the  (hν =23 eV) and Z (hν = 35 eV) points along the -M and
Z-A directions at T = 100 and 12 K, respectively. Twohole bands appear at both the  and Z points because of S
polarization, which contrasts with previous studies that report
three hole bands at the  point [12,13,24]. The use of S
polarization prevents the innermost hole band at the  pointfrom being clearly recognized in Fig. 1. The band detectedby P polarization is shown in Supplemental Fig. S1 [25].
The observed inner and outer hole bands are attributed todyz and dxy orbitals, respectively [12]. Figures 1(e) and 1(f)compare the dispersion of each band at T = 100 and 12 K
T = 100 K

Binding Energy (eV)

0.0

(a)

T = 12 K

Γ

Γ

(b)

T = 100 K
T = 12 K

0.2
0.0

Γ

(e)

(C)

(d)

Z

(f)

Z

MDC
EDC

Z

T = 100 K
MDC
T = 12 K
EDC
28 meV shift up

0.2
-0.4

0.0

0.4

T = 100 K T = 80 K

-0.4

0.0

ky (Å-1)

T = 60 K

0.4

T = 40 K

-0.4

0.0

T = 30 K

0.4
T = 20 K

Binding Energy (eV)

(g)
0.0

0.1
(h)
0.0

0.1

ky (Å-1)

0.4 Å-1

FIG. 1. (a)–(d) ARPES images along the -M and Z-A directions
obtained by S polarization at  (hν = 23 eV) and Z (hν = 35 eV)points at T = 100 and 12 K, respectively. The insets in (a) and (c)indicate the schematic FSs and measured momentum lines. (e), (f)Comparison of each band dispersion at the  and Z points between
T = 100 and 12 K. The solid and open circles/squares show the peak
positions of the MDCs and EDCs, respectively. The cross marks in(f) are the same as the inner hole band at T = 12 K after shifting up
by 28 meV. (g), (h) Temperature-dependent ARPES images divided
by the Fermi-Dirac function at the  and Z points. Solid circles andlines are the peak positions determined by the MDC fitting and its
parabolic fitting, respectively.

at the  and Z points, respectively. The solid and open
circles/squares in Figs. 1(e) and 1(f) were determined using thepeak positions of the momentum-distribution curves (MDCs)
and the energy-distribution curves (EDCs), respectively. At
the  point shown in Fig. 1(e), the two observed bands do notshift with temperature. The innermost hole band attributed tothe dxz orbital seems to be almost independent of temperature,
as shown in Supplemental Fig. S1 [25].
At the Z point shown in Fig. 1(f), however, the inner holeband attributed to the dyz orbital rigidly shifts by 28 meV tohigher binding energies with decreasing temperature, although
the outer hole band is almost independent of temperature.
To clarify the temperature-dependent band shift of the innerhole band, we show in Figs. 1(g) and 1(h) the temperaturedependent ARPES images divided by the Fermi-Dirac function
at the  and Z points, respectively. The solid lines are
determined by fitting the MDC peak positions to a parabola.
Clearly, the top of the inner hole band at the Z point shifts
below T = 40 K, but the inner hole band at the  point is
independent of temperature. The Fermi wave vector kF of theouter hole band at the Z point might shift slightly, but it canbe negligible, as discussed in the Supplemental Material [25].
Next, we focus on the electron bands at the zone corner: theA and M points. Figures 2(a) and 2(b) show ARPES images
at the A point (hν = 18 eV) along the Z-A direction at T =150 and 15 K, respectively. As shown in Figs. 2(a2)–2(b3),which are second-derivative images of the EDCs [Figs. 2(a2)and 2(b2)] and MDCs [Figs. 2(a3) and 2(b3)] of the intensity
images in Figs. 2(a1) and 2(b1), two electron bands centered at
the A point appear at both temperatures. The deep and shallow
electron bands are attributed to the dxy and dxz/yz orbitals,
respectively [12]. At T = 150 K, both electron bands have asimilar kF despite the different band bottoms at approximately
20 (shallow) and 90 (deep) meV. At T = 15 K, the bottomof the shallow electron band rigidly shifts to higher binding
energies by approximately 20 meV, but the bottom of the
deep electron band does not shift (see also Supplemental
Fig. S4 [25]). Figure 2(c) shows the temperature dependenceof the MDCs at EF at the A point. The vertical lines indicate
the kF ’s determined by Lorentzian fitting. Above T = 80 K,
the shallow electron band has the same kF as the deep band.
At T = 50 K, a shoulder of the MDC at EF , which originatesfrom the shallow band, suddenly appears on the outer sideof the main peak. On further decreasing the temperature, theshoulder structure shifts toward more outer wave vectors; thisindicates that the bottom of the shallow electron band shifts
toward higher binding energies.
To check the three-dimensionality of this temperaturedependence of the band shift, we now turn our attention to
the M point (hν = 26 eV) in the -M direction. Figures 2(d)and 2(e) are ARPES images (lower panels) and MDCs at
EF (upper panels) at the M point at T = 100 and 20 K,
respectively. Two electron bands across EF and centered at
the M point appear at both temperatures. In contrast to the
A point, the kF ’s and the bottoms of both electron bands at
40 and 100 meV do not shift with temperature, as shownin Figs. 2(e) and 2(f). These results at the M and A points
suggest that the shallower band at the A point shifts withdecreasing temperature but that at the M point does not shift
with temperature. These are the same relationships observed

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ORBITAL-DEPENDENT ELECTRON CORRELATION IN . . .

0.0(a) T = 150 K(a1)A(b) T = 15 K
(b1)
A

PHYSICAL REVIEW B 93, 024503 (2016)

A

(a)

(c)

Inner (Z point)
Inner (Γ point)

-40

0.0

(a2)

2

2

A ∂ I/∂E (b2)22

A ∂ I/∂E

0.1
0.0

Binding energy (meV)

150 K

0.1

(a3)

A ∂2I/∂k2 (b3)A ∂2I/∂k2

Intensity (arb. units)

Binding energy (eV)

T=
250 K

125 K
100 K
80 K

80 K
50 K
40 K
20 K

0.1

(b)
Deep (A point)
Shallow (A point)
Deep (M point)
Shallow (M point)

40

80

15 K
0.0

ky (Å-1)

0.3

-0.3

0.0

ky (Å-1)(d) T = 100 K(e) T = 20 K

M

M

0.0

0.3

0.0

ky (Å-1)

0.3

-0.3

0.0

ky (Å-1)

0.0

0.3

ky (Å-1)

0

0.3

100 K
20 K

0.2

50

100

150

200

250

300

Temperature (K)(f) k = 0 Å

0.1
-0.3

-0.3

Intensity (arb. units)-0.3

Binding energy (eV)0FIG. 3. (a) Temperature dependence of the top of the inner holeband at the  and Z points and (b) bottom of the electron bands at
the M and A points.

0.0

Binding energy (eV)FIG. 2. (a), (b) ARPES results at the A point (hν = 18 eV) along
the Z-A direction at T = 150 and 15 K, respectively. (a1), (b1)
ARPES images; (a2), (b2) EDC’s second-derivative images of (a1)and (b1), respectively; (a3), (b3) MDC’s second-derivative imagesof (a1) and (b1), respectively. Electron bands are evaluated by aparabolic fitting of the EDC peak positions around the band bottoms
and MDC peak positions around EF . Hole bands are guides for theeyes. (c) The temperature-dependent MDCs at EF at the A point. The
vertical lines indicate the Fermi wave vectors obtained by the MDC
fitting. MDC at 80 K is also plotted by a dashed line below 50 K
as a guide. (d), (e) ARPES images (lower panels) and MDCs at EF(upper panels) at the M point (hν = 26 eV) along the -M direction
at T = 100 and 20 K, respectively. (f) Comparison of EDCs at bothtemperatures at the M point.

between the inner hole band at the Z point and that at the point.
Figure 3 summarizes the energy shifts of the top (bottom)of the hole (electron) bands at the  and Z (M and A)
points as a function of temperature. The energies of the top(bottom) of the hole (electron) bands were evaluated by aparabolic fitting of the EDC/MDC and the EDC’s/MDC’s
second-derivative peak position, as shown in Figs. 1 and 2.
Figure 3(a) shows that the peak position of the Z point
rapidly shifts below T ∼ 50 K, which is approximately 2.5
times greater than Tc , in contrast to the lack of temperaturedependence at the  point. At the M and A points [Fig. 3(b)],the shallow electron band around the A point also shifts below
T = 50 K, but the deep electron band at the A point and thetwo electron bands at the M point are almost independent of
temperature. It is noted that the reproducibility was checkedby cleaving at both high (above 100 K) and low temperature(12 K). The shifted hole and electron bands are attributed

to the dyz and dxz/yz orbitals, respectively [12]. Therefore,
our observations suggest that only the dxz and dyz orbitals
exhibit an orbital-dependent electron correlation in LiFeAs.
For 122-type AFe2−y Se2 systems (A = K, Rb), only the dxyorbital has been reported to have orbital-dependent electron
correlations, but these systems have no temperature-dependent
band shifts [26]. Therefore, the observations in our study differ
completely from those of 122-type AFe2−y Se2 systems.
To date, orbital ordering/fluctuations [9] and/or thermally
excited carriers among the narrow bands [11] have been
invoked to explain the temperature-dependent band shift in
122-type iron pnictide superconductors. However, in LiFeAs,
neither the pseudogap nor the orbital-polarized electronic
structure between the dxz and dyz orbitals at the M andA points are observed in our study; this suggests that theoverall electronic structure in LiFeAs is not affected byorbital ordering/fluctuations. This is consistent with a recent
scanning-tunneling-microscopy study in which LiFeAs does
not have a symmetry-broken electronic structure, such as a
122-type nematic phase [27]. In addition, we observe thatthe narrow band at the  and M points does not shift but
the narrow hole and electron bands at the Z and A points
shift with temperature. The thermal excitation of carriers
should be equivalent in a 3D momentum space; therefore,
the temperature dependence of the band shift appears not tobe due to the thermal excitation of carriers from the narrow
bands.
Recently, a pseudogaplike feature below T = 55 K causedby antiferromagnetic fluctuations has been observed in ultrafast optical measurements for LiFeAs [28]. Indeed, thespin fluctuation is enhanced below T ∼ 50 K [14,15]. Thistemperature of approximately 50 K is consistent with that of
the observed band shift. This finding possibly suggests that theband shift is strongly related to spin fluctuations. In addition,in LiFeAs, a Lifshitz transition is observed in the hole FS with

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PHYSICAL REVIEW B 93, 024503 (2016)

only the dyz orbital at the Z point and without the SDW/AFM
transitions [29], possibly because of spin fluctuations [30].
Our observation might imply the violation of the Luttinger’s
theorem below T = 50 K (i.e., the hole concentration decreases, whereas the electron concentration increases). Thisfeature is also observed in the normal state of NaFeAs, whichis explained by short-range spin fluctuations [31] rather thana structural transition and/or fourfold-rotational-symmetry
breaking [32]. An important difference between LiFeAs and
NaFeAs is that, in the former, no structural transition exists(nor SDW). Thus, the one of the plausible explanations forthe band shift is the existence of short-range spin fluctuations,as discussed in Ref. [31]. As stated in that study, fast probes
such as ARPES are likely to capture the effect of short-range(local and fluctuating) ordering. In a previous study [31],band folding was observed, accompanied by a band shift,which is not observed in the present study. The intensity of
the folded band in LiFeAs may be very weak as comparedwith that in NaFeAs; this may be due to the absence of
SDW even at low temperatures. In LiFeAs, longitudinalmagnetoresistance is observed below T = 50 K, which issimilar to what happens in Ba(Fe1−x Cox )2 As2 because of
short-range spin fluctuations [33]. Therefore, one of theplausible interpretations for the selective band shift of LiFeAs
below 50 K is accompanied by short-range spin fluctuations
but with no SDW transition.

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To summarize, we performed ARPES measurementsof the stoichiometric superconductor LiFeAs to clarify
the temperature-dependent electronic structure at the highsymmetry points. The results show that the dyz hole band at
the Z point and the dxz/yz electron band at the A point shift tohigher binding energies below approximately 50 K, whereas
the other bands have almost no temperature dependence.
These results might suggest that a strong 3D orbital-dependent
correlation exists above Tc , possibly accompanied by shortrange spin fluctuations.
ACKNOWLEDGMENTS

The authors gratefully acknowledge M. Sakai for his
technical assistance during the experiments. Part of thiswork was supported by the Use-of-UVSOR Facility Program(BL7U, 2012, 2013) 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.I. acknowledges
support from Grant-in-Aid for Challenging Exploratory Research from JSPS (Grant No. 26610085). T.H. was supported
by a Grant-in-Aid for JSPS Fellows (Grant No. 13J02477).

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[25] See Supplemental Material at http://link.aps.org/supplemental/
10.1103/PhysRevB.93.024503 for the details regarding theinnermost hole band at the  point, the temperature dependence
at the Z, and the EDC at the A point.
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