Role of bonding angle on superconductivity in iron pnictides through

Role of bonding angle on superconductivity in iron pnictides through orbital mixing :
Comparative electronic structure study of LiFeAs and Sr2 VO3 FeAs
Y. K. Kim,1, 2 Y. Y. Koh,1 W. S. Kyung,1 G. R. Han,1 B. S. Lee,3 Kee Hoon Kim,3 J. M. Ok,4
J. S. Kim,4 M. Arita,5 K. Shimada,5 H. Namatame,5 M. Taniguchi,5 S.-K. Mo,2 and C. Kim1, ∗
1
Institute of Physics and Applied Physics, Yonsei University, Seoul 120-749, Korea
Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
3
CeNSCMR, Department of Physics and Astronomy,
Seoul National University, Seoul 151-747, Korea
4
Department of Physics, Pohang University of Science and Technology, Pohang 790-784, Korea
5
Hiroshima Synchrotron Radiation Center, Hiroshima University, Higashi-Hiroshima, Hiroshima 739-0046, Japan
(Dated: May 27, 2014)
2
The correlation between As-Fe-As bonding angle and superconducting transition temperature,
universal among different iron pnictides species, has been largely overlooked despite its potential
importance in understanding mechanisms of superconductivity. Here we present comparative electronic structure studies on two representative systems LiFeAs and Sr2 VO3 FeAs. Without any dopant
in the system, they provide a rather clean example of bonding angle dependence of transition temperature. Our results suggest that the distinct difference in inter-orbital coupling strength is the
key element of the bonding angle dependence.
PACS numbers: 74.25.Jb,74.70.Xa,78.70.Dm
The special relation between As-Fe-As bonding angle
and superconductivity is one of the most remarkable universal feature in iron-based supercondutor. The maximum transition temperature (Tc ) can only be achieved
with the optimal bonding angle that makes FeAs4 tetrahedron regular[1, 2], without respect to the individual
species of pnictides family. This indicates an important
role of bonding angle to the superconductivity in iron
based superconductors. Despite its importance, a hinge
behind the relationship between bonding angle and Tc is
unclear and less considered so far.
One of the key elements that vary with bonding angle is
the momentum dependent electronic structure. Theoretically, for example, the electronic structure can be modified significantly and orbital-dependently upon bonding angle change, particularly for bands around the Γpoint.[3] As a result, at optimal angle, every hole band
top locate near the Fermi level and generate a high density of state near the Fermi energy (EF ). The rich density
of states near EF could account for the enhancement of
Tc .
However, experimental studies, using a direct tool
such as angle-resolved photoemission (ARPES), to probe
changes in the momentum dependent electronic structure
upon bonding angle change have been lacking. LiFeAs
and Sr2 VO3 FeAs may be a good candidate system to resolve the issue. LiFeAs has a small bonding angle with
relatively lower Tc at 18 K[2, 4], while Sr2 VO3 FeAs shows
higher Tc at 37 K[1, 7] and its bonding angle is close
to the optimal value. Further, both showing superconductivity without any doping[4, 7] guarantee that the
dominant acting parameter is bonding angle only. In a
technical point of view, contrast to other phases in iron
based superconductors, both systems have neutral cleav-
age planes that fit to ARPES experiment exploring the
intrinsic electronic structure.
In this letter, we present a comparative electronic
structure study on LiFeAs and Sr2 VO3 FeAs. Using
ARPES, the band dispersion including kz dependence
and its orbital characters are explored. Detailed analysis reveals Sr2 VO3 FeAs electronic structure has orbital
mixed nature and relatively strong Fermi surface nesting instability which are not shown in LiFeAs electronic
structure and indicate strong inter-orbital coupling. Finally, the role of bonding angle will be discussed in terms
of the different inter-orbital coupling strength.
Single crystalline LiFeAs was synthesized with Sn-flux
method[6] and self-flux method. Sr2 VO3 FeAs single crystal was grown with self-flux method[–]. LiFeAs sample preparation have been done in argon atmosphere
to avoid sample damaging. Sample surface contamination was strictly monitored during the measurements
by monitoring the spectral weight near the Fermi edge.
ARPES measurements on LiFeAs were performed at various beamlines including the beamline 9 in Hiroshima
synchrotron radiation center (HiSoR), beamline 5-4 in
Stanford synchrotron radiation lightsource and beamline
7.0.2 in Advanced light source (ALS). Measurements on
Sr2 VO3 FeAs were performed at beamline 10.0.1 in ALS.
Samples were cleaved at 10 K. Subsequent experiments
were also performed at 10 K in a vacuum better than
4×10−11 Torr. Polarization was controlled by undulator
at the HiSoR and by rotating the sample or analyzer at
the ALS.
In Fig. 1, Fermi surfaces and band dispersions of two
systems are provided. Note that data for LiFeAs and
Sr2 VO3 FeAs are plotted with gold and gray color scales
throughout this Letter, respectively, to avoid possible
2
(a)
1.0
1.0
X
Sr2VO3FeAs
dyz
0.05
dxy
kx
Γ
dyz
dxy
kx
Γ
Χ
Χ
0.00
0.5
0.5
-1
ky (Å )
LiFeAs
(b)
X
-0.05
0.0
LiFeAs
0.0
0.5
-1
-0.15
Γ
0.0
0.5
kx (Å )
0.05
(c)
Binding energy (eV)
0.00
kx
-0.05
β
β
γ
-0.10
-0.15
0.05
Γ
Χ
LiFeAs
(d)
Sr2VO3FeAs
Γ
ky
(f)
ky
Χ
0.00
Γ
0.0
LiFeAs
0.4
Χ
0.8
Sr2VO3FeAs
Γ
1.2
0.0
0.4
0.8
1.2
σ-pol
dzx
kx
kx
Γ
Χ
(g)
(c)
π-pol
dzx
0.05
Χ
(g)
dxy
ky
Γ
π-pol
dzx
dyz
ky
Γ
Χ
Χ
0.00
Γ
Χ
(h)
Γ
0.00
Χ
-0.05
-0.10
X
Binding energy (eV)
(f)
dzx
Χ
Momentum (Å )
-0.15
-0.10
-0.15
Χ
0.00
-0.15
-1
-0.05
σ-pol
Γ
ky
Γ
Χ
(b)
0.05
-0.10
α
-0.10
0.05
-0.15
σ-pol
-0.05
α
-0.05
-0.15
-0.10
(e)
dyz
ky
Γ
γ
-0.05
σ-pol
dyz
0.05
1.0
-1
kx (Å )
(e)
kx
0.00
(a)
Sr2VO3FeAs
1.0
Binding energy (eV)
0.0
-0.10
Γ
Sr2VO3FeAs
Sr2VO3FeAs
Momentum (Å )
-1
(d)
0.0
π-pol
0.4
0.8
1.2
(h)
0.0
π-pol
0.4
0.8
1.2
Momentum (Å-1)
(i)
FIG. 1: (Color online) Fermi surfaces of (a)LiFeAs and
(b)Sr2 VO3 FeAs. Band dispersion along two different high
symmetry direction (kx and ky ) for (c),(d) LiFeAs and
(e),(f) Sr2 VO3 FeAs. Stacked EDCs around the Γ-point of
Sr2 VO3 FeAs along (g) kx and (h) ky directions.
confusion. Band dispersions along the two different ΓX directions are plotted in Fig. 1 (c)-(f). Depending on
the geometry that the incident light and the detection
plane make, two Γ-X directions in these panels can be
distinguished and show enhanced intensity for selective
dispersions. Combining the band dispersions in two cuts,
it is shown that overall electronic structure of both systems shares general features with that of other iron pnictides systems[8–12]. Especially fact that the bands near
EF of Sr2 VO3 FeAs show general iron pnictide band dispersion again confirm the absence of the vanadium bands
near the EF as previous ARPES study reported[13].
In comparison, near EF , the size of electron pockets at
the zone corner in both systems are similar, while those
of hole pockets at the zone center are not. Particularly,
the size of most outer γ hole pockets in LiFeAs is much
large than that in Sr2 VO3 FeAs. In LiFeAs, one of the
inner hole bands, β band crosses the Fermi level while
the other inner hole band, α band, remains below EF .
Both α and β bands in Sr2 VO3 FeAs do not cross EF .
FIG. 2: (Color online) Polarization dependence of ARPES
data for different incident directions and for σ- and πpolarizations on (a)-(d) LiFeAs and (e)-(h) Sr2 VO3 FeAs.
Color bars indicate the transition allowed orbital in each geometry with color cole dxy (blue), dyz (green), dzx (red),
dx2 −y2 (sky blue).(i) Two different experimental geometries,
φ-polarization (left) and σ-polarization (right).
In Sr2 VO3 FeAs, the hole band tops near the Γ point are
located right below the Fermi level, and additional tiny
electron band appears close to EF . This electron band
can be seen more clearly with energy distribution curves
(EDCs) around the Γ-point shown in Fig. 1(g) and (h).
To investigate orbital character of both system, which
is an essential step for iron pnictide electronic structure
study, polarization dependent measurements has been
performed. In Fig. 2, a clear polarization dependence
is shown in each geometry and each direction, kx and ky
axes determined by the light propagation direction, x axis
(see Fig. 3(i)). The transition-allowed orbitals in each
relevant geometry, determined according to the parity arguments considered in previous studies[17–20], are given
3
(a)
LiFeAs (b)
Sr2VO3FeAs
kz=0
kz=0
1.0
X
0.0
0.5
0.5
-1
ky (Å )
1.0
X
β
0.0
Γ
γ
Γ
γ
LiFeAs
1.0
1.0
Sr2VO3FeAs
kz=π
R
0.0
0.5
0.5
-1
ky (Å )
kz=π
R
β
0.0
Ζ
γ
0.0
Ζ
γ
β
0.5
1.0
0.0
0.5
-1
kx (Å )
(c) kz=0
0.0
0.1
0.3
0.4
γ
Ζ
Sr2VO3FeAs
Γ
0.2
R
β
γ
Sr2VO3FeAs
-0.1
(d) kz=π
X
α
1.0
-1
kx (Å )
MDCs (Arb. unit)
above each panel with color codes: red for dzx orbital,
green for dyz orbital and blue for dxy orbital. Based on
these, assignments of the orbital characters for each band
have been made as indicated with color coded solid lines.
For examples, in Fig. 2(a), only two hole bands appear
out of the three hole bands around the Γ-point. As the
transition allowed orbital in given geometry are dxy and
dyz , the orbital characters of these two hole bands can
be assigned as dyz for β and dxy for γ bands considering
the consistency with the other geometrical appearances.
A noticeable aspect is, especially for hole bands, that
polarization dependence is rather weak and anomalous
in Sr2 VO3 FeAs. While LiFeAs has strong polarization
dependence so that each band appear only in the transition allowed geometry and disappear in the transition
forbidden geometry. For Sr2 VO3 FeAs, even it is rather
weak, the spectral weight from the γ band survives in every geometry. Once the γ band in Sr2 VO3 FeAs has dxy
orbital character just as in LiFeAs or other iron based
superconductors[17–20], the γ band should not appear
in the geometries where the transition from dxy orbital is
forbidden. Also β band shows unusual polarization dependence, distinctly different from other iron pnictides.
The band can only be seen in one geometry where transition from dxy orbital is allowed and does not appears in
the other geometries where dxy transition is forbidden.
A natural explanation of this unusual polarization dependences is that bands in Sr2 VO3 FeAs have the mixed
orbital characters, particularly for hole bands. For example, the γ band is not solely of dxy , but a mixture of dxy ,
dyz , and dzx (|i = A|xyi+a|yz, zxi). The contribution of
the other orbital, dyz,zx , can produce the spectral weight
in the dxy forbidden geometry. In a similar manner, the
α and β bands also have a mixture of dxy contribution
which can explain the polarization dependence of the β
band, that is, appears only when the transition from dxy
orbital is allowed.
Once γ has orbital mixed state and no longer has inplane orbital character (dxy ) only, γ band will show finite
kz dispersion by the contribution of dyz/zx orbital while
generally in iron based superconductor, the band with
an in-plane orbital character does not show any strong
kz dependence[14–16]. To explore the kz dependence of
the electronic structure, photon energy dependent measurements were carried out. Results are given in Fig. 3
with Fermi surfaces of both systems at kz =0 and kz =π.
In LiFeAs case, relatively weak kz dependence can be
seen only in inner hole pocket and electron pockets, consistent with previous results[17]. Sizes of both pockets
slightly increase at kz =π, while the size of the γ hole
pocket remains unchanged. Sr2 VO3 FeAs shows a similar trends except for the γ pocket, which shows strong
modulation along the kz direction. Obviously, size and
shape are changed along kz which can be seen clearly
with stacked momentum distribution curves (MDCs) at
EF at different kz (see Fig. 3 (c) and (d)).
0.5
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
-1
kx (Å )
FIG. 3: (Color online) Fermi surfaces of (a) LiFeAs and (b)
Sr2 VO3 FeAs at kz =0 (upper) and π (lower). Stacked MDCs
of Sr2 VO3 FeAs at EF along kx direction taken from constant
energy map at (c) kz =0 and (d) kz =π.
The orbital mixing again can explain the unusual
strong kz dependence of the γ band in Sr2 VO3 FeAs. A
portion of dyz,zx orbital can induce the kz dependence
that cannot be realized by dxy orbital only, since dxy does
not have a dependence in z-direction. The similarity between the observed kz dependence of the γ band and the
general kz dependence of the inner hole bands of iron
pnictides, which have dyz,zx orbital characters[14, 16, 17]
supports the above explanation. In short, both the polarization and the kz dependences indicate the orbital
mixed states in Sr2 VO3 FeAs.
In Fig. 4 (a), the band dispersions with orbital characters are summarized. The orbital characters are indicated
in the same color code used in Fig. 2. kz dependence of
each band are reflected by line width.
The hole bands near Γ point shows different characters between LiFeAs and Sr2 VO3 FeAs, while the electron bands share similarities. Of particular interest is
that γ bands in respective systems show dramatic differences. In LiFeAs, γ band top locates in much higher
than Fermi level while other two band tops are close
4
(a)
Γ
γ
β
α
Binding energy (eV)
that Sr2 VO3 FeAs shows the higher TC than LiFeAs, the
inter-orbital coupling instability can be assigned as the
importance ingredient of superconductivity and the potential hinge between the bonding angle and TC . Our
results is the first experimental revealing of the presence
and the possible role of the inter-orbital coupling instability which is so far has been considered to be important
for the superconductivity in the number of theoretical
studies[21–23].
Χ
LiFeAs
EF
0.0
0.2
0.4
dxy
Γ
0.6
0.8
dyz
Χ
Sr2VO3FeAs
EF
1.0
dzx
γ
β
α
0.0
0.2
0.4
0.6
0.8
1.0
Momentum (π/a)
(b)
LiFeAs
Sr2VO3FeAs
electron FS
hole FS
Γ/Χ
Γ/Χ
kz=0
kz=π
(c)
LiFeAs
Sr2VO3FeAs
102 °
109 °
dxy
dxz, dyz
dxy,dyz,dxz
FIG. 4: (Color online) (a) Summary of orbital character
of each band for LiFeAs (upper) and Sr2 VO3 FeAs (lower).
Width of lines indicates kz dispersions of bands. Same color
code is used as in figure 3. Stripe means orbital mixed state.
(b) Schematic of Fermi surface nesting conditions with transfer momentum ~
q = (π, π). Band dispersions and size of pockets are extracted from the experimental data. (c) Schematics
of FeAs4 tetrahedron and relative t2g orbital levels of both
systems.
to Fermi level. Meanwhile all three hole band tops in
Sr2 VO3 FeAs are closely located near Fermi level. Furthermore, as discussed before, Sr2 VO3 FeAs γ band shows
rather anomalous features: strong kz dependence and the
orbital mixed nature, distinctly different from LiFeAs.
Also, the band dispersions of both systems hold different Fermi surface nesting instability conditions. In Fig. 4
(b), the hole and electron Fermi surfaces of both systems
are overlapped to visualize the degree of the Fermi surface nesting instabilities. Again, the colored area indicate
the kz dependence of the hole Fermi surfaces. Clearly,
Sr2 VO3 FeAs shows the stronger nesting instability than
LiFeAs, especially at kz =0, as hole Fermi surface matches
well with electron Fermi surface in Sr2 VO3 FeAs while
LiFeAs Fermi surfaces show poor overlap in entire kz
range.
Both the orbital mixing and the strong nesting instability consistently imply the strong inter-orbital coupling
instability only in Sr2 VO3 FeAs. Together with the fact
As mentioned earlier, the dominant distinguishing parameter between LiFeAs and Sr2 VO3 FeAs is the bonding
angle α. LiFeAs has bonding angle α = 102◦ and FeAs4
tetrahedron is elongated. Meanwhile, Sr2 VO3 FeAs has
bonding angle α = 109◦ close to optimal value and FeAs4
tetrahedron is almost regular (see Fig. 4 (c)). Thus one
can consider that three t2g orbital states have similar
energy level and are nearly degenerated in Sr2 VO3 FeAs
case while dxy orbital locates in a higher energy level
than other orbital states in LiFeAs[3], which is reflected
in measured band dispersion of both system shown in Fig.
4 (a). The degeneracy introduces the orbital mixed states
and also the scattering channel for the inter-orbital coupling, which may enhance the superconductivity. This,
we believe, gives a natural explanation on the observed
correlation between the bonding angle and the transition
temperature. We also note that only dxy orbital level is
being modified strongly than other bands upon the bonding angle change which can be understand by its localized
nature compare to other orbital [24].
In conclusion, by comparative electronic structure
studies on LiFeAs and Sr2 VO3 FeAs, we have established
the possible role of bonding angle on the superconductivity as follow. As bonding angle changes close to the optimal value, localized dxy orbital state shifts in the way all
three orbital state closely degenerated. This degeneracy
enhances inter-orbital coupling instability strongly which
can be seen by occurrence of the orbital mixing and the
nesting instability in the electronic structure. The strong
inter-orbital coupling may enhance the superconductivity
through activating electron pair instability, for example,
mediated by a bosonic mode of electronic origin such as
an spin and/or orbital fluctuation.
This work was supported through NRF Grant No.
20100018092 and KICOS Grant No. K20062000008. The
work at SNU was supported by the National Creative Research Initiative Grant No. 2010-0018300. PLS is supported by BSRP through the NRF funded by the MEST
(2009-0088969).
∗
Electronic address: [email protected]
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