Original Research ARTICLE
Orbital character and electron correlation effects on two- and three-dimensional Fermi surfaces in KFe2As2 revealed by angle-resolved photoemission spectroscopy
- 1Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo, Japan
- 2JST, Transformative Research-Project on Iron Pnictides, Chiyoda, Chiyoda, Tokyo, Japan
- 3Stanford Institute of Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA
- 4Departments of Physics and Applied Physics, and Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA, USA
- 5Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, CA, USA
- 6Advanced Light Source, Lawrence Berkeley National Lab, Berkeley, CA, USA
- 7Energy Technology Research Institute, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan
- 8Electronics and Photonics Research Institute, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan
- 9Department of Physics, Kobe University, Kobe, Hyogo, Japan
We have investigated orbital character and electron correlation effects on Fermi surfaces in the hole-overdoped iron pnictide superconductor KFe2As2, which shows a low Tc of ~4 K, by angle-resolved photoemission spectroscopy. From the polarization-dependence of the ARPES spectra, we have determined the orbital character of each Fermi surface. Electron mass renormalization of each band is quantitatively consistent with de Haas-van Alphen results. The outer β and middle ζ Fermi surfaces show large renormalization factor of m*/mb ~6–7, while the inner α Fermi surface has a smaller factor m*/mb ~2. Middle hole Fermi surface ζ has strong three-dimensionality compared to other Fermi surfaces, indicating the d3z2–r2 orbital character, which may be related to the “octet-line nodes” recently observed by laser ARPES. The observed orbital-dependent mass renormalization would give constraints on the pairing mechanism with line nodes of this system.
In contrast to the d-wave superconducting gaps in the high-Tc cuprate superconductors, experimental results on most of the iron-pnictide superconductors have indicated that superconducting gaps are nodeless and on the entire Fermi surfaces (FSs) . However, some of the iron pnictide superconductors show signatures of the nodes in the superconducting gaps. For example, thermal conductivity measurements of isovalent substituted system BaFe2(As1 − xPx)2  and the electron doped systems Ba(Fe1 − xCox)2As2 and Ba(Fe1 − xNix)2As2  in the superconducting state have shown signature of line nodes. According to the theories of spin fluctuation-mediated superconductivity, line nodes may appear when the pnictogen height becomes small [4, 5], the hole FS of dxy character around the zone center disappears and nesting between hole and electron FSs becomes weakened. (Here, x and y are referred to the direction of the nearest neighbor Fe atoms). The hole FSs of these systems exhibit strong three-dimensionality [6–8], resulting in poor nesting between the hole and electron FSs.
The end member compound of K-doped BaFe2As2 (K-Ba122) system, KFe2As2, with a low Tc of ~4 K  also shows signature of line nodes in penetration depth , thermal conductivity , and nuclear quadrupole resonance (NQR) measurements . In fact, a recent laser angle-resolved photoemission (ARPES) study of KFe2As2 has revealed a superconducting gap with “octet-line nodes” on the middle hole FS (ζ FS) . The observed nodes and a clear FS sheet dependence in the superconducting-gap size were well explained by a calculation with spin-fluctuation mechanism. However, the result is in strong contrast to the optimally doped K-Ba122 , while this is consistent with the evolution of the gaps as a function of K doping . Such a doping dependence in the superconducting gap may be related to the change in the FS topology. In going from the optimally [15, 16] to the overdoped region [17, 18] in K-Ba122 system, the electron pockets around the zone corner are replaced by small hole pockets surrounding the zone corner in a clover shape.
If the spin fluctuations are dominant in the pairing mechanism in KFe2As2, orbital dependent mass renormalization would be observed as a signature of spin fluctuations. So far, strong mass renormalization has been observed from the electronic specific heat coefficient γ as large as ~70–100 mJ/K2 mol [12, 19]. Also, both the ARPES  and dHvA studies [20, 21] have indicated the enhancement of the electron masses compared to those predicted by the band-structure calculation.
Although three hole FSs (α, β, and ζ) have been clearly resolved in our previous ARPES study , the mass renormalization factor for each FS has not been clarified yet. In the present study, in order to reveal the orbital dependent mass renormalization in the iron-based superconductors, we have performed an ARPES study of KFe2As2 using high-quality single crystals. We have determined the orbital character of the FSs by polarization dependent measurements and have revealed strongly orbital dependent correlation effects.
Experiment and Band-Structure Calculation
ARPES measurements were performed at beamline 5–4 of Stanford Synchrotron Radiation Lightsource (SSRL) and at BL10.0.1 of Advanced Light Source (ALS). Scienta SES-R4000 electron analyzers and linearly polarized light were used at both beamlines. The typical energy resolutions were 10 meV at SSRL and 20 meV at ALS, respectively. Single crystals of KFe2As2 were grown from a self-flux method. Resistivity measurements on some of the grown crystals showed the residual resistivity ratio of ~600. Samples were cleaved in situ and measured at a temperature of 15 K in a pressure better than 5 × 10−11 Torr. We have performed the measurements at photon energies from hν = 14 to 40 eV. The in-plane (kX, kY) and out-of-plane (kZ) momentum are expressed in units of π/a and 2π/c, respectively, where a = 3.864 Å and c = 13.87 Å. Here, the X and Y axes point toward the Fe-As bond direction, while the x and y axes are rotated by 45° from the X-Y coordination. The electronic band structure of KFe2As2 was calculated within the local density approximation (LDA) by using the full potential LAPW (FLAPW) method. We used the program codes TSPACE  and KANSAI-06. The experimental crystal structure  including the atomic position zAs of As (pnictogen height) was used for the calculation.
Results and Discussion
Band dispersions for a cut along the diagonal of the two-dimensional Brillouin zone (BZ) taken with hν = 25 eV  and 30 eV are shown in Figures 1A,B. All the energy bands predicted by the calculation (Figure 1C) are observed. While three bands (α, β, and ζ) form hole FSs around the zone center, the ε band forms small hole FSs around the zone corner. The structure around 0.15 eV below EF in Figure 1A is z2 band shown in Figure 1C, which has a strong three dimensionality . Another hole-like band crossing EF near the zone center is a surface state . While the ζ band is nearly degenerated with the α band at hν = 25 eV, these bands are separated at hν = 30 eV, indicating three-dimensionality of the band dispersions. Note that the order of the α, β, and ζ bands from the zone center is different between theory and experimental data. We shall describe the present assignment of the band dispersions based on the matrix-element effect data as below.
Figure 1. Band dispersions of KFe2As2 in the zone diagonal direction. (A,B) ARPES spectra taken at hν = 25 eV  and 30 eV, respectively, corresponding to kz = 6.5 and 7.0 (2π/c). SS denotes surface states. (C) Band dispersions predicted by band-structure calculation.
FS mapping in kX-kY plane is shown in Figures 2A,B. By assuming the inner potential V0 = 13.0 eV (Figures 2A,B) approximately represent kX-kY planes including the Γ and the Z point, respectively. All the three hole FSs around the center of the 2D BZ have been clearly resolved and small hole FSs appear around the BZ corner due to heavy hole doping. In Figure 2B, the surface states near the zone center form ridge-like structures extending to the kX and kY directions, causing the peculiar cross-like intensity distribution . We found that the middle hole FS (ζ) has different shape between the Γ and the Z point, indicating strong three dimensionality.
Figure 2. FSs of KFe2As2 observed by ARPES. ARPES intensity at EF mapped in the kX-kY plane taken at different photon energies corresponding to kz ~ Γ (A) and kz ~ Z (B). Red dots indicate kF positions determined by the peak positions of momentum distribution curves (MDC's) and white dotted lines indicate FSs deduced from the kF positions.
In Figure 3, we compare the FSs obtained by ARPES with the band-structure calculation. As seen in (Figures 3A,B), the sizes of the observed α and β FSs do not show appreciable change with kz. On the other hand, the shape of the ζ FS significantly changes between kz ~ Γ and Z. While the ζ FS has a diamond-like cross-section for kz ~ Γ and is nearly degenerate with the α FS in the zone diagonal direction, it has a circular cross-section for kz ~ Z. Such a change is seen in the inner-most calculated hole FS in Figures 3C,D.
Figure 3. Comparison of FSs obtained by ARPES and those predicted by band-structure calculation. (A,B) FSs determined by ARPES. kF positions in Figure 2 have been symmetrized in the first BZ. (C,D) FSs given by the band-structure calculation. A small FS around the Z point comes from a three-dimensional dz2 band.
In order to determine the orbital character of the FSs, we have investigated the polarization dependence of the ARPES intensity as shown in Figure 4. FS mapping shown in (Figures 4A,B) indicates clear polarization dependence in the intensity distribution for each FS. We have simulated the intensity distribution by using the following assumptions. Based on the result of the band-structure calculation, we assume that three orbitals xy, yz, and zx constitute the FSs. We refer to the three band as xy, yz, and zx band according to the orbital character of the band with momentum in the zone diagonal kx (// kX + kY) direction. Using the angle θ around the Γ point, the orbital character of the xy, zx, and yz band can be approximately expressed by |xy>, cosθ |zx> + sinθ |yz> and -sinθ |zx> + cosθ |yz>, respectively. By assuming the dipole approximation of the transition matrix element |< i|ε · r|f >|2, where |i>, |f >, and ε are the initial state, the final state, and the polarization vector, respectively, one can predict the intensity distribution. For example, when |i >=|xy>, ε //x and |f > is a wave function of a free electron, the transition matrix element |< i|ε · r|f >|2 is proportional to k2y in the lowest order in k.
Figure 4. Polarization dependence of the FS mapping for KFe2As2. (A,B) Measured ARPES intensity at EF in the kX-kY plane taken at hν = 40 eV (kz ~ Γ). Electric vectors are shown by arrows. (C,D) Simulation of the ARPES intensity distribution corresponding to (A,B). Shapes of FSs have been taken from Figure 2. By assuming certain orbital character for each FS, intensity distribution has been simulated and is shown by thickness of the curves (For details, see the text).
Figures 4C,D are the results of the intensity simulations of the FSs whose shapes have been determined by the present experimental data. Here, we assign the inner, middle, and outer FSs to the yz, xz, and xy-band, respectively, so that we can reproduce the experimental intensity distribution. This assignment of the orbital character is different from the band-structure calculation where the inner, middle, and outer FSs have xz, xy, and yz orbital character, respectively. However, the present ARPES result is consistent with the previous ARPES result of Co-Ba122  and the theoretical prediction of LDA+DMFT , which indicate the energy inversion of the xy and yz/xz bands due to orbital-dependent correlation effect. This trend is also consistent with an ARPES result of LiFeAs . That is, the xy band in most strongly affected by electron correlation and is shifted upward relative to the other bands.
Another discrepancy from the band-structure calculation is the inversion of the yz and xz bands in the kX (kY) direction. In the result of the band-structure calculation, the inner FS has xz character (in the kX direction) with rounded-square shape around the Γ point and becomes circular around the Z point because of hybridization with the z2 orbital. In the present ARPES result, such a character has been observed in the middle ζ FS. According to the angular-dependent magnetoresistance oscillations, such a rounded-square FS is also bigger than a circular hole FS . The observed inversion of the xz, yz bands is consistent with the ARPES result of Co-Ba122  and the LDA+DMFT calculation for KFe2As2 .
In the dHvA study, the sizes of the hole FSs are found to be smaller than those predicted by band-structure calculations . We have determined the cross-sectional area of the FSs as listed in Table 1 together with those of the dHvA measurements and the band-structure calculation. The cross-sectional areas for the α and ζ FSs observed by ARPES are close to those obtained by the dHvA result and are smaller than the band-structure calculation. On the other hand, the area of the β and ε FSs determined by ARPES are much larger than the calculation results. The total hole count from the observed FSs yields the hole FS volume of 61% of the BZ, indicating a deviation from the value of 50% expected from the chemical composition, because most of the FSs observed by ARPES are nearly 10–20% larger than those observed by dHvA. The deviation of the FS volume implies that there is excess hole doping of 0.11 per Fe atom at the sample surface. Nevertheless, the surface effect is not so serious as those in 1111 system where excess 0.5–0.6 holes per Fe are doped , and one can still discuss mass renormalization from the present result.
The effective masses determined by ARPES are compared with those derived from the dHvA measurements and the band-structure calculation in Table 1. For all the FSs, the effective mass ratio m*/me, where me is the free electron mass, determined by ARPES is in good agreement with those obtained by dHvA. For the hole FSs around the zone center, the outer β and middle ζ FSs show large renormalization factor of m*/mb ~6–7, while the inner α FS has a smaller factor m*/mb ~2. The strong mass enhancement for the β and ζ band may be due to the fact that the orbitals are directed to the Fe-As bond direction, causing the enhancement of electron correlation effects. Particularly, according to LDA+DMFT calculation [19, 25], a larger mass renormalization is expected in the xy band than those of the yz/xz bands. Thus, the observed mass enhancement factors indicate moderate to strong electron correlation. From the effective masses m* listed in Table 1, the electronic specific heat coefficient γ is calculated to be γ~90 mJ/molK2, which is close to γ = 103 mJ/molK2 estimated from specific heat measurements .
The penetration depth  and thermal conductivity  measurements of KFe2As2 suggest that line nodes exist in the superconducting gap. Particularly, recent thermal conductivity result  has been interpreted based on the d-wave symmetry in KFe2As2. Because the small hole FSs around the zone corner are too small to account for the linear temperature dependence of the superfluid density , the node should be on the zone-centered hole FSs. In fact, the “octet-node” has been observed in the ζ hole FS by the laser ARPES study . Based on the spin-fluctuation-mediated model calculation, the octet node can be interpreted as vertical nodes with A1g gap symmetry, which originates from the 3z2−r2 orbital character of the ζ hole FS. Such octet nodes may not contradict with the observation of the node on the small hole pockets in Ba0.1K0.9Fe2As2 , if the vertical nodal line with A1g gap symmetry rapidly shifts in the momentum space with hole doping. On the other hand, a small-angle neutron scattering measurement on KFe2As2 has suggested the existence of a horizontal node . One should note that both the vertical and horizontal nodes [32–34] can be realized in the region of the FS with 3z2−r2 orbital character. In the present work, we revealed that the ζ FS has a strong three-dimensionality compared to the other FSs, implying a significant amount of the 3z2−r2 character in the ζ FS.
We have performed an ARPES study of KFe2As2 to investigate orbital-dependent correlation effects. The orbital character of each FS is determined by the polarization dependence of the ARPES intensity. The value of the electron mass renormalization for each band indicates orbital-dependent correlation effects and is consistent with the dHvA result [20, 21] and the DMFT calculation . Particularly, the β and ζ FS show large mass enhancement of m*/mb ~ 6–7. Only the middle hole FS ζ shows a clear three-dimensionality, suggestive of 3z2−r2 orbital character, which may be related to the “octet nodes” . The precise determination of the orbital dependent mass renormalization in the present study would give constraint on the pairing mechanism with line nodes.
Conflict of Interest Statement
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
We are grateful to K. Kuroki, R. Arita, H. Fukazawa, T. Terashima and M. Kimata for enlightening discussions. Thanks are also due to K. Haule for showing us the result of LDA-DMFT calculations prior to publication. This work was supported by the Japan-China-Korea A3 Foresight Program and a Grant-in-Aid for Young Scientist (B) (22740221) from the Japan Society for the Promotion of Science. SSRL is operated by the US DOE Office of Basic Energy Science Divisions of Chemical Sciences and Material Sciences. ALS is supported by the U.S. DOE (Contract No. DE-AC02-05CH11231).
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Keywords: iron pnictide superconductor, angle-resolved photoemission spectroscopy, electron correlation
Citation: Yoshida T, Ideta S-I, Nishi I, Fujimori A, Yi M, Moore RG, Mo S-K, Lu D, Shen Z-X, Hussain Z, Kihou K, Shirage PM, Kito H, Lee C-H, Iyo A, Eisaki H and Harima H (2014) Orbital character and electron correlation effects on two- and three-dimensional Fermi surfaces in KFe2As2 revealed by angle-resolved photoemission spectroscopy. Front. Physics 2:17. doi: 10.3389/fphy.2014.00017
Received: 22 December 2013; Accepted: 05 March 2014;
Published online: 01 April 2014.
Edited by:Christos Panagopoulos, Nanyang Technological University, Singapore
Reviewed by:Fengqi Song, Nanjing University, China
Anjan Soumyanarayanan, Massachusetts Institute of Technology, USA
Hong Ding, Chinese Academy of Sciences, China
Copyright © 2014 Yoshida, Ideta, Nishi, Fujimori, Yi, Moore, Mo, Lu, Shen, Hussain, Kihou, Shirage, Kito, Lee, Iyo, Eisaki and Harima. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Teppei Yoshida, Graduate School of Human and Environmental Studies, Kyoto University, Yoshida-Nihonmatsu-cyo, Sakyo-ku, Kyoto 606-8501, Japan e-mail: email@example.com
†Present address: Teppei Yoshida, Graduate School of Human and Environmental Studies, Kyoto University, Sakyo-ku, Kyoto, Japan