# Orbital character and electron correlation effects on two- and three-dimensional Fermi surfaces in KFe_{2}As_{2} revealed by angle-resolved photoemission spectroscopy

^{1}Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo, Japan^{2}JST, Transformative Research-Project on Iron Pnictides, Chiyoda, Chiyoda, Tokyo, Japan^{3}Stanford Institute of Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA^{4}Departments of Physics and Applied Physics, and Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA, USA^{5}Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, CA, USA^{6}Advanced Light Source, Lawrence Berkeley National Lab, Berkeley, CA, USA^{7}Energy Technology Research Institute, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan^{8}Electronics and Photonics Research Institute, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan^{9}Department 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 KFe_{2}As_{2}, which shows a low *T*_{c} 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**/*m*_{b} ~6–7, while the inner α Fermi surface has a smaller factor *m**/*m*_{b} ~2. Middle hole Fermi surface ζ has strong three-dimensionality compared to other Fermi surfaces, indicating the *d*_{3z2–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.

## Introduction

In contrast to the *d*-wave superconducting gaps in the high-*T*_{c} 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) [1]. 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 BaFe_{2}(As_{1 − x}P_{x})_{2} [2] and the electron doped systems Ba(Fe_{1 − x}Co_{x})_{2}As_{2} and Ba(Fe_{1 − x}Ni_{x})_{2}As_{2} [3] 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 *d*_{xy} 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 BaFe_{2}As_{2} (K-Ba122) system, KFe_{2}As_{2}, with a low *T*_{c} of ~4 K [9] also shows signature of line nodes in penetration depth [10], thermal conductivity [11], and nuclear quadrupole resonance (NQR) measurements [12]. In fact, a recent laser angle-resolved photoemission (ARPES) study of KFe_{2}As_{2} has revealed a superconducting gap with “octet-line nodes” on the middle hole FS (ζ FS) [13]. 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 [14], while this is consistent with the evolution of the gaps as a function of K doping [15]. 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 KFe_{2}As_{2}, 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/K^{2} mol [12, 19]. Also, both the ARPES [18] 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 [18], 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 KFe_{2}As_{2} 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 KFe_{2}As_{2} 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 *h*ν = 14 to 40 eV. The in-plane (*k*_{X}, *k*_{Y}) and out-of-plane (*k*_{Z}) 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 KFe_{2}As_{2} was calculated within the local density approximation (LDA) by using the full potential LAPW (FLAPW) method. We used the program codes TSPACE [22] and KANSAI-06. The experimental crystal structure [23] including the atomic position *z*_{As} 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 *h*ν = 25 eV [18] 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 *E*_{F} in Figure 1A is *z*^{2} band shown in Figure 1C, which has a strong three dimensionality [18]. Another hole-like band crossing *E*_{F} near the zone center is a surface state [18]. While the ζ band is nearly degenerated with the α band at *h*ν = 25 eV, these bands are separated at *h*ν = 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 KFe _{2}As_{2} in the zone diagonal direction. (A,B)** ARPES spectra taken at

*h*

**ν**= 25 eV [18] and 30 eV, respectively, corresponding to

*k*

_{z}= 6.5 and 7.0 (2

**π**/

*c*). SS denotes surface states.

**(C)**Band dispersions predicted by band-structure calculation.

FS mapping in *k*_{X}-*k*_{Y} plane is shown in Figures 2A,B. By assuming the inner potential *V*_{0} = 13.0 eV (Figures 2A,B) approximately represent *k*_{X}-*k*_{Y} 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 *k*_{X} and *k*_{Y} directions, causing the peculiar cross-like intensity distribution [18]. 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 KFe _{2}As_{2} observed by ARPES**. ARPES intensity at

*E*

_{F}mapped in the

*k*

_{X}-

*k*

_{Y}plane taken at different photon energies corresponding to

*k*

_{z}~ Γ

**(A)**and

*k*

_{z}~

*Z*

**(B)**. Red dots indicate

*k*

_{F}positions determined by the peak positions of momentum distribution curves (MDC's) and white dotted lines indicate FSs deduced from the

*k*

_{F}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 *k*_{z}. On the other hand, the shape of the ζ FS significantly changes between *k*_{z} ~ Γ and *Z*. While the ζ FS has a diamond-like cross-section for *k*_{z} ~ Γ and is nearly degenerate with the α FS in the zone diagonal direction, it has a circular cross-section for *k*_{z} ~ *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. *k*_{F} 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 *d*_{z2} 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 *k*_{x} (// *k*_{X} + *k*_{Y}) 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

*k*

^{2}

_{y}in the lowest order in

**.**

*k***Figure 4. Polarization dependence of the FS mapping for KFe _{2}As_{2}. (A,B)** Measured ARPES intensity at

*E*

_{F}in the

*k*

_{X}-

*k*

_{Y}plane taken at

*h*

**ν**= 40 eV (

*k*

_{z}~ 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 [24] and the theoretical prediction of LDA+DMFT [25], 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 [26]. 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 *k*_{X} (*k*_{Y}) direction. In the result of the band-structure calculation, the inner FS has *xz* character (in the *k*_{X} direction) with rounded-square shape around the Γ point and becomes circular around the *Z* point because of hybridization with the *z*^{2} 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 [27]. The observed inversion of the *xz*, *yz* bands is consistent with the ARPES result of Co-Ba122 [24] and the LDA+DMFT calculation for KFe_{2}As_{2} [25].

In the dHvA study, the sizes of the hole FSs are found to be smaller than those predicted by band-structure calculations [9]. 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 [28], and one can still discuss mass renormalization from the present result.

**Table 1. Cross-sectional areas and effective masses of FSs of KFe _{2}As_{2} determined by ARPES and dHvA experiment [20, 21]**.

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**/*m*_{e}, where *m*_{e} 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**/*m*_{b} ~6–7, while the inner α FS has a smaller factor *m**/*m*_{b} ~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/molK^{2}, which is close to γ = 103 mJ/molK^{2} estimated from specific heat measurements [19].

The penetration depth [10] and thermal conductivity [11] measurements of KFe_{2}As_{2} suggest that line nodes exist in the superconducting gap. Particularly, recent thermal conductivity result [29] has been interpreted based on the *d*-wave symmetry in KFe_{2}As_{2}. Because the small hole FSs around the zone corner are too small to account for the linear temperature dependence of the superfluid density [10], 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 [13]. Based on the spin-fluctuation-mediated model calculation, the octet node can be interpreted as vertical nodes with A_{1g} gap symmetry, which originates from the 3*z*^{2}−*r*^{2} 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 Ba_{0.1}K_{0.9}Fe_{2}As_{2} [30], if the vertical nodal line with A_{1g} gap symmetry rapidly shifts in the momentum space with hole doping. On the other hand, a small-angle neutron scattering measurement on KFe_{2}As_{2} has suggested the existence of a horizontal node [31]. One should note that both the vertical and horizontal nodes [32–34] can be realized in the region of the FS with 3*z*^{2}−*r*^{2} 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 3*z*^{2}−*r*^{2} character in the ζ FS.

## Conclusion

We have performed an ARPES study of KFe_{2}As_{2} 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 [25]. Particularly, the β and ζ FS show large mass enhancement of *m**/*m*_{b} ~ 6–7. Only the middle hole FS ζ shows a clear three-dimensionality, suggestive of 3*z*^{2}−*r*^{2} orbital character, which may be related to the “octet nodes” [13]. 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.

## Acknowledgments

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 KFe_{2}As_{2} 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, SingaporeReviewed by:

Fengqi Song, Nanjing University, ChinaAnjan 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: yoshida.teppei.8v@kyoto-u.ac.jp

^{†}Present address: Teppei Yoshida, Graduate School of Human and Environmental Studies, Kyoto University, Sakyo-ku, Kyoto, Japan