Unconventional Cooper pairing originating from spin or orbital fluctuations has been proposed for iron-based superconductors. Such pairing may be enhanced by quasi-nesting of two-dimensional electron and hole-like Fermi surfaces (FS), which is considered an important ingredient for superconductivity at high critical temperatures (high-Tc). However, the dimensionality of the FS varies for hole and electron-doped systems, so the precise importance of this feature for high-Tc materials remains unclear. Here we demonstrate a phase of electron-doped CaFe2As2 (La and P co-doped CaFe2As2) with Tc = 45 K, which is the highest Tc found for the AEFe2As2 bulk superconductors (122-type; AE = Alkaline Earth), possesses only cylindrical hole- and electron-like FSs. This result indicates that FS topology consisting only of two-dimensional sheets is characteristic of both hole- and electron-doped 122-type high-Tc superconductors.
Iron-based superconductors are considered to be important for understanding high temperature superconductivity from a new perspective due to the presence of a high superconducting critical temperature (Tc) that cannot be explained within the framework of conventional phonon-mediated BCS superconductivity. Moreover, the electronic states of the parent compounds and the superconducting symmetry in these systems are different from those for high-Tc cuprate superconductors1,2,3. Spin fluctuation-mediated superconductivity, as proposed for cuprate and heavy fermion systems, and orbital fluctuation-mediated superconductivity have been proposed as mechanisms for superconductivity4,5,6,7. Such fluctuations are believed to be derived from the quasi-nesting between the hole- and electron-like Fermi surfaces (FSs) (Fig. 1a). There is much discussion surrounding the relevance of the FS topology to iron-based superconductivity.
In order to clarify the relevance of the Fermi surface to the mechanism of superconductivity in iron-based superconductors from an experimental perspective, numerous angle-resolved photoemission spectroscopy (ARPES) measurements, which are a direct measurement of the Fermi surface, have been conducted on iron-based superconductors8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27. A number of substances with Tc > 50 K have been discovered for REFeAsO (1111-type; RE = Rare Earth) superconductors28, which has drawn corresponding interest in the electronic structures that manifest such high values of Tc. However, few ARPES measurements have been performed in these materials, due to the difficulty in fabricating single crystals of large dimensions8,9,10. In addition, bulk band structures are difficult to determine due to substantial surface effects originating from the existence of the REO layers10. As a result, little is known about the Fermi surface topology in the 1111-type materials. In contrast, numerous ARPES measurements have been performed for AEFe2As2 (122-type; AE = Alkaline Earth) iron-based superconductors17,18,19,20,21,22,23,24,25,26,27, which do not possess REO layers. ARPES measurements are more feasible for this system due to the availability of larger single crystals and the lack of surface effects associated with REO layers. ARPES experiments in the 122 system are thus believed to more closely reflect bulk electronic structure. ARPES studies in the 122 system reveal the presence of hole-like and electron-like Fermi surfaces at the center of the Brillouin zone and the corner, respectively, and the cylindrical shape of the electron-like Fermi surfaces at the zone corner are common features of the electronic structure in high-Tc 122-type superconductors.
However, as shown in Fig. 1b and 1c, the shape of the Fermi surface at the zone center varies depending on the particular compound. The kz dispersion is weak for the hole-doped 122-type Ba1-xKxFe2As2 (Tc = 38 K) and so the FSs is nearly two-dimensional24,25. However, FSs with strongly three-dimensional oval shapes exist in the vicinity of the zone center for Ba(Fe1-xCox)2As2 (Tc = 25 K)26,27. Two-dimensional FSs, which are more conducive to nesting, are considered to be linked to the emergence of high-Tc in iron-based superconductors. However, since the FS dimensionality varies for these two iron-based superconductors with high-Tc, the importance of a two-dimensional Fermi surface topology is unclear.
An electron-doped CaFe2As2 superconductor derived by co-doping La and P was recently discovered with Tc = 45 K29. The Tc of this new iron-based superconductor is the highest among the 122-type bulk superconductors that have ever been studied with ARPES. Thus, it is important to study the electronic structure using ARPES to clarify the FS topology of the iron-based superconductors at such a high Tc.
In our study, we revealed the Fermi surface of the electron-doped CaFe2As2. ARPES measurements were conducted with three photon polarizations to resolve multiple bands and tunable excitation photon energy to observe the three-dimensional shape of the Fermi surfaces (kz dispersion of Fermi surfaces). All Fermi surfaces of this new superconductor had a weak kz dispersion. Since this characteristic is common to Ba1-xKxFe2As2, which has the maximum Tc among hole-doped 122-type superconductors, the two-dimensional topology of the Fermi surface is relevant to the presence of high Tc in the iron-based superconductors and does not rely on the character of doped carriers.
Polarization and photon energy dependent ARPES
In Fig. 2a–f, we show polarization dependent ARPES intensity plots (for the geometrical measurement configuration, see Supplementary Fig. S1) along the cuts passing through the Γ point (hν = 31 eV) and the Z point (hν = 19 eV), together with peak positions determined from energy distribution curve (EDC) and momentum distribution curve (MDC) analyses (See, Supplementary Fig. S2 and S3 for corresponding intensity plots, intensity plots normalized with the Fermi-Dirac distribution function, and selected MDCs and EDCs.). At both points, ARPES intensity plots exhibit marked polarization dependence, which enables us to distinguish the dispersions of the three bands. At the Γ point, using ARPES data for s-polarized (s-pole) light (Fig. 2b, S2e–h), we found an intense hole-like dispersion with an energy maximum around 25 meV (α1). The multiple structure of MDC at EF (and its detailed line shape analysis) (Fig. S2g) also indicates the existence of EF crossings of another band (α2). In ARPES data for circular-polarized (c-pole) light (Fig. 2a, S2a–d), we found that the hole-like band (α2) approaches and crosses EF, as evident from multiple structures in the MDC at EF (and its detailed line shape analysis) (Fig. S2c) and the parabolic dispersion in the EDCs (Fig. S2d). In addition, we found a hole-like feature (β) crossing EF outside of the α2 band in ARPES data for p-polarized (p-pole) light (Fig. 2c, S2i–k), which is more easily observed in MDCs for a higher binding energy region (Fig. S2k). At the Z point, while the intense hole-like α1 band with an energy maximum around 10 meV is similarly found in s-pole data (Fig. 2e, S3d–f), the β band is observed in c- and p-pole data (Fig. 2d and 2f, S3a–c and S3g–h). Although intensities of the α2 band are weaker than that of the β band at the Z point (hν = 19 eV), the existence of kFs can be confirmed by the multiple structure in the MDC at EF (and its detailed line shape analysis) taken with hν = 82 eV, which corresponds to another Z point (Supplementary Figs. S3i–k). These data and analyses confirm the existence of three bands consistent with band structure calculations4,5.
Having established the existence of three bands, we now examine the kz dispersion of the bands from photon energy-dependent ARPES. The peak positions of the normal emission spectra in Fig. 2h, corresponding to α1, measured with various photon energies show a periodic variation consistent with the periodicity of the bulk Brillouin zone. More importantly, the peak positions are located below EF for all kzs measured, indicating that this band does not contribute to the FS. For α2 and β, we found that hole-like Fermi surfaces are formed at both Γ and Z points. ARPES data at hν = 23 eV, corresponding to kz between Γ and Z, also shows EF crossings of these bands (Fig. 2g and S4a–d). We found that photon energy-dependent MDCs at EF for the  direction near the zone center can be well reproduced with four Lorentzian functions (Supplementary Fig. S5). We plotted the kFs determined from fitting the MDCs at EF in Fig. 2i. We now find that the α2 and β bands form a nearly cylindrical small and large hole-like FS, respectively.
In Fig. 3a and 3b, ARPES intensity plots at EF as functions of the two-dimensional wave vectors (kx, ky) around the M and A point, respectively, together with the positions of kF (filled circles) obtained from fits to the MDC are shown. We observed two electron-like FSs. These FSs originate from the inner ε and outer δ electron-like bands, as shown in Fig. 3c and 3d. We identified these bands from the detailed analysis of the MDCs (Supplementary Fig. S6a and S6b). We separate the two electron-like bands at the A point by performing polarization dependent ARPES taken at hν = 24 eV, which corresponds to another A point (Supplementary Fig. S6c and S6d). The elliptical shape of the intersections of the inner ε and outer δ electron-like FSs rotates 90° from M to A, which is consistent with the shape of the boundary of the body-centered tetragonal Brillouin zone. In Fig. 3e, we show the results of the FS mapping in the k‖-kz plane near the zone corner. The direction of k‖ is the same as the cuts in Fig. 3a and 3b. The electron-like FSs show a sizeable undulation along the kz direction (Fig. 3e), reflecting the elliptical shape of these FSs and the shape of the zone boundary, as described above.
The Fermi surface topology determined by ARPES
From these ARPES measurements, we draw the shape of the FSs corresponding to the observed bands crossing EF (α2, β, ε, δ), as shown in Fig. 4a and 4b. We now find four FSs: two around the zone center derived from the hole-like bands (α2, β) and two around the zone corner derived from the electron-like bands (ε, δ). All the FSs around the zone center and the corner are found to be nearly cylindrical with a small undulation. Here, hole-like FSs shifted by the AFM wave vector (π/a, π/a, 2π/c) of CaFe2As230,31, where a = 3.914 Å and c = 11.48 Å are the in-plane and out-of-plane lattice constants of Ca0.82La0.18Fe2(As0.94P0.06)2, are shown with broken blue and sky blue lines in Fig. 4a. Some values for kF of the inner ε electron-like FS overlap with those of the shifted β FS. Note that the back folding of the bands, which has been observed in the 122-type parent compounds32 and Ca0.83La0.17Fe2As2 with trace superconductivity33, is absent in the present compound, consistent with the absence of AFM ordering. The total hole and electron count from the observed FS yields a hole volume of 6 ± 2% and an electron volume of 18 ± 5%. Here, we assume that the hole-like parts of the FS are circular. The deduced total carrier number of 0.12 ± 0.07 electrons per Fe is consistent with the value of 0.09 electrons per Fe expected from the chemical composition, indicating that our measurements reflect the observation of the bulk electronic structure of La and P co-doped CaFe2As2.
We discuss the implication of the present ARPES results for iron-based superconductivity. As shown in Fig. 1b and 1d, all hole-like FSs in hole-doped Ba1-xKxFe2As2 and electron-doped Ca0.82La0.18Fe2(As0.94P0.06)2 have a nearly two-dimensional shape24,25. We find that a two-dimensional FS topology, which favors electron pair scattering between quasi-nested FSs, is universal for high-Tc superconductivity regardless of the type of doped carrier. This observation supports the exotic pairing mechanisms proposed for iron-pnictide superconductors. Here it is noted that the quasi-nesting between hole- and electron-like FSs would not explain the high Tc of KxFe1-ySe2 superconductors where hole-like FSs are absent14,15,16.
One of the most important questions is the origin of high-Tc superconductivity in the electron-doped superconductor Ca0.82La0.18Fe2(As0.94P0.06)2 (Tc = 45 K). We shall discuss the FS topology in three-dimensional momentum space. As described above, the size of the β hole-like FS is nearly the same as that of the ε electron-like FS and both FSs have a weak kz dispersion, giving rise to a partial overlapping of kFs. These observations are similar to that for electron-doped Ba(Fe1-xCox)2As2 (Tc = 25 K)22. An observable difference between Ca0.82La0.18Fe2(As0.94P0.06)2 and Ba(Fe1-xCox)2As2 in terms of FS topology is the dimensionality of the inner hole-like FS, as shown Fig. 1c and 1d. For Ba(Fe1-xCox)2As2, the inner hole-like FS shows a strong kz dispersion and is closed near the Γ point25,26. In contrast, the inner hole-like FS (α2) shows a cylindrical shape and survives near the Γ point in Ca0.82La0.18Fe2(As0.94P0.06)2. These results suggest that an enhancement of the two-dimensionality of the inner hole-like FS induces a large Tc difference in the two materials, possibly due to an increased tendency toward quasi-nesting between α2 and ε parts of the FS. Regarding the orbital character of the bands in Ca0.82La0.18Fe2(As0.94P0.06)2, the polarization dependence of the odd symmetry with respect to the mirror plane and kz dispersion of α1 enable us to suggest a dYZ character for α1, where X and Y refer to the direction rotated by 45 degrees from the Fe-Fe direction and Z is normal to the XY plane. The observable ARPES intensity of the α2 band with both s-pole and p-pole light (Fig. 2a–c) suggests a mixed orbital character of even and odd symmetry. The mixed orbital character of bands near EF (dXY and dX2-Y2) were reported from polarization dependent ARPES of Ba(Fe1-xCox)2As2 and LiFeAs11,19. The β band has even symmetry. The lifting of the hole-like band degeneracy at the Γ point does not agree with previous calculations4,5, where bands with dXZ and dYZ orbital characters are degenerate. However, recent calculations in Refs. 34 and 35 taking into account the change of the Fe-As-Fe bond angle and the change of the positive charge in the blocking layer predicted the lift of the degeneracy, in agreement with the present study.
In iron-based superconductors, band structure calculations predict that the shapes of the hole-like FSs become more three-dimensional with a reduction in pnictogen height36. This theoretical prediction holds for Ba(Fe1-xCox)2As2 and Ba1-xKxFe2As2, as the pnictogen height of Ba(Fe1-xCox)2As2 is shorter than that of Ba1-xKxFe2As237,38. For Ca0.82La0.18Fe2(As0.94P0.06)2, the pnictogen height is not available thus far. As for the c parameter, that of Ca0.82La0.18Fe2(As0.94P0.06)2 is the shortest among the three compounds. However, this does not necessarily mean a shorter pnictogen height in Ca0.82La0.18Fe2(As0.94P0.06)2, due to the difference in alkaline earths. In order to verify this relationship, detailed structural studies of Ca0.82La0.18Fe2(As0.94P0.06)2 are indispensable.
In summary, we have investigated the three-dimensional electronic structure near EF in electron-doped Ca0.82La0.18Fe2(As0.94P0.06)2 (Tc = 45 K). The observed FS topology is nearly two-dimensional and similar to that of Ba1-xKxFe2As2, indicating the existence of universality in the FS topology for realizing high-Tc in 122-type superconductors.
High quality Ca0.82La0.18Fe2(As0.94P0.06)2 single crystals were grown as described elsewhere25. Polarization dependent ARPES measurements (hν = 19–31 eV) were carried out at BL-9A of Hiroshima Synchrotron Radiation Center (HSRC). ARPES measurements using circularly polarized light (hν = 40–86 eV) were carried out at BL-28A of the Photon Factory. The total energy resolution was set to 10–30 meV. Clean surfaces were obtained by in situ cleaving of the crystal in a working vacuum better than 3 × 10−8 Pa and measured at 60 K (above Tc). The inner potential was determined to be 14 eV from photon energy-dependent ARPES studies as described above. Calibration of EF of the sample was achieved using a gold reference.
We acknowledge S. Nagira and H. Fujiwara for technical assistance and Y. Inada for Laue x-ray diffraction experiments. We thank K. Kuroki for the valuable discussions. We also thank A. Ino and R. Yoshida for their ARPES data analysis program. Polarization dependent ARPES experiments at HSRC were performed with the approval of HSRC (Proposal No. 13-A-4). ARPES experiments at the Photon Factory were approved by the Photon Factory Program Advisory Committee (Proposal No. 2011G086). Part of this work was performed at the Advanced Science Research Center at Okayama University. This work was partially supported by MEXT KAKENHI Grant Number 20102003 and JSPS Grant Number 25400372. This work was also partially supported by the Funding Program for World-Leading Innovative R&D in Science and Technology (FIRST program) from JSPS and the program for promoting the enhancement of research universities from MEXT.
Supplementary information for Characteristic two-dimensional Fermi surface topology of high-Tc iron-based superconductors