Characteristic two-dimensional Fermi surface topology of high-Tc iron-based superconductors

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.

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-T c 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 k z dispersion is weak for the hole-doped 122-type Ba 1-x K x Fe 2 As 2 (T c 5 38 K) and so the FSs is nearly two-dimensional 24,25 . However, FSs with strongly three-dimensional oval shapes exist in the vicinity of the zone center for Ba(Fe 1-x Co x ) 2 As 2 (T c 5 25 K) 26,27 . Two-dimensional FSs, which are more conducive to nesting, are considered to be linked to the emergence of high-T c in ironbased superconductors. However, since the FS dimensionality varies for these two iron-based superconductors with high-T c , the importance of a two-dimensional Fermi surface topology is unclear.
An electron-doped CaFe 2 As 2 superconductor derived by co-doping La and P was recently discovered with T c 5 45 K 29 . The T c 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 T c .
In our study, we revealed the Fermi surface of the electron-doped CaFe 2 As 2 . 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 (k z dispersion of Fermi surfaces). All Fermi surfaces of this new superconductor had a weak k z dispersion. Since this characteristic is common to Ba 1-x K x Fe 2 As 2 , which has the maximum T c among hole-doped 122-type superconductors, the two-dimensional topology of the Fermi surface is relevant to the presence of high T c in the iron-based superconductors and does not rely on the character of doped carriers.

Results
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 C point (hn 5 31 eV) and the Z point (hn 5 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 C 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 (a 1 ). The multiple structure of MDC at E F (and its detailed line shape analysis) (Fig. S2g) also indicates the existence of E F crossings of another band (a 2 ). In ARPES data for circular-polarized (c-pole) light (Fig. 2a, S2a-d), we found that the hole-like band (a 2 ) approaches and crosses E F , as evident from multiple structures in the MDC at E F (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 (b) crossing E F outside of the a 2 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 a 1 band with an energy maximum around 10 meV is similarly found in s-pole data (Fig. 2e, S3d-f), the b band is observed in c-and p-pole data ( Fig. 2d and 2f, S3a-c and S3g-h). Although intensities of the a 2 band are weaker than that of the b band at the Z point (hn 5 19 eV), the existence of k F s can be confirmed by the multiple structure in the MDC at E F (and its detailed line shape analysis) taken with hn 5 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 calculations 4,5 .
Having established the existence of three bands, we now examine the k z dispersion of the bands from photon energy-dependent ARPES. The peak positions of the normal emission spectra in Fig. 2h, corresponding to a 1 , 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 E F for all k z s measured, indicating that this band does not contribute to the FS. For a 2 and b, we found that hole-like Fermi surfaces are formed at both C and Z points. ARPES data at hn 5 23 eV, corresponding to k z between C and Z, also shows E F crossings of these bands ( Fig. 2g and S4a-d). We found that photon energydependent MDCs at E F for the [100] direction near the zone center can be well reproduced with four Lorentzian functions (Supplementary Fig. S5). We plotted the k F s determined from fitting the MDCs at E F in Fig. 2i. We now find that the a 2 and b bands form a nearly cylindrical small and large hole-like FS, respectively.
In Fig. 3a and 3b, ARPES intensity plots at E F as functions of the two-dimensional wave vectors (k x , k y ) around the M and A point, respectively, together with the positions of k F (filled circles) obtained from fits to the MDC are shown. We observed two electron-like FSs. These FSs originate from the inner e and outer d 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 hn 5 24 eV, which corresponds to another A point (Supplementary Fig. S6c and S6d). The elliptical shape of the intersections of the inner e and outer d electron-like FSs rotates 90u 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 || -k z 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 k z 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 E F (a 2 , b, e, d), as shown in Fig. 4a  and 4b. We now find four FSs: two around the zone center derived from the hole-like bands (a 2 , b) and two around the zone corner derived from the electron-like bands (e, d). 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 (p/a, p/a, 2p/c) of CaFe 2 As 2 30,31 , where a 5 3.914 Å and c 5 11.48 Å are the in-plane and out-of-plane lattice constants of Ca 0.82 La 0.18 Fe 2 (As 0.94 P 0.06 ) 2 , are shown with broken blue and sky blue lines in Fig. 4a. Some values for k F of the inner e electron-like FS overlap with those of the shifted b FS. Note that the back folding of the bands, which has been observed in the 122-type parent compounds 32 and Ca 0.83 La 0.17 Fe 2 As 2 with trace superconductivity 33 , 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 6 2% and an electron volume of 18 6 5%. Here, we assume that the hole-like parts of the FS are circular. The deduced total carrier number of 0.12 6 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 CaFe 2 As 2 .

Discussion
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 holedoped Ba 1-x K x Fe 2 As 2 and electron-doped Ca 0.82 La 0.18 Fe 2 (As 0.94 P 0.06 ) 2 have a nearly two-dimensional shape 24,25 . We find that a twodimensional FS topology, which favors electron pair scattering between quasi-nested FSs, is universal for high-T c 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 T c of K x Fe 1-y Se 2 superconductors where hole-like FSs are absent [14][15][16] .
One of the most important questions is the origin of high-T c superconductivity in the electron-doped superconductor Ca 0.82 La 0.18 Fe 2 (As 0.94 P 0.06 ) 2 (T c 5 45 K). We shall discuss the FS topology in three-dimensional momentum space. As described above, the size of the b hole-like FS is nearly the same as that of the e electron-like FS and both FSs have a weak k z dispersion, giving rise to a partial overlapping of k F s. These observations are similar to that for electron-doped Ba(Fe 1-x Co x ) 2 As 2 (T c 5 25 K) 22 . An observable difference between Ca 0.82 La 0.18 Fe 2 (As 0.94 P 0.06 ) 2 and Ba(Fe 1-x Co x ) 2 As 2 in terms of FS topology is the dimensionality of the inner hole-like FS, as shown Fig. 1c and 1d. For Ba(Fe 1-x Co x ) 2 As 2 , the inner hole-like FS shows a strong k z dispersion and is closed near the C point 25,26 . In contrast, the inner hole-like FS (a 2 ) shows a cylindrical shape and survives near the C point in Ca 0.82 La 0.18 Fe 2 (As 0.94 P 0.06 ) 2 . These results suggest that an enhancement of the two-dimensionality of the inner hole-like FS induces a large T c difference in the two materials, possibly due to an increased   tendency toward quasi-nesting between a 2 and e parts of the FS. Regarding the orbital character of the bands in Ca 0.82 La 0.18 Fe 2 (As 0.94 P 0.06 ) 2 , the polarization dependence of the odd symmetry with respect to the mirror plane and k z dispersion of a 1 enable us to suggest a d YZ character for a 1 , 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 a 2 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 E F (d XY and d X2-Y2 ) were reported from polarization dependent ARPES of Ba(Fe 1-x Co x ) 2 As 2 and LiFeAs 11,19 . The b band has even symmetry. The lifting of the hole-like band degeneracy at the C point does not agree with previous calculations 4,5 , where bands with d XZ and d YZ 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 height 36 . This theoretical prediction holds for Ba(Fe 1-x Co x ) 2 As 2 and Ba 1-x K x Fe 2 As 2 , as the pnictogen height of Ba(Fe 1-x Co x ) 2 As 2 is shorter than that of Ba 1-x K x Fe 2 As 2 37,38 . For Ca 0.82 La 0.18 Fe 2 (As 0.94 P 0.06 ) 2 , the pnictogen height is not available thus far. As for the c parameter, that of Ca 0.82 La 0.18 Fe 2 (As 0.94 P 0.06 ) 2 is the shortest among the three compounds. However, this does not necessarily mean a shorter pnictogen height in Ca 0.82 La 0.18 Fe 2 (As 0.94 P 0.06 ) 2 , due to the difference in alkaline earths. In order to verify this relationship, detailed structural studies of Ca 0.82 La 0.18 Fe 2 (As 0.94 P 0.06 ) 2 are indispensable.
In summary, we have investigated the three-dimensional electronic structure near E F in electron-doped Ca 0.82 La 0.18 Fe 2 (As 0.94 P 0.06 ) 2 (T c 5 45 K). The observed FS topology is nearly two-dimensional and similar to that of Ba 1-x K x Fe 2 As 2 , indicating the existence of universality in the FS topology for realizing high-T c in 122-type superconductors.

Methods
High quality Ca 0.82 La 0.18 Fe 2 (As 0.94 P 0.06 ) 2 single crystals were grown as described elsewhere 25 . Polarization dependent ARPES measurements (hn 5 19-31 eV) were carried out at BL-9A of Hiroshima Synchrotron Radiation Center (HSRC). ARPES measurements using circularly polarized light (hn 5 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 3 10 28 Pa and measured at 60 K (above T c ). The inner potential was determined to be 14 eV from photon energy-dependent ARPES studies as described above. Calibration of E F of the sample was achieved using a gold reference.