First-principles Electronic Structure of Superconductor Ca 4 Al 2 O 6 Fe 2 P 2 : Comparison with LaFePO and Ca 4 Al 2 O 6 Fe 2 As 2
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First-Principles Electronic Structure of Superconductor Ca Al O Fe P :Comparison with LaFePO and Ca Al O Fe As Taichi Kosugi , Takashi Miyake , , , and Shoji Ishibashi , Nanosystem Research Institute (NRI) “RICS”, AIST, 1-1-1 Umezono, Tsukuba 305-8568, Japan Japan Science and Technology Agency, CREST, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan Japan Science and Technology Agency, TRIP, 5 Sanbancho, Chiyoda, Tokyo 102-0075, Japan
We investigate the electronic structures of iron-based superconductors having perovskite-likeblocking layers, Ca Al O Fe P and Ca Al O Fe As , from first principles. Ca Al O Fe P is found to have two hole-like Fermi surfaces around Γ, and one hole-like Fermi surface aroundM in the unfolded Brillouin zone. This is in contrast with LaFePO, where no Fermi surface isfound around M. The relationship between their band structures and measured transition tem-peratures of superconductivity is discussed. The number of Fermi surfaces in Ca Al O Fe P isalso different from that in Ca Al O Fe As , in which only one Fermi surface is formed aroundΓ. Analysis using maximally localized Wannier functions clarifies that the differences betweentheir band structures originate mainly from the difference in pnictogen height. We then ana-lyze the alloying effect on the electronic structure of Ca Al O Fe AsP. It is found that thiselectronic structure is similar to those of Ca Al O Fe P and Ca Al O Fe As with averagecrystal structures, though Ca Al O Fe AsP contains pnictogen height disorder. We calculatethe generalized susceptibility for Ca Al O Fe (As − x P x ) and clarify the factors determiningits tendency. KEYWORDS: Fe-based superconductor, Ca Al O Fe P , Ca Al O Fe As , LaFePO, electronic structure,first-principles calculation, maximally localized Wannier function
1. Introduction
Since the discovery of iron-based superconductors inLaFePO with its transition temperature T c of 5 K andin LaFeAsO with T c = 26 K, many attempts to clar-ify the material properties and to realize higher T c havebeen continued, and Fe-based superconductors with var-ious chemical formulae and crystal structures have beenreported, among which SmFeAsO has shown the highest T c of 55 K to date is realized. An Fe-based superconductor comprises two-dimensional iron (Fe)-anion ( A ) layers. The elec-tronic bands near the Fermi level have a strong Fe d character, which should be responsible for thesuperconductivity. Lee et al. plotted the T c of variousFe-based superconductors as a function of the A -Fe- A bond angle α and demonstrated that the T c shows apeak at nearly 109 . ◦ , for which Fe A forms a regulartetrahedron. Much attention has thus been paid to thestrong correlation between T c and the local geometryof an Fe A tetrahedron, namely, the lattice constant a , the Fe- A bond length d , the bond angle α , and theanion height h A . Two of these four geometry constantsare independent. A small a or d leads to a small densityof states at the Fermi level and is thus expected to beunfavorable for superconductivity. On the other hand,a large h A allows a robust hole Fermi surface around( π, π ), which interacts with electron Fermi surfaces andis thus expected to be favorable for superconductivity. The measured T c ’s, however, are not necessarily higherat larger h A ’s. Mizuguchi and coworkers
11, 12) provided aplot of T c as a function of h A , which obeys a symmetriccurve with a peak at approximately 1 .
38 ˚A, common to 1111-, 122-, 111-, and 11-type superconductors.Since the reports for Sr Sc O Fe P andSr V O Fe As , Fe-based materials with perovskite-type blocking layers have been known to show super-conductivity for various combinations of their formulaeand thickness.
They include Ca Al O Fe As ( a = 3 .
713 ˚A and c = 15 .
407 ˚A, α = 102 . ◦ , and h As = 1 .
500 ˚A) with T c = 28 . and Ca Al O Fe P ( a = 3 .
692 ˚A and c = 14 .
934 ˚A, α = 109 . ◦ , and h P = 1 .
306 ˚A) with T c = 17 . Among the Fe-based superconductors reported so far,Ca Al O Fe As and Ca Al O Fe P are of particularinterest since they have rather small a ’s, owing to thesmall ion radius of Al , and Ca Al O Fe As has arather large h As . Furthermore, it is important to an-swer why the T c of Ca Al O Fe P is higher than thatof LaFePO to elucidate the mechanism of superconduc-tivity in systems consisting of FeP layers. Our previ-ous work revealed that α has a strong impact onthe band rearrangement and the Fermi surface topologyin Ca Al O Fe As . Subsequently, Usui and Kuroki pointed out that the superconductivity of an Fe-basedsuperconductor is optimized for α of a regular tetrahe-dron, which maximizes the hole Fermi surface multiplic-ity.The superconducting properties of Fe-based systemsdepend sensitively on multiple factors related to the crys-tal structure and formula, as outlined above. It is thusimportant to investigate the electronic properties of suchsystems with the crystal structure and/or formula varied,focusing on the behavior of Fermi surfaces and electronicorbitals in the vicinity of the Fermi level. In the present Full Paper
Author Name study, we therefore perform first-principles electronicstructure calculations for Ca Al O Fe (As − x P x ) . Wefirst compare the band structures of Ca Al O Fe P and Ca Al O Fe As , and determine the origins of thedifferences in their band structures by comparing thetransfer integrals between localized electronic orbitals.We extract the transfer integrals by constructing max-imally localized Wannier functions, which provide apicture of localized electronic orbitals in solid. The re-sults of this analysis suggest that the band structuresof Ca Al O Fe (As − x P x ) are determined mainly bycrystal structure, not by chemical composition. We thendemonstrate that electronic structure calculation forCa Al O Fe AsP corroborates this idea by unfolding itsband structure. We calculate the generalized susceptibil-ity χ , which correlates with superconductivity in gen-eral, of Ca Al O Fe (As − x P x ) and clarify the factorsdetermining the behavior of χ .
2. Computational Details
We used the computational code QMAS based onthe projector augmented-wave method, which hasbeen applied to the study of the ground state propertiesof LaFeAsO,
6, 29)
SrFe As , and Ca Al O Fe As . The PBE exchange-correlation functional within thegeneralized gradient approximation (GGA) was adopted.The pseudo wave functions were expanded in plane waveswith an energy cutoff of 40 Ry. We employed a 12 × × k point mesh for systems with conventional tetragonalcells and an 8 × × k point mesh with supercells. Theelectronic band structure in the vicinity of the Fermi levelis analyzed in detail using the maximally localized Wan-nier function technique. For the Ca Al O Fe P and Ca Al O Fe As crystal structures, the experimental values of tetragonallattice constants and atomic coordinates are used in thepresent work.In the analyses of the alloying effect onCa Al O Fe AsP, we unfold its band dispersionobtained for a supercell, following the proceduresproposed by Ku et al.
The unfolded band dispersionis given as a sum of weighted delta functions: A kn,kn ( ω ) = X J |h kn | KJ i| δ ( ω − ε KJ ) , (1)where K is the wave vector in the folded Brillouin zonecorresponding to the wave vector k in the unfolded Bril-louin zone. J is the band index for the supercell and n denotes the Wannier function in the primitive cell. | KJ i is the eigenstate of the Kohn-Sham Hamiltonian for thesupercell, whereas | kn i is the Fourier transform of theWannier function in the primitive cell. We are able tounfold 20 Fe d bands to 5 bands by choosing the propergauge of the Wannier functions. We calculate the generalized susceptibility χ ofCa Al O Fe P and Ca Al O Fe As with graduallyvarying their crystal structures. Its expression for a sys- tem with time reversal symmetry is given by χ ( q ) = 12 X m,n, k f m k − f n k + q ε n k + q − ε m k , (2)where f m k is the occupation number and ε m k is the en-ergy eigenvalue. χ reflects the nesting property of thesystem and is expected to correlate with superconduc-tivity. We evaluate eq. (2) as a summation for 40 × × k points by interpolating the band dispersion using theWannier functions of Fe d bands.
3. Results and Discussion Al O Fe P in compar-ison with those of Ca Al O Fe As The nonmagnetic electronic band structures ofCa Al O Fe P and Ca Al O Fe As obtained with thefirst-principles calculation are shown as circles in Fig.1(a). In each of the systems, the unit cell contains twoFe atoms and ten bands having a strong Fe d charac-ter lie near the Fermi level. The most prominent differ-ence in the calculated band structure between these twosystems is the multiplicity of Fermi surfaces around Γ:Ca Al O Fe P has three, whereas Ca Al O Fe As hastwo. We note here that LaFePO has two Fermi surfacesaround Γ, which would explain why Ca Al O Fe P has a higher T c than LaFePO. Figure 1 (b) shows theFermi surfaces of Ca Al O Fe P in an undoped caseand doped cases with ± . P n ) p bands atM. The top of P p bands in Ca Al O Fe P lies close to − . p bands is not at Mand those bands are below − . We constructed maximally lo-calized Wannier functions from the ten Fe d bands ( d model) and plotted the interpolated band dispersion ascurves in Fig. 1(a). It is found that the Wannier func-tions accurately reproduce the DFT-GGA band struc-tures near the Fermi level. The Wannier function of theFe d X − Y ( d xy ) orbital in Ca Al O Fe P is shown inFig. 1(c). [The X - and Y -axes refer to the conventionalunit cell containing two Fe atoms, whereas the rotationof them by 45 ◦ defines the x - and y -axes. (see Fig. 2)]Although the shape of this Wannier function is mainlyof the d X − Y character, it involves contributions fromP p orbitals. We observed that the positive (blue) lobe ofthe d X − Y orbital is pushed down the c direction to hy-bridize with the P p orbitals below the Fe layer, while thenegative (yellow) lobe is pushed up to hybridize with theP p orbitals above, as shown in Fig. 1(c). We confirmedthat the shape of the corresponding Wannier function inCa Al O Fe As (not shown) has smaller contributionsfrom the As p orbitals. This reflects (i) the Fe-P dis-tance, which is smaller than the Fe-As distance, and (ii)the energy separation of the Fe d and the As p bands inCa Al O Fe As , which is larger than that of the Fe d and the P p bands in Ca Al O Fe P . . Phys. Soc. Jpn. Full Paper
Author Name 3 -3-2-10123 E n e r gy ( e V ) -3-2-10123 Ca Al O Fe AsCa
Al O Fe PΓ X M Γ Z Γ X M Γ Z hole-doped undoped electron-doped (a)(b)(c) cac X ( ) b Y ( ) a X ( ) b Y ( ) FeP
Fig. 1. (Color) (a) Nonmagnetic electronic band structures ofCa Al O Fe P and Ca Al O Fe As . Circles represent DFT-GGA bands and curves represent bands interpolated using themaximally localized Wannier functions of d models. The originsof energy are set to the respective Fermi levels. (b) Fermi sur-faces for hole-doped (left), undoped (middle), and electron-doped(right) Ca Al O Fe P . (c) A bird’s-eye view of maximally lo-calized Wannier function of Fe d X − Y orbital is shown on theleft. The Wannier function viewed along the c axis is shown onthe right. The a and b directions are parallel to the X - and Y -axes, respectively. Brown and purple balls represent Fe and Patoms, respectively. These figures were drawn with VESTA. To simplify the analysis of the electronic band struc-ture, we unfolded the interpolated 10-band dispersion of d models following the procedure proposed by Kuroki et al. The resultant 5-band structures obtained withthe lattice parameters and the atomic coordinates fixed,while varying the chemical composition of the system,are shown in Fig. 3. It is found that the overall bandstructures with the same crystal structure look quitesimilar, especially in the vicinity of the Fermi level. Forthe Ca Al O Fe P (Ca Al O Fe As ) crystal struc-ture, there exist three (two) Fermi surfaces around Γin the original Brillouin zone irrespective of chemicalcomposition, which correspond to the two (one) α holepockets around (0 ,
0) and one γ hole pocket around( π, π ), as shown in Fig. 3. The numbers of Fermi sur-faces around (0 ,
0) and ( π, π ) in the unfolded Brillouinzone for Ca Al O Fe As and Ca Al O Fe P with theirown crystal structures are summarized in Table I. Weobserve in Fig. 3 that the calculated band widths of d t X t t t Fe Pn XY xy a b t Z Fig. 2. (Color online) Schematic illustration of transfer integralsof a dpp model. Solid lines represent unit cells. Fe d X − Y or-bitals and P n p X and p Z orbitals are shown. We define the x - and y -axes by rotating the original X - and Y -axes by 45 ◦ .Transfer integrals are shown as red arrows. t i ( i = 1 , ,
3) is thatbetween the d X − Y orbitals at the i -th nearest neighbors, while t j ( j = X, Z ) is that between the p j orbital and its nearest-neighboring d X − Y orbital. models for Ca Al O Fe As with the Ca Al O Fe As and Ca Al O Fe P crystal structures are 4 .
64 and 5 . Al O Fe P with theCa Al O Fe As and Ca Al O Fe P crystal structuresare 4 .
29 and 5 .
28 eV, respectively. The Ca Al O Fe P crystal structure gave a larger band width than theCa Al O Fe As crystal structure when the same chem-ical composition was used, since the former has asmaller a and a smaller h P n . On the other hand, theCa Al O Fe P composition gave a smaller band widththan the Ca Al O Fe As composition when the samecrystal structure was used, since the ion radius of the Patom is smaller than that of the As atom. Table I. Numbers of Fermi surfaces around (0 ,
0) and ( π, π ) in un-folded Brillouin zone for Ca Al O Fe As and Ca Al O Fe P .Those for LaFeAsO and LaFePO are also shown for comparison.(0 ,
0) ( π, π )Ca Al O Fe As Al O Fe P It was demonstrated in our previous work that theFe d X − Y ( d xy ) orbital plays an important role in theband rearrangement of Ca Al O Fe As when the lo-cal geometry of the Fe P n tetrahedron is varied. Forthe quantitative analysis of the electronic structure of J. Phys. Soc. Jpn.
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Author Name E n e r gy ( e V ) (0, 0) (π, 0) (π, π) (0, 0)-3-2-10123-3-2-10123 (0, 0) (π, 0) (π, π) (0, 0) E n e r gy ( e V ) Ca Al O Fe P structurestructure Ca Al O Fe As Ca Al O Fe PCa
Al O Fe AsCa
Al O Fe PCa
Al O Fe As
Fig. 3. (Color online) Unfolded 5-band structures of d mod-els for Ca Al O Fe P and Ca Al O Fe As as solid anddashed curves, respectively. The upper (lower) panel showsthe band structures obtained using the crystal structure ofCa Al O Fe P (Ca Al O Fe As ). The origins of energy areset to the respective Fermi levels. Ca Al O Fe P along this line, we constructed dpp mod-els of the four systems mentioned above and examinedhow their chemical composition and crystal structuresaffect the electronic band structures. Each of the dpp models consists of 10 Fe d , 6 P n p , and 18 O p or-bitals. The transfer integrals and orbital energies of the d X − Y orbitals, which are equivalent to the xy orbitals,and the P n p orbitals are shown in Table II. Although | t | ≫ | t | in the dpp models, t in the d models aresmall in magnitude; consequently, t and t are compa-rable in the d models. Although the Wannier functionsin the d model are spatially extended and have con-siderable weight at the pnictogen site, the d Wannierfunctions in the dpp model are localized and atomic-orbital-like.
36, 37)
Hence, we can say that t in the dpp model contains only direct hopping between the neigh-boring Fe sites, whereas t in the d model contains in-direct hopping via the pnictogen site as well. This in-dicates that the indirect electron hopping of Fe-
P n -Fepartly cancels the direct hopping between the nearest-neighboring d X − Y orbitals. In the comparison of dpp t ’sfor the same chemical composition but different crystalstructures, the difference between t i ( i = 1 , t X and t Z are much larger in the Ca Al O Fe P crystalstructure than in the Ca Al O Fe As crystal structurefor both chemical compositions. This is because the hy-bridization between the d X − Y and p orbitals is strongerfor a smaller h P n . Since t X and t Z in the dpp models can be regarded to be incorporated into t ’s in the d models,the differences in band dispersion between the systemswith the same chemical composition but different crystalstructures come from the differences between the indi-rect hopping of Fe- P n -Fe. The two-dimensional shape ofthe d X − Y orbital allows a larger hybridization with the p Z orbital than with the p X orbital, leading to t Z muchlarger than t X for all the four systems. In the compar-ison of dpp t ’s for the same crystal structure but dif-ferent chemical compositions, those for Ca Al O Fe As are basically larger than those for Ca Al O Fe P owingto the ion radius of the As atom larger than that of the Patom. t X is, however, larger in Ca Al O Fe P than inCa Al O Fe As if their crystal structures are the same.This is probably because the p electrons of a P n atomare depleted for the hybridization between the p Z orbitaland its neighboring d X − Y orbitals.As clarified above, the differences between the bandstructures of Ca Al O Fe P and Ca Al O Fe As withtheir own crystal structures, shown in Fig. 1(a), origi-nate mainly not from the difference in chemical compo-sition, but from that in pnictogen height. By defining thecontribution t ind1 from the indirect hopping Fe- P n -Fe asthe difference between the t ’s of the d and dpp mod-els ( t ind1 ≡ t d − t dpp ), we can estimate t ind1 to be 0 . Al O Fe P and 0 .
337 eV in Ca Al O Fe As .In our previous work, we estimated t ind1 for LaFeAsO( h As = 1 .
319 ˚A) to be 0 .
394 eV. These values are reason-able because a smaller h P n gives a larger t ind1 for thesethree systems. The direct hopping of LaFeAsO, t dpp = − .
243 eV, is much smaller than those of Ca Al O Fe P and Ca Al O Fe As , which is due to the larger a ofLaFeAsO. Table II. Orbital energies and transfer integrals (in eV) of Fe d X − Y and P n p
Wannier orbitals of dpp models. The descrip-tions P and As indicate Ca Al O Fe P and Ca Al O Fe As ,respectively, for the chemical composition and crystal structure.Transfer integrals obtained from d models are also shown inparentheses. The origins of orbital energies ε are set to the re-spective Fermi levels. Crystal structureComposition P As ε X − Y − . . − . − . t − . . − . − . t − . . − . . t − . − . − . − . ε X − . − . ε Z − . − . t X .
153 0 . t Z − . − . ε X − Y − . . − . − . t − . . − . − . t − . . − . . t − . − . − . − . ε X − . − . ε Z − . − . t X .
128 0 . t Z − . − . Full Paper
Author Name 5 Al O Fe AsP
To study whether or not even the electronic struc-ture of a system in which P and As coexist is de-termined mainly by crystal structure, we unfolded theband structures and compared them in the three casesof Ca Al O Fe (As − x P x ) : Ca Al O Fe P ( x = 1),Ca Al O Fe As ( x = 0), and Ca Al O Fe AsP ( x =0 . x = 1 and 0 systems, the average crystalstructure of Ca Al O Fe P and Ca Al O Fe As wasused. The fractional height of the pnictogen atoms usedis thus z P n = 0 . x = 0 . √ × √ × x = 1 and 0 systems. The P and As atoms were set atthe experimental heights in Ca Al O Fe P ( h P = 1 . Al O Fe As ( h As = 1 .
500 ˚A), respectively.The fractional height of the pnictogen atoms used arethus z P = 0 . z As = 0 . √ × √ × d bands of the x = 0 . d character and then unfolded theinterpolated band structure by regarding the supercell asconsisting of four primitive cells, each of which containsone Fe site: a sc = 2 a pc , b sc = 2 b pc , and c sc = c pc . Weprovide in Fig. 4(b) the unfolded band structure for the x = 0 . x = 0 . π,
0) to ( π, π ) (cor-responding to wave vectors along the b direction) and theother from (0 , π ) to ( π, π ) (corresponding to wave vec-tors along the a direction), owing to the inequivalenceof the a and b directions [see Fig.4(a)]. Noticeable gapopenings of three of the unfolded bands are seen on thelatter path, while the continuity of the unfolded bandson the former path looks firmer. They originate from thedifference between the arrangement of atoms of differ-ent species along the a direction, and that of the samespecies along the b direction.Figure 4(c) shows the unfolded band structures forthe x = 0 ,
1, and 0 . x = 0 and 1 systems, for whichthe exact unfolding is possible, but also that for the x = 0 . Al O Fe P (Ca Al O Fe As ) with an average crystal structure ex-cept for the P (As) atom with its experimental height hasthree (two) Fermi surfaces around Γ. This indicates thatpnictogen height is a crucial factor for the multiplicityof Fermi surfaces around Γ. It is interesting to see theproximity of the Fermi level at (0 ,
0) for the x = 0 . . x = 0 and 1 systems with an averagecrystal structure despite the x = 0 . x = 0 . x = 0and 1 systems, as shown in Fig. 4(c). These results cor-roborate the independence of the electronic structure ofa Ca Al O Fe (As − x P x ) system of the chemical com-position. We expect an accurate calculation of a bandstructure near the Fermi level for an arbitrary x using acrystal structure modeled simply by linearly connectingthe Ca Al O Fe P and Ca Al O Fe As crystal struc-tures. Al O Fe (As − x P x ) Given the results obtained above, we calculated thegeneralized susceptibility χ of Ca Al O Fe P andCa Al O Fe As with gradually varying their crystalstructures. We expect that the χ calculated in sucha way accurately reproduces the qualitative behaviorof Ca Al O Fe (As − x P x ) for arbitrary x . The lat-tice parameters and atomic coordinates c used are lin-early parametrized by the crystal structure ratio λ as c ( λ ) = λc P + (1 − λ ) c As . λ = 0 and 1 correspondto the Ca Al O Fe As and Ca Al O Fe P crystalstructures, respectively. We calculated χ ( q ) using eq.(2) and plotted it in Fig. 5(a) for Ca Al O Fe As and Ca Al O Fe P with λ = 0 , .
5, and 1. Those indoped cases with ± . χ is seen to be sensitive to the difference in chemi-cal composition compared with the band energy. Thepeaks of χ are located at M in the undoped cases ofboth Ca Al O Fe As and Ca Al O Fe P , while, in thedoped cases, the peaks are located at incommensurate q ’s close to M. We observe that the heights of the peaksare reduced by doping for both Ca Al O Fe As andCa Al O Fe P , which suggests that their magnetic in-stability is suppressed under doping. Figure 5(b) showsthe χ (M)’s of Ca Al O Fe P and Ca Al O Fe As asfunctions of λ . Although the Ca Al O Fe P systemswith smaller band widths give a larger χ (M) than theCa Al O Fe As systems, the qualitative behavior ofmonotonic decrease in χ (M) for both Ca Al O Fe P and Ca Al O Fe As are found to be the same in theentire range of λ . We found that, with increasing λ , thenumber of the α Fermi surfaces around (0 ,
0) increasesfrom one to two near λ = 0 .
75 for both Ca Al O Fe P and Ca Al O Fe As . The larger number of Fermi sur-faces for λ > .
75 would be preferable to larger χ be-cause of the larger number of scattering channels. The J. Phys. Soc. Jpn.
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Author Name -3-2-10123 E n e r gy ( e V ) -3-2-10123 E n e r gy ( e V ) (c) (b)(a) abc P AsFe Ca Al O Fe PCa
Al O Fe As a sc b sc (0, 0) (π, 0) (π, π) (0, π)(0, 0) (π, π) (0, 0) (π, 0) (π, π) (0, π)(0, 0) (π, π) Fig. 4. (Color) (a) Bird’s-eye view of an Fe layer of a √ ×√ × x = 0 . c -axis is shown on the right, together withthe primitive lattice vectors of the supercell. Brown, purple, andgreen balls represent Fe, P, and As atoms, respectively. (b) Theblurred curves are for the unfolded 20 bands of the d model forthe x = 0 . x = 0 ,
1, and 0 . x = 1 and 0 systems, respectively, with the crystal structurefixed at the average of Ca Al O Fe P and Ca Al O Fe As .The origins of energy are set to the respective Fermi levels. calculated χ , however, exhibits the trend of a mono-tonic decrease. To examine the factors determining thistrend, we plot the band energies E xy ( π, π ) in Fig. 5(c)for the undoped systems as functions of λ . E xy ( π, π ) isthe height of the d X − Y -derived band. As is shown, asmaller λ gives a higher E xy ( π, π ) and thus a more ef-fective γ Fermi surface, and the difference in chemicalcomposition has only a minor effect on the values of E xy ( π, π ). Furthermore, a smaller λ (a larger a and alarger h P n ) leads to narrower bands and a larger density of states. These observations suggest that the effects of asmall λ overcome the difference in the number of α Fermisurfaces. λ χ ( M ) ( a r b . un it ) Ca Al O Fe P hole-dopedelectron-doped Ca Al O Fe As hole-dopedelectron-doped undopedundoped (b)(c) E ( π , π ) x y ( e V ) Ca Al O Fe P Ca Al O Fe As χ ( a r b . un it ) Γ X M Γ Γ Γ Γ ΓX XM M hole-dopedundopedelectron-doped λ=0 λ=0.5 λ=1Γ X M Γ Γ Γ Γ ΓX XM Mλ=0 λ=0.5 λ=1 hole-dopedundopedelectron-doped (a) χ ( a r b . un it ) Ca Al O Fe P undoped Ca Al O Fe As undoped
Fig. 5. (Color) (a) Generalized susceptibilities χ ( q ) ofCa Al O Fe P and Ca Al O Fe As for crystal structureratios λ = 0 , . χ (M) in doped and undoped cases of Ca Al O Fe P and Ca Al O Fe As as functions of λ . (c) Band energies of d X − Y -derived bands at ( π, π ) for undoped systems.
4. Conclusions
We performed first-principles calculations ofthe electronic structures of Ca Al O Fe P and . Phys. Soc. Jpn. Full Paper
Author Name 7 Ca Al O Fe As . Ca Al O Fe P (Ca Al O Fe As )was found to have three (two) Fermi surfaces aroundΓ. We found that the systems of the same crystalstructure but different chemical compositions give riseto similar band structures. By constructing the maxi-mally localized Wannier functions and analyzing theirtransfer integrals, we demonstrated that the differencesbetween the band structures of Ca Al O Fe P andCa Al O Fe As originate mainly from the difference inpnictogen height. Specifically, the hybridization betweenthe p Z orbital and its neighboring d X − Y orbitals playsimportant roles in determining the electronic structures.We analyzed the electronic structure ofCa Al O Fe AsP by unfolding its electronic bands.We found that its band structure resembles the bandstructures of Ca Al O Fe P and Ca Al O Fe As withan average crystal structure, although Ca Al O Fe AsPcontains pnictogen height disorder. We therefore ex-pected that an accurate calculation of band structuresfor an arbitrary x is possible using a crystal structuremodeled by linearly connecting the crystal structures ofCa Al O Fe P and Ca Al O Fe As .We then calculated the generalized susceptibility χ for Ca Al O Fe (As − x P x ) using crystal structuresconstructed from the linear interpolation of the crystalstructures of Ca Al O Fe P and Ca Al O Fe As . Itwas found that a smaller crystal structure ratio λ leadsto a larger χ because of the larger density of states andthe more effective γ Fermi surface.Further theoretical and experimental investigations ofthe structural and magnetic properties of perovskite-typesystems are required to clarify and optimize the super-conducting properties of such systems.
Acknowledgement
We thank Professor K. Terakura for discussions. Wealso thank Dr. A. Iyo, Dr. H. Eisaki, Dr. C. H. Lee,Dr. P. M. Shirage, Dr. K. Kihou, and Dr. H. Kitofor discussions and for providing us with experimentaldata prior to publication. This work was partly sup-ported by the Strategic International Collaborative Re-search Program (SICORP), Japan Science and Technol-ogy Agency, by the Next Generation Super Comput-ing Project, Nanoscience Program, and by a Grant-in-Aid for Scientific Research on Innovative Areas, ”Ma-terials Design through Computics: Complex Correlationand Non-Equilibrium Dynamics” (No. 22104010) fromMEXT, Japan. The calculations were performed usingcomputational facilities at TACC, AIST as well as at theSupercomputer Center of ISSP and at the InformationTechnology Center, both at the University of Tokyo.
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