A Possible Family of Ni-based High Temperature Superconductors
AA Possible Family of Ni-based High Temperature Superconductors
Congcong Le,
1, 2
Jinfeng Zeng,
1, 3
Guang-Han Cao, and Jiangping Hu
1, 2, 5, ∗ Beijing National Laboratory for Condensed Matter Physics,and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China Kavli Institute of Theoretical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China University of Chinese Academy of Sciences, Beijing 100049, China Department of Physics, Zhejiang University, Hangzhou 310058, China Collaborative Innovation Center of Quantum Matter, Beijing, China (Dated: December 19, 2017)We suggest that a family of Ni-based compounds, which contain [Ni M O] − (M=chalcogen) layerswith an antiperovskite structure constructed by mixed-anion Ni complexes, NiM O , can be poten-tial high temperature superconductors upon doping or applying pressure. The layer structures havebeen formed in many other transitional metal compounds such as La B Se O (B=Mn, Fe,Co). Forthe Ni-based compounds, we predict that the parental compounds host collinear antiferromagneticstates similar to those in the iron-based high temperature superconductors. The electronic physicsnear Fermi energy is controlled by two e g d-orbitals with completely independent in-plane kinemat-ics. We predict that the superconductivity in this family is characterized by strong competitionbetween extended s-wave and d-wave pairing symmetries. Since the discovery of cuprates[1], the Cu-based hightemperature superconductors, more than thirty yearsago, there have been intensive efforts to find Ni-basedcounterparts[2–5] as Ni is the nearest neighbor elementto Cu among the 3d transition metal elements in thePeriod Table. However, although numerous discoveredNi-based compounds share similar physics in a variety ofaspects to cuprates, none of the known Ni-based materi-als exhibits high T c superconductivity.Recently, we have suggested that there is a directroadmap to design possible high T c materials[6, 7]. Inorder to achieve unconventional high T c , it is neces-sary to have an electronic structure in which those d-orbitals of transition metal atoms with the strongest in-plane coupling to the p-orbitals of anions have to be iso-lated near Fermi energy. In such an electronic struc-ture, the superexchange antiferromagnetic interactionscan be maximized to provide superconducting pairing.Both cuprates and the recently discovered iron-basedsuperconductors[8] are shown to satisfy this condition.Specifically, in the perovskite-type of structure such ascuprates, the d x − y e g orbital can only be isolated nearthe d filling configuration at Cu , and in the iron-based superconductors, the d configuration of Fe isan unique configuration to isolate the t g orbitals nearFermi energy[6, 7]. More importantly, we have pointedout that such an electronic environment exists very rarelyin nature because of symmetry and chemistry reasons.Thus, the condition can be considered as the gene ofunconventional high T c superconductors to serve as aguide to search for or design high T c materials. Follow-ing this understanding, we have predicted that there aretwo specific cases in which the condition can be satis-fied with a d filling configuration, namely, Co -basedcompounds[6, 9, 10].The d-orbital filling configuration in Ni atoms is d . In the d configuration, it is difficult to design a struc-ture to meet the above condition. The reasons are asfollows. With the even filling configuration, similar toiron-based superconductors, it is necessary to isolate twonear-degenerated orbitals at Fermi energy and both ofthem should strongly couple to in-plane p-orbitals. Theisolation requires a large energy separation between theselected two orbitals and the rest. The octahedra com-plex is the only complex structure to achieve large en-ergy separation in which the two e g orbitals have muchhigher energy than the three t g orbitals. Unfortunately,in the conventional perovskite-type structure, the two e g orbitals have completely different in-plane kinematics asthe d z orbital has little in-plane coupling to p-orbitals.These facts can explain why it is difficult for Ni-basedmaterials to achieve high T c superconductivity.In this letter, we show that it is possible to make bothe g orbitals to strongly participate in-plane kinematics ina structure with mixed anion Ni-octahedra complexes,NiM O as shown in Fig.1(a). The idea is to rotate thecomplex and connect them so that the apical oxygenscan form a square lattice as shown in Fig.1(c). In thiscase, the layered sheets of [B M O] − compose of face-sharing tilted Ni M O octahedra where the Ni atom issurrounded by two axial oxygen atoms and four M atoms.The two d z and d x − y e g orbitals before the rotationare labeled as d x − y and d xz/yz orbitals in the new axiscoordination as shown in Fig.1(a). The new d x − y gainsin-plane kinematics through oxygens and the new d xz/yz strongly couples to M anions and maintains in-plane kine-matics through M anions. The in-plane kinematics of thetwo orbitals are completely decoupled because of the in-plane mirror symmetry.We demonstrate the above idea in the layered com-pounds, La Ni Se O as shown in Fig.1(b), which arecomposed of the [Ni Se O] − layers. It is found that the a r X i v : . [ c ond - m a t . s up r- c on ] D ec FIG. 1: (color online). (a) The illustration of the BM O complex under two different axis coordinations and the energyof the crystal field together with orbital characters; (b) Thecrystal structure of La B Se O ; (c) The B M O layer in the ab plane in which magnetic exchange interactions between NN J , NNN J xz , NNN J yz , NNN J O,x − y and NNN J Se,x − y are indicated; (d) show the C-type collinear AFM state. superexchange antiferromagnetic(AFM) exchange cou-plings are maximized in the Ni-based compound to forma collinear AFM state, the same magnetic state in theparental compounds of iron-based superconductors[11].The low energy electronic physics is controlled entirely bythe two e g orbitals which form two independent electronicband structures. Considering that the superconductingpairing originates from the AFM superexchange interac-tions, we predict that the compound is characterized bythe strong competition between d-wave and extended s -wave pairing symmetries. While the extended s-wave isfavored upon hole doping, the d -wave can become highlycompetitive under electron doping or by adjusting latticeparameters, which can lead to a rich phase diagram toinclude possible time reversal symmetry breaking pairingstates.We first use density functional theory(DFT) to in-vestigate the magnetism and electronic structures ofLa B Se O (B=Fe,Co,Ni) which has the space group I /mmm . This type of calculation has been success-fully applied to other electron-electron correlated sys-tems. In particular, the calculation can qualitatively pre-dict both the electronic structures and magnetic orders inthe different family of iron-based superconductors[12–14].Our calculations are performed using density functionaltheory (DFT) as implemented in the Vienna ab initiosimulation package (VASP) code [15–17]. The Perdew-Burke-Ernzerhof (PBE) exchange-correlation functionaland the projector-augmented-wave (PAW) approach areused. Throughout the work, the cutoff energy is set to be550 eV for expanding the wave functions into plane-wave FIG. 2: (color online). The average superexchangeAFM interaction strength (namely, the NNN AFM, J ) inLa B Se O (B=Fe, Co, Ni), which are extracted from theGGA + U calculations with the values U = (0.0, 1.0, 2.0, 3.0,4.0) eV. basis. In the calculation, the BZ is sampled in the k spacewithin Monkhorst-Pack scheme[18]. On the basis of theequilibrium structure, the k mesh used is 10 × ×
3. Werelax the lattice constants and internal atomic positionswith GGA, where the plane wave cutoff energy is 600eV. Forces are minimized to less than 0.01 eV/˚Ain therelaxation. The GGA plus on-site repulsion U method(GGA+ U ) in the formulation of Dudarev et al .[19] is em-ployed to describe the electron correlation effect.The Mn, Co and Fe compounds have been experi-mentally studied and theoretically investigated[20–30].A very good qualitative agreement between theoreticalcalculations and experimental results has been reached.The Fe and Co compounds are reported to possess Mott-insulating behavior and a small band gap of the Fecompound is found to be approximately 0 . − . (cid:126)Q = (0 . , , . , asshown in Fig.1(c). The NN AFM interactions are mainlyfrom direct exchange couplings between two d-orbitals.As we will show later, the situation becomes very differ-ent in the Ni-based compounds. For the Ni-based ones,the C-type of collinear antiferromagnetic striped state isfavored, which indicates the dominance of the next NN(NNN) AFM exchange couplings. The NNN AFM inter-actions are from superexchange couplings through anionp-orbitals. This magnetism trend in La O B Se fromFe/Co to Ni is very similar to the one in the family ofmaterials related to iron-based superconductors. In the TABLE I: Optimized structural parameters of La Bi M O by GGA. La Ni S O La Ni Se O La Ni Te O a(˚A) 4.0197 4.0834 4.1409c(˚A) 16.8855 17.3271 18.7978Ni-M(˚A) 2.4920 2.5740 2.6920M-M(˚A) 2.9450 3.1360 3.4400 α (Ni-M-Ni) 107.543 ◦ ◦ ◦ study of iron-based superconductors and related materi-als, such as BaB As (B=Cr, Mn, Fe), the Cr and Mn-based compounds exhibit the G-type AFM states butthe Fe-based compounds exhibit the C-type AFM state.Thus, the trend from Fe/Co to Ni in La B Se O exactlyresembles the one from Cr/Mn to Fe in BaB As [14]. Aswe have discussed in the beginning, the fact that onlyFe-based compounds become high temperature supercon-ductors upon doping or applying pressure has led us toargue that only NNN superexchange couplings can leadto superconducting pairing[7]. Thus, here we have iden-tified a new system to justify the assumption.For the Ni-based compounds, we calculate differentchalcogen compounds, La Ni M O (M=S, Se, Te). Welist the optimized structural parameters in Table.I. TheC-type Collinear AFM state is always favored in ourcalculations with different U values. The ordered mag-netic moments increase from 0.86 µ B at U=0 to 1.44 µ B atU=4eV. When U is less than 2.0eV, the magnetic stateis metallic. However, at U=3eV, it becomes an insu-lator with an insulating gap about 0.15eV and the gapincreases further to about 0.5eV when U=4.0eV.We follow the same procedure in ref.[14] to estimatethe average effective magnetic interaction strength. Bycalculating the energies in the different magnetic states,including the ferromagnetic(FM) state, the G-type AFMstate and the C-type stripe states, we can extract theaverage effective NNN AFM superexchange strengths forLa B Se O (B = Fe, Co, Ni). The result is plotted inFig.2. The NNN magnetic interactions in the Fe/Co-based compounds are consistently weak with the changeof U. However, it is strongly antiferromagnetic in the Ni-based compounds under all calculations with different Uvalues. The result proves that the superexchange AFMexchange interactions, namely the NNN AFM interac-tions in the Ni layer, are dominating.Second, we show that the presence of strong NNNAFM interactions is consistent with the presence of thetwo near half-filling e g orbitals at Fermi energy in theparamagnetic state. We label the Ni atoms as shown inFig.1(b). Specifically, the e g orbitals of Ni(2,3) as in-dicated in Fig.1(b) are d x − y and d yz , and the e g or-bitals of Ni(1,4) are d x − y and d xz . The band struc-tures of La Ni M O for different chalcogens are verysimilar. Therefore, in the following, we simply focus on FIG. 3: (color online) (a) The band structure ofLa O Ni Se O, The orbital characters of bands are repre-sented by different grayscales; (b) The band structure of theeffective model; (c), (d) and (e) show Fermi surfaces of theeffective model at 0.2 electron doping, half filling and 0.28hole doping, respectively. The orbital contributions on Fermisurfaces are shown with different coded colors: Ni3 d yz (red),Ni4 d x − y (green) Ni4 d xz (blue) and Ni3 d x − y orbitals(black). La Ni Se O . Fig.3 shows the band structure in whichdifferent colors mark the orbital characters. The elec-tronic structure is rather quasi-two dimensional. Themain electronic physics is clearly attributed to the mono-layer Ni M O. The bands near the Fermi level are domi-nated by the e g orbitals. The d x − y orbital contributesto an electron pocket at the Γ point and a hole pocketat the M point, and the d xz,yz orbital contributes a holepocket at the Γ point and an electron pocket at the Xpoint. Both orbitals are near half-filling.We can construct a minimum effective tight bindingmodel, H , to capture the two dimensional band struc-ture near Fermi surfaces of the single layer Ni Se O. Weconsider the base of the four e g orbitals at two different Nisites (Ni3 d x − y , Ni3 d yz , Ni4 d x − y , Ni4 d xz ). H canbe written as a 4 × x − y and d xz/yz orbitals by sym-metry, the nonzero elements of H matrix are given by H ( k x , k y ) = (cid:15) + 2 t xx cos ( k x ) + 2 t yy cos ( k y ) H = 4 t xy cos (0 . k x ) cos (0 . k y ) H ( k x , k y ) = (cid:15) + 2 t yy cos ( k y ) + 2 t yyyy cos (2 k y )+4 t xxyy cos ( k x ) cos ( k y ) + 4 t yyyyxx cos ( k x ) cos (2 k y ) H = − t xy sin (0 . k y ) sin (0 . k x ) (1)with H , ( k x , k y ) = H , ( k y , k x ) and H , ( k x , k y ) = H , ( k y , k x ). We use eV as the energy unit for all param-eters. By fitting to the band structure of La O Ni Se Oat the k z = 0 plane, we have (cid:15) = 7 . (cid:15) = 7 . d x − y and d xz,yz . The cor-responding hopping parameters in above equation are t xx = − . t yy = − . t xy = − . t yy =0 . t xy = − . t xxyy = − . t yyyy = 0 . t yyyyxx = 0 . H is plotted in Fig.3(b) and the typ-ical Fermi surfaces at three different doping levels arealso plotted in Fig.3(c)-(e). Both well capture the DFTband structures of the e g orbitals. Summarizing aboveresults on the magnetism and electronic structure, it isclear that the Ni-based compounds meet our necessarycondition for unconventional high T c superconductivity.Finally, we provide a general analysis to qualitativelyunderstand the possible superconducting states in theNi-based compounds. Instead of carrying out detailedtheoretical calculations, we analyze the material basedon energy scale and general principle emerged in under-standing both cuprates and iron-based superconductors.First, if there is an unified superconducting mechanismfor unconventional high T c superconductors, the maxi-mum T c must represent the energy scale of the underlin-ing model. This argument is supported by experimentalresults in cuprates and iron-based superconductors. Ifwe compare the maximum T c achieved in cuprates andiron-based superconductors, their ratio is about 3. If wecompare the effective hopping generated through anions,it is about 0.42eV in cuprates[34] and about 0.15eV iniron-based superconductors[12]. Their ratio is also about3. Second, the pairing symmetries in cuprates and iron-based superconductors can be unified within the Hu-Dingprinciple[35, 36] which states that in order to generatinghigh T c superconductivity, the momentum space formfactor of the superconducting pairing gap function whichis determined by the AFM superexchange couplings musthave large overlap with Fermi surfaces and the most fa-vored pairing symmetry is the one which has the largestoverlap strength[35].For the Ni-based compounds, we can find that thethree NNN hoppings, t xx , t yy , and t yy , are mediatedthrough the p-orbitals of O/Se anions based on theirsigns. Comparing their values with those in cuprates andiron-based superconductors, we can notice that the valueof t xx ∼ . eV , which is mediated through oxygen, iscomparable to cuprates and the left two hopping param-eters t yy and t yy , which is mediated through Se, are com-parable to those of iron-based superconductors. Thesethree hoppings are associated with three AFM superex-change interactions, J o,x − y , J Se,x − y and J Se,xz/yz ,specified in Fig.1(c).Based on the above energy scaling and assuming thatthe superconducting pairing is provided by short AFMexchange interactions, we can use one superconduct-ing gap parameter ∆ to write the pairing forms in FIG. 4: (color online) The superconducting gap structure forextended s-wave and d-wave based at the three different dop-ing levels:(a, b), (c, d) and (e, f) are corresponding to 0.2electron doping, half filling and 0.28 hole doping, respectively. momentum space between two NN Ni(2,3) atoms be-ing ∆ ( cos ( k x ) + cos ( k y )) for d x − y and ∆ cos ( k y )for d yz , and between two NN Ni(1,4) atoms being ± ∆ ( cos ( k y )+ cos ( k x )) for d x − y and ± ∆ cos ( k x ) for d xz . The positive and negative signs are correspondingto the extended s-wave and d-wave pairing symmetries.With this choice of pairing functions, we can compare thegap values on different type of Fermi surfaces. The gapvalues and the signs on the three type of Fermi surfacesin Fig.3(c) are plotted in Fig.4 by taking ∆ = 0 . eV .The overlap strength between the form factors and theFermi surfaces for the extended s-wave is 1.6, 2 and 5times larger than the d-wave at 0.2 electron doping, halffilling and 0.28 hole doping, respectively. Therefore, theextended s-wave in hole doping region is reasonably muchstronger than the d-wave. However, in the electron dop-ing region, the d-wave is competitive to the extendeds-wave, which suggests a possible rich physics diagram inthis family of possible superconductors. As the averageenergy scale is higher than those of iron-based supercon-ductors, the maximum T c should be higher than those ofiron-based superconductors as well.In summary, we have identified a possible new familyof Ni-based high temperature superconductors, in whichtwo e g orbitals can be isolated near the d filling config-uration to carry electronic physics. This key electroniccharacter has been missed in all known Ni-based com-pounds. Synthesizing this Ni-based family of compoundscan provide us ultimate information to settle unconven-tional high T c mechanism.It is also worth addressing a few points and mention-ing material perspectives. First, in the search of Ni-basedhigh temperature superconductors[2], the attention hasbeen paid to compounds with low valence Ni +1 whichresembles Cu +2 . Ni +1 is not a very natural valence con-figuration in chemistry and can result in valence orders.Moreover, as correlated electronic physics is required tobe carried by d-orbitals, mixing with 4s-orbital in Ni +1 can significantly weaken correlation effects. These rea-sons can be the major fact why unconventional high T c superconductors, so far, appear only in +2 valence tran-sitional metal compounds. Second, since the La B M O structure is realized for B = Mn, Fe, and Co, it seemsto be likely that the Ni-based analogue can also be syn-thesized. However, further exploration on different anioncombinations is needed to search for the best suitableconditions. For example, we may investigate new Ni-compounds by replacing chalcogens by pnictides or chlo-ride and oxygen by fluorine. Third, the Ni-compoundsshare many similarities on material and physical aspectsto iron-based superconductors, including multi-orbitaland multi-Fermi surface pocket structures, we can inves-tigate mechanisms or origins associated with other or-ders and degrees of freedom besides superconductivity,for example, the origin of nematicity. Finally, we havenot addressed effects on superconductivity from the in-teractions between two orbitals. This effect can result inmuch rich pairing pictures such as broken time reversalsymmetry superconducting states. Moreover, althoughthe maximum T c in this family should exceed those iniron-based superconductors from the energy scale argu-ment, T c is expected to be sensitive to lattice parametersand bond angles as witnessed in iron-based superconduc-tors so that external pressure can have a major effect onphysical and superconducting properties. Acknowledgements
The work is supported by the Min-istry of Science and Technology of China 973 program(No. 2015CB921300, No. 2017YFA0303100), NationalScience Foundation of China (Grant No. NSFC-1190020,11534014, 11334012), the Strategic Priority ResearchProgram of CAS (Grant No.XDB07000000), and the KeyResearch Program of the CAS(Grant No. XDPB08-1). ∗ Electronic address: [email protected][1] J. G. Bednorz and K. A. Muller, Z. Phys. B , 189(1986).[2] V. I. Anisimov, D. Bukhvalov, and T. M. Rice, Phys.Rev. B , 7901 (1999). [3] K. W. Lee and W. E. Pickett, Phys. Rev. B , 165109(2004).[4] P. Lacorre, J. Solid State Chem. , 495 (1992).[5] V. V. Poltavets, M. Greenblatt, G. H. Fecher, andC. Felser, Phys. Rev. Lett. , 046405 (2009).[6] J. Hu, C. Le, and X. Wu, Phys. Rev. X , 041012 (2015).[7] J. Hu, Science Bulletin , 561 (2016).[8] Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono,JACS , 3296 (2008).[9] J. Hu and C. Le, Science Bulletin , 212 (2017).[10] C. Le, S. Qin, and J. Hu, Science Bulletin , 563 (2017).[11] P. Dai, Rev. Mod. Phys. , 855 (2015).[12] K. Kuroki, S. Onari, R. Arita, H. Usui, Y. Tanaka,H. Kontani, and H. Aoki, Phys. Rev. Lett. , 087004(2008).[13] J. An, A. S. Sefat, D. J. Singh, and M.-H. Du, Phys. Rev.B , 075120 (2009).[14] J. Zeng, S. Qin, C. Le, and J. Hu, Phys. Rev. B ,174506 (2017).[15] G. Kresse and J. Hafner, Phys. Rev. B , 558 (1993).[16] G. Kresse and J. Furthmller, Comp. Mat. Sci. , 15(1996).[17] G. Kresse and J. Furthm¨uller, Phys. Rev. B , 11169(1996).[18] H. J. Monkhorst and J. D. Pack, Physical Review B ,5188 (1976).[19] S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J.Humphreys, and A. P. Sutton, Phys. Rev. B , 1505(1998).[20] C. Wang, M.-Q. Tan, C.-M. Feng, Z.-F. Ma, S. Jiang,Z.-A. Xu, G.-H. Cao, K. Matsubayashi, and Y. Uwatoko,J. Am. Chem. Soc. , 7069 (2010).[21] H. Wu, Phys. Rev. B (2010).[22] J. X. Zhu, R. Yu, H. Wang, L. L. Zhao, M. D. Jones,J. Dai, E. Abrahams, E. Morosan, M. Fang, and Q. Si,Phys. Rev. Lett. , 216405 (2010).[23] Y. Fuwa, T. Endo, M. Wakeshima, Y. Hinatsu, andK. Ohoyama, JACS , 18020 (2010).[24] Y. Fuwa, M. Wakeshima, and Y. Hinatsu, Solid StateComm. , 1698 (2010).[25] M. Gnther, S. Kamusella, R. Sarkar, T. Goltz,H. Luetkens, G. Pascua, S. H. Do, K. Y. Choi, H. D.Zhou, C. G. F. Blum, et al., Phys. Rev. B (2014).[26] E. E. McCabe, C. Stock, E. E. Rodriguez, A. S. Wills,J. W. Taylor, and J. S. O. Evans, Phys. Rev. B (2014).[27] J. M. Mayer, L. F. Schneemeyer, T. Siegrist, J. V.Waszczak, and B. Van Dover, Angew. Chemi. Int. Ed.Engl. , 1645 (1992).[28] H. Kabbour, E. Janod, B. Corraze, M. Danot, C. Lee,M.-H. Whangbo, and L. Cario, JACS , 8261 (2008).[29] F. Takeiri, Y. Matsumoto, T. Yamamoto, N. Hayashi,Z. Li, T. Tohyama, C. Tassel, C. Ritter, Y. Narumi,M. Hagiwara, et al., Phys. Rev. B , 184426 (2016).[30] N. Ni, E. Climent-Pascual, S. Jia, Q. Huang, and R. J.Cava, Phys. Rev. B , 214419 (2010).[31] H. Lei, E. S. Bozin, A. Llobet, V. Ivanovski, V. Koteski,J. Belosevic-Cavor, B. Cekic, and C. Petrovic, Phys. Rev.B (2012).[32] D. G. Free and J. S. O. Evans, Phys. Rev. B (2010).[33] G. Jin, Y. Wang, X. Dai, X. Ren, and L. He, Phys. Rev.B (2016).[34] W. E. Pickett, Rev. Mod. Phys. , 433 (1989).[35] J. Hu and H. Ding, Sci Rep , 381 (2012).[36] J. C. S. Davis and D.-H. Lee, PNAS110