A proposal to improve Ni-based superconductors
AA proposal to improve Ni-based superconductors
Zi-Jian Lang ( 郎 子 健 ), Ruoshi Jiang ( 姜 若 诗 ), and Wei Ku ( 顧 威 )
1, 2, ∗ Tsung-Dao Lee Institute & School of Physics and Astronomy,Shanghai Jiao Tong University, Shanghai 200240, China Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shanghai 200240, China (Dated: January 28, 2021)Recently discovered superconductivity in hole-doped nickelate Nd . Sr . NiO caught intensive attentionin the field. An immediate question is how to improve its superconducting properties. Guided by the keycharacteristics of electronic structures of the cuprates and the nickelates, we propose that nickel chalcogenideswith a similar lattice structure should be a promising family of materials. Using NdNiS as an example, wefind this particular crystal structure a stable one, through first-principle structural optimization and phononcalculation. We justify our proposal by comparing with CaCuO and NdNiO the strength of the charge-transfercharacteristics and the trend in their low-energy many-body effective Hamiltonians of doped hole carriers. Theseanalysis indicates that nickel chalcogenides host low-energy physics closer to that of the cuprates, with strongermagnetic interaction than the nickelates, and thus deserve further experimental exploration. Our proposal alsoopens up the possibility of a wide range of parameter tuning through ligand substitution among chalcogenides,to further improve superconducting properties. Hole doped nickelate, Nd − x Sr x NiO [1, 2], as a first Ni-based high-temperature superconductor, has recently attractedgreat attention in condensed matter physics recently. It dis-plays type-II superconductivity, dome-shaped superconduct-ing phase [2] and strange metal (linear resistivity) behav-ior in its normal state [1]. All of these characteristics sug-gest that this material represents a new family of unconven-tional superconductors. Meanwhile, their strong temperatureand doping dependent hall coefficient [2], negative magneto-resistance [3], absence of long-range magnetic order [4, 5] inthe parent compound, and increasing normal-state resistivityin the overdoped regime [2, 6] also indicate rich underlyingphysics in this new superconductor that might be absent in thecuprates [7–10]. Obviously, these nickelate superconductorsare of a promising family to help unravel the long-standingpuzzles of high-temperature superconductivity and even tofind higher transition temperature T c beyond the cuprates.So far within limited attempts, the highest T c of nickelates isonly about 12K [2, 6], one order of magnitude lower than thebest cuprates [10, 11]. Furthermore, at present, superconduc-tivity is only found in thin films but not in bulk samples [3],for reasons yet to be understood. Significant experimentalprogress is thus expected upon improvement of sample qual-ity. On the other hand, it is of equal importance to seek otherapproaches to improve the superconducting properties besidesthe sample quality.Here we address this timely issue by first comparing thehigh-energy electronic structure of the cuprates and nicke-lates to identify their key characteristics being the strengthof charge transfer. Based on this, we propose a new familyof material, nickel chalcogenides, as a promising candidate toimprove the superconducting properties. Taking NdNiS asan example, through density functional structure optimizationand phonon calculation, we first demonstrate that this com-pound is stable under the same crystal structure as NdNiO .The corresponding high-energy electronic structure confirmsour expectation of an enhanced charge-transfer characteris- tic. Furthermore, our local many-body diagonalization givesa ground state similar to those of the cuprates and nickelates,namely a spin-singlet state with doped holes mostly resid-ing in ligand- p -orbitals [12]. As anticipated, the correspond-ing effective eV-scale Hamiltonian of hole carriers containsstronger spin interactions than NdNiO , suggesting a highertemperature scale in the phase diagrams. Our study indi-cates that nickel chalcogenides are promising candidates forimproved superconducting properties, and ligand substitution,e.g. NdNiS − x O x and NdNiS − x Se x , would introduce a greatdeal of tunability for future experimental exploration.To identify the key difference between the cuprates andnickelates, we compare their high-energy electronic structureusing density functional theory(DFT). Since both the cupratesand nickelates host strong antiferromagnetic (AFM) correla-tion [13, 14] inherited from the unfrustrated square lattice ofspin 1/2 local moment [15], we calculate the band structuresunder AFM order within the LDA+ U approximation [16–18] CaCuO NdNiS NdNiO E - E F ( e V ) Cu/Ni d Ca/Nd d O/S p Γ ZX ZM AΓ R
Γ Z X ZM AΓ
R Γ Z X ZM AΓ R -21 E - E F ( e V ) FIG. 1. Comparison of LDA+ U band structures of CaCuO , NdNiS and NdNiO under AFM order, unfolded in the one-Cu/Ni Brillouinzone. The red, blue and green colors represent the weights of Cu/Ni,Ca/Nd and O/S orbitals, and Nd f -orbitals are set transparent. Thelower panel shows the magnified band structure of the purple dashedboxes in the upper panel. Notice the trend in the relative energies ofO/S and Cu/Ni orbitals. a r X i v : . [ c ond - m a t . s up r- c on ] J a n DO S ( m e V - / un it ce ll ) Γ M X Γ Z A R Z E n e r gy ( m e V ) a bc (a) (b) S Nd Ni FIG. 2. (a) Crystal structure of NdNiS , where grey, orange and yel-low balls represent the Ni, Nd and S atoms respectively. (b) Phonondispersion and corresponding density of states of NdNiS . The pos-itivity of all phonon frequencies confirms the stability of the crystalstructure. and unfold them to the one-Ni unit cell for a simpler visual-ization [19]. Fig. 1(a)(c) show that compared with NdNiO ,the main difference of CaCuO at the large energy scale is themuch lower energy of its d -orbitals (in red) relative to the O p -orbitals (in green), reflecting a much stronger charge-transfernature well known to the community [20]. Given that bothfamilies are doped spin 1/2 systems, it is reasonable to expectthat promoting such a charge transfer characteristic should im-prove significantly the superconducting properties, due to var-ious considerations of low-energy physics such as enhancedsuper-exchange interaction [15] and renormalized kinetic en-ergy. Since there is no chemical way to further lower the or-bital energy of Ni (other than replacing it by Cu), we are leftwith no choice but to raise the energy of the ligand p -orbitals,for example by substituting O with S or Se.Taking NdNiS as an example, we first examine the sta-bility of this compound under the same crystal structure [c.f.Fig. 2(a)] as the nickelates. Our structure optimization cal-culation [18] gives lattice constants a = b = .
505 ˚A and c = .
703 ˚A. With these structural parameters, further phononcalculation finds that phonon frequencies are all positive, asshown in Fig. 2(b). This confirms a stable structure realizablein the lab.Next, we verify the enhanced charge-transfer characteristicof this material. Fig. 1(b) shows the similar unfolded bandstructure of AFM NdNiS . As expected from above chemi-cal intuition, substituting O by S raises the energy of the p -orbitals (in green) quite significantly, thereby enhancing thecharge-transfer nature. The density of state (DOS) plots inFig. 3 illustrate a similar trend. Right below the Fermi energy,the relative weight of the most relevant ligand p // -orbitals (ingreen) to the d x − y -orbital (in red) grows systematically fromNdNiO to NdNiS and CaCuO . (Here, p // refers to O/S p -orbitals pointing toward nearest Cu/Ni atoms.) Indeed, substi-tuting O by S enhances the charge-transfer nature and bringsnickel chalcogenides closer to the cuprates.To reveal the physical benefits of a stronger charge-transfercharacteristic, we proceed to investigate the low-energy ef-fective Hamiltonian using well-established approaches for thecuprates [12, 18, 21, 22]. Using DFT-parameterized high-energy many-body Hamiltonian, we calculate the local many-body ground state via exact diagonalization. The ground statewith a doped hole is a spin-singlet state similar to the well- DO S ( e V - / un it ce ll ) Energy (eV)
CaCuO NdNiS NdNiO (a) (b)(c) Cu/Ni 𝑑 −𝑟 Cu/Ni 𝑑 𝑥 −𝑦 O/S p // Nd d FIG. 3. Comparison of orbital resolved Density of States in CaCuO ,NdNiS and NdNiO . Notice the gradual reduction of the relativeweights of O/S (green) p // -orbitals against (red) Cu/Ni d x − y -orbitalsright below the Fermi energy from CaCuO to NdNiO . known Zhang-Rice singlet [22] with (self-)doped hole mostlyresiding in the ligand p -orbitals.Note that such a strong singlet formation introduces animportant correction to Fig. 1 and 3: it pulls the energy of x − y orbital closest to the chemical potential, even beyondthe 3 z − r orbital. This effect, however, will still respect theabove mentioned trend concerning the relative energies of O/Sorbitals and Cu/Ni orbitals.Using this singlet state as basis, the low-energy Hamilto-nian of hole carriers resembles the well-known t - J model:(The subspace spanned by this singlet state form the basis forthe low-energy effective Hamiltonian, upon integrating out therest of the Hilbert space perturbatively.) H = ∑ ii (cid:48) ν t ii (cid:48) ˜ c † i ν ˜ c i (cid:48) ν + ∑ < i , j > J S i · S j , (1)where ˜ c † i ν create a dressed hole at site i of spin ν . S i = ∑ ν , ν (cid:48) ˜ c † i ν σ ν , ν (cid:48) ˜ c i ν (cid:48) denotes the spin operator and σ ν , ν (cid:48) is thevector of Pauli matrices.Table I shows our resulting nearest neighbor hopping pa-rameters t ii (cid:48) and super-exchange parameters J for the threematerials. Despite the larger lattice constant in NdNiS , t ii (cid:48) turns out to be similar in all three materials owing to thelarger radius of S p -orbitals. In contrast, J is systematicallyenhanced from NdNiO , to NdNiS and CaCuO . This is be-cause a stronger charge-transfer nature (higher p -orbital en-ergy) gives a reduced charge-transfer gap ∆ CT (approximateenergy to return an electron from the p // -orbital back to Cu/Ni d x − y -orbital.) With the intra-atomic repulsion roughly thesame in Cu and Ni, this in turn enhances the super-exchangeprocesses ( ∝ ∆ − CT ) [12, 23]. We stress that despite the sim-plicity of such an estimation, the qualitative trend among thesematerials is robust.The enhanced J is likely very important for the super-conducting properties. It would not only lead to a strongermagnetic correlation that dominates the low-energy physicalHilbert space, but also give rise to a larger renormalized ki-netic energy [10, 24]. In other words, a larger J can stretch TABLE I. Comparison of energy difference of d x − y and p // , ∆ pd = ε p // − ε d x − y ; estimated charge transfer gap, ∆ CT ; hybridization be-tween d x − y and p // orbitals, t pd ; nearest neighbor hopping t andexchange parameter J in one band t − J model and T c [2, 25] forthree different materials, CaCuO , NdNiS and NdNiO . ∆ pd ∆ CT t pd t J T c CaCuO ∼ ∼ > ∼ ∼ ∼ ∼ ∼ the energy scale of all the low-energy physics, effectively pro-ducing a larger temperature scale in the phase diagram. Onecan therefore expect that NdNiS should have better super-conducting properties than the nickelates.An interesting feature of NdNiS is that the possibleelectron-carrier density in the parent compound will increaseas a result of higher-energy p -orbitals (c.f. Fig. 1 and 3). Onthe one hand, since the electron carriers are shown to be nearlydecoupled from the hole carriers [12] in the nickelates (andthe same is found in NdNiS [18]), their existence should notinterfere much with the hole superconductivity. On the otherhand, these weakly correlated electron carriers might intro-duce additional physical effects absent in the cuprates (forexample, strengthening the essential superconducting phasestiffness.) Further experimental investigation of the nickelchalcogenides will prove highly illuminating.Finally, we note that it is not just S that has a good p -orbital energy, Se having a similar chemical orbital energyshould also be suitable from our consideration. This opensup a wide range of tunability in material design, for exampleNdNiS − x O x or NdNiS − x Se x , to optimize superconductingproperties, or to explore systematic trends for better physicalunderstanding.In conclusion, aiming to improve the superconductingproperties of the newly discovered unconventional nickelatesuperconductors, we identify the degree of charge transfer asthe key difference with the cuprates in their high-energy elec-tronic structure. Guided by this, we propose a new familyof material nickel chalcogenides as a promising candidate forimproved superconducting properties. Taking NdNiS as anexample, we find this compound stable under the desired crys-tal structure and thus realizable in laboratory. The resultinghigh-energy electronic structure displays the anticipated en-hancement of the charge-transfer nature. We then reveal thephysical benefits of a stronger charge-transfer characteristicvia derivation of low-energy effective Hamiltonian. The re-sulting Hamiltonian encapsulates a stronger super-exchangespin-interaction, implying a higher temperature scale for alllow-energy physics, including superconductivity. Our studypaves the way to discover more nickel-based superconduc-tors in nickel chalcogenides with improved superconductingproperties, for examples NdNiS − x O x and NdNiS − x Se x . 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