Hole superconductivity in infinite-layer nickelates

Hole superconductivity in infinite-layer nickelates

Physica C: Superconductivity and its applications 566 (2019) 1353534 Contents lists available at ScienceDirect Physica C: Superconductivity and its ...

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Physica C: Superconductivity and its applications 566 (2019) 1353534

Contents lists available at ScienceDirect

Physica C: Superconductivity and its applications journal homepage: www.elsevier.com/locate/physc

Hole superconductivity in infinite-layer nickelates ⁎,a

J.E. Hirsch , F. Marsiglio a b



Department of Physics, University of California, San Diego, La Jolla, CA 92093-0319, United States Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada


We propose that the superconductivity recently observed in Nd0.8Sr0.2NiO2 with critical temperature in the range 9–15 K results from the same charge carriers and the same mechanism that we have proposed give rise to superconductivity in both hole-doped and electron-doped cuprates: pairing of hole carriers in oxygen pπ orbitals, driven by a correlated hopping term in the effective Hamiltonian that lowers the kinetic energy, as described by the theory of hole superconductivity. We predict a large increase in Tc with compressive epitaxial strain.

1. Introduction Superconductivity has been recently observed in Nd0.8Sr0.2NiO2 [1]. The system has the same planes as the cuprate superconductors with Ni+ instead of Cu++ ions. The parent compound NdNiO2 is metallic at high temperatures and the resistivity turns upward at around 50 K. When it is doped with holes by substituting Nd+++ by Sr++ the resistivity continues to decrease below 50 K and drops to zero below the superconducting transition, which onsets around 9–15 K depending on sample preparation. Key questions include: (i) how do these compounds relate to holedoped and electron-doped cuprate superconductors? (ii) where do the doped holes go? (iii) what is the nature of the charge carriers? (iv) what is the mechanism of superconductivity? (v) can Tc be increased? In this paper we address each of these questions. The infinite-layer phase of these materials has no apical oxygens, and is the same structure as that of infinite-layer electron-doped cuprates [2] Sr1 x LnxCuO2 with Ln = La, Nd, Sm or Eu, which have superconducting transition temperatures in the range 35–40 K. The parent compound of those electron-doped cuprates, SrCuO2, is insulating when undoped and can only be doped with electrons, not with holes. Instead, NdNiO2, the parent compound of these new nickelate superconductors, is metallic and (so far) can only be doped with holes. There are also some infinite layer cuprates that appear to be hole-doped, such as Ca1 x SrxCuO2 [3], but generally hole-doped cuprate structures, such as La1 x BaxCuO4 contain apical oxygens [4]. It is easy to understand these doping characteristics. LaCuO4 can be doped with holes because the presence of O apical oxygens lowers the electrostatic potential at the Cu++ site. Another way to lower the electrostatic potential at the cation site is to replace Cu++ by Ni +, without apical oxygens. For that reason, these new nickelates [1] can be ⁎

Corresponding author. E-mail address: [email protected] (J.E. Hirsch).

https://doi.org/10.1016/j.physc.2019.1353534 Received 4 September 2019; Accepted 9 September 2019 Available online 10 September 2019 0921-4534/ © 2019 Elsevier B.V. All rights reserved.

doped with holes. Instead, with Cu ++ and no apical oxygens the electrostatic potential is higher so it is easier to dope with electrons rather than with holes. Notwithstanding the type of dopant charges, we have proposed that superconductivity in hole-doped [5] and electron-doped [6] cuprates arises from the same carriers through the same mechanism [7]. The fact that the same type of carriers appear to be responsible for the superconductivity of hole-doped and electron-doped cuprates has in our view been firmly established by extensive experimental evidence [9–15]. The newly discovered superconducting nickelates share with the hole-doped cuprates the fact that they are hole-doped, and share with electrondoped cuprates the fact that the structure has no apical oxygens. It would not be very surprising if the same carriers and the same mechanism account for the superconductivity of these new materials also. Fig. 1 shows the relevant orbitals in the NiO (or CuO) planes. The consensus for the cuprates is that both under hole or electron doping the doped carriers go into the Cu-d x 2 y 2 O-pσ band, and give rise to superconductivity. Instead, we have proposed that it is always holes in O-pπ orbitals that give rise to superconductivity. For electron-doped cuprates, electrons go into the Cu-d x 2 y 2 O-pσ band and induce holes into the O-pπ orbitals [7]. Instead, for hole-doped cuprates and nickelates, the doped holes go directly into the O-pπ band. We have argued that for both hole- and electron-doped cuprates orbital relaxation of the highly negatively charged oxygen anion lifts the O-pπ orbitals to the Fermi level [8], contrary to what band structure calculations predict. Clearly the same argument applies here. Fig. 2 shows the energy level structure we envision for cuprates and nickelates, in a hole representation. Both in the hole-doped cuprates (left panel) and in the hole-doped nickelates (right panel) the added hole will go into the oxygen pπ level because adding it to the cation would cost a high Hubbard U. In the electron-doped cuprates (center

Physica C: Superconductivity and its applications 566 (2019) 1353534

J.E. Hirsch and F. Marsiglio

Fig. 4. Measured Hall coefficient in undoped and doped superconducting nickelates, from Ref. [1]. Fig. 1. Ni d x 2


panel), removing a hole (adding an electron) causes the other hole to ‘fall’ into the O-pπ orbital. In the hole-doped infinite layer nickelates removing a hole (adding an electron) costs more energy than in the electron-doped infinite layer cuprates, so it is not likely that these new materials can be doped with electrons. Experiments have so far been reported for one hole concentration. Fig. 3 shows the predicted dependence of Tc on hole concentration for a typical set of parameters in our model. Within this model Tc increases rapidly when the distance between atoms in the plane decreases, as we showed in Ref. [5]. Therefore we predict a large enhancement of Tc under compressive epitaxial strain. The dashed line in Fig. 3 shows the expected behavior of Tc versus hole concentration under such strain, with an increase in Tc at all hole concentrations. We expect the Hall coefficient in this material to be positive at low temperatures, reflecting conduction of holes in a single nearly full band. Fig. 4 shows the measured Hall coefficient [1], which turns positive below 50 K. At higher temperature the negative Hall coefficient presumably results from contribution to conduction from both the Ni-O pσ band and the O-pπ band, with higher mobility for the carriers in the NiO band. Note that in the undoped case the conduction is metallic above 50K (Fig. 3(b) in Ref. [1]), presumably due to the smaller on-site repulsion U compared to the cuprates, and the Hall coefficient is negative as seen in Fig. 4. Within our model, superconductivity is caused by a correlated hopping term in the effective Hamiltonian describing conduction of oxygen pπ holes in a nearly full band [5], which arises due to the contraction and expansion of the oxygen orbitals depending on their charge content [16]. Superconductivity is driven by lowering of quantum kinetic energy, and neither phonons nor spin fluctuations play a significant role. It requires conduction by holes. We have proposed that this is also the mechanism responsible for superconductivity in iron pnictides [17], magnesium diboride [18,19], H2S [20] and all other superconducting materials [21]. Correlated hopping has also recently been proposed to be responsible for superconductivity in twisted bilayer graphene [22] and for superfluidity in systems of ultracold atoms in optical lattices [23,24]. As pointed out in Ref. [1] and also emphasized by Sawatzky [25], the discovery of superconductivity in these nickelates poses a challenge to proposed explanations of cuprate superconductivity that rely on magnetism, Zhang–Rice singlets, Mott physics, RVB, large Hubbard U, spin fluctuations, etc. Even though in elemental form Ni is magnetic, there is so far no evidence for magnetism in the newly discovered nickelates, and the parent undoped compound is metallic rather than insulating. In some sense these compounds appear closer to the class of superconducting bismuthates [26], for which both conventional [27,28] and ‘negative U’ [29] mechanisms have been proposed. Of course in other respects, e.g. structurally, the nickelates are much closer to the cuprates. Botana and Norman [30] have argued that the

and oxygen orbitals in the Ni-O planes. In the undoped parent Ni +

compound the nominal valence is and and there is one hole in the filled Ni d10 orbital. The O-pπ orbitals point in a direction perpendicular to the Ni-O bonds, and the pσ orbitals in a direction that is parallel. We propose that doped holes reside in a band resulting principally from overlapping O-pπ orbitals, the same as for both hole- and electron-doped cuprates. O=

Fig. 2. Illustration of how oxygen pπ hole carriers are created in hole-doped cuprates, electron-doped cuprates, and hole-doped nickelates, in the hole representation. Arrows on the energy levels denote holes. The difference in the relative locations of the O= and Cu++ orbitals for hole-doped and electrondoped cases arises due to their different crystal structures, T versus T′ or infinite layer. For the nickelates, the Ni+ level is lower relative to the oxygen levels compared to the electron-doped cuprates due to the lower atomic number.

Fig. 3. Tc versus hole concentration nh, the number of holes per oxygen atom. This behavior is generic for this model. Values for the bandwidth, correlated hopping parameter, on-site and nearest neighbor repulsion used are D = 5 eV, t = 0.3725 eV, U = 5 eV, and V = 0, respectively. The dashed line indicates the behavior expected under application of pressure in the plane, with the hopping parameter t increased to 0.375 eV.


Physica C: Superconductivity and its applications 566 (2019) 1353534

J.E. Hirsch and F. Marsiglio

electronic structure of nickelates is similar to that of cuprates and suggested a common mechanism. Others would surely argue that so far at least there is no evidence that the nickelates are anything other than conventional BCS-electron-phonon superconductors. In summary, it is clear that the discovery of the infinite-layer nickelates [1] with a significant superconducting critical temperature adds an important new member to a growing number of superconducting materials classes [31]. Commonalities and differences between the different classes [32] should help to significantly narrow down the range of plausible theories. In our view, most compelling is the reported Hall coefficient reproduced in our Fig. 4, which indicates the importance of hole carriers also in this new class. Measurements of the superconducting Tc and Hall coefficient at other hole concentrations will help to support our model, as will experiments reporting on the pressure dependence of Tc and on tunneling asymmetry [5,7]. We don’t see any reason not to expect significantly higher transition temperatures in this new class of oxide superconductors, particularly if the in-plane lattice constant can be reduced and the carrier concentration optimized.

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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC). References [1] D. Li, et al., Superconductivity in an infinite-layer nickelate, Nature 572 (2019) 624–627. [2] P. Fournier, T′ and infinite-layer electron-doped cuprates, Physica C 514 (2015) 314–338. [3] M. Azuma, et al., Superconductivity at 110 k in the infinite-layer compound (Sr 1 x Cax )1 y CuO2 , Nature 356 (1992) 775–776. [4] C.W. Chu, L.Z. Deng, B. Lv, Hole-doped cuprate high temperature superconductors, Physica C 514 (2015) 290–313. [5] J.E. Hirsch, F. Marsiglio, Superconducting state in an oxygen hole metal, Phys. Rev. B 39 (1989) 11515–11525. F. Marsiglio and J.E. Hirsch, ‘Hole Superconductivity and the High-Tc Oxides’, Phys. Rev. B41, 6435–6456 (1990). [6] J.E. Hirsch, F. Marsiglio, On the dependence of superconducting Tc on carrier