Correlated interface electron gas in infinite-layer nickelate versus cuprate films on SrTiO_3(001)
CCorrelated interface electron gas in infinite-layer nickelate versus cuprate films on SrTiO (001) Benjamin Geisler ∗ and Rossitza Pentcheva † Department of Physics and Center for Nanointegration (CENIDE),Universität Duisburg-Essen, Lotharstr. 1, 47057 Duisburg, Germany (Dated: February 23, 2021)Based on first-principles calculations including a Coulomb repulsion term, we identify trends in the electronicreconstruction of A NiO /SrTiO (001) ( A = Pr, La) and A CuO /SrTiO (001) ( A = Ca, Sr). Common to allcases is the emergence of a quasi-two-dimensional electron gas (q2DEG) in SrTiO (001), albeit the higherpolarity mismatch at the interface of nickelates vs. cuprates to the nonpolar SrTiO (001) substrate ( / vs. / ) results in an enhanced q2DEG carrier density. The simulations reveal a significant dependence of theinterfacial Ti d xy band bending on the rare-earth ion in the nickelate films, being - larger for PrNiO and NdNiO than for LaNiO . Contrary to expectations from the formal polarity mismatch, the electrostaticdoping in the films is twice as strong in cuprates as in nickelates. We demonstrate that the depletion of the self-doping rare-earth d states enhances the similarity of nickelate and cuprate Fermi surfaces in film geometry,reflecting a single hole in the Ni and Cu d x − y orbitals. Finally, we show that NdNiO films grown on a polarNdGaO (001) substrate feature a simultaneous suppression of q2DEG formation as well as Nd d self-doping. I. INTRODUCTION
The very recent observation of superconductivity in Sr-doped NdNiO and PrNiO films grown on SrTiO (001)(STO) [1–3] has sparked considerable interest in infinite-layernickelates, since their formal Ni ( d ) valence state ren-ders them close to cuprates [4–16]. In the quest for a funda-mental understanding of the underlying mechanisms, severalaspects are noteworthy and so far unresolved. In particular,superconductivity could not be confirmed experimentally inSr-doped bulk NdNiO [17] and was not observed in LaNiO films on STO(001) [1] despite its similar electronic structureto NdNiO and PrNiO in the bulk, apart from the Nd andPr f states [18].A considerable electronic reconstruction emerges inNdNiO /SrTiO (001) due to the polar discontinuities at theinterface and the surface [19], which comprises (i) the for-mation of a quasi-two-dimensional electron gas (q2DEG) atthe interface by occupation of Ti d states despite the metal-lic screening of the nickelate film; (ii) the depletion of theself-doping Nd d states, resulting in a cuprate-like Fermisurface; and (iii) an enhanced and modulated Ni e g orbitalpolarization throughout the film due to electrostatic dop-ing. Notably, the q2DEG was found to be far more pro-nounced than its counterpart emerging in the paradigmaticLaAlO /SrTiO (001) system (LAO/STO [20, 21]) beyond 4monolayers (ML) of LAO [22, 23], which is known to exhibitintriguing correlation-driven physics such as superconductiv-ity [24].In this context, the analogies frequently drawn betweeninfinite-layer nickelates and cuprates [5, 9, 13] appear in anovel light. A fundamental difference between these two ma-terials classes remains, namely, the formal polarity of the con-secutive (001) layers, being, for instance, Ca (CuO ) − andSr (CuO ) − in the superconducting infinite-layer cuprates ∗ [email protected] † [email protected] and Nd (NiO ) − , Pr (NiO ) − , and La (NiO ) − inthe infinite-layer nickelates. This implies distinct behaviorbetween cuprates and nickelates in film geometry on a non-polar substrate such as STO(001) despite the same formal d configuration.Here we systematically explore the impact of thepolar discontinuities at the interface and the sur-face on the structural and electronic properties ofPrNiO /STO(001), LaNiO /STO(001), CaCuO /STO(001),and SrCuO /STO(001) in film geometry by performingfirst-principles calculations including a Coulomb repulsionterm. In each system, we find that the polarity mismatchdrives an electronic reconstruction, inducing the formation ofa q2DEG at the interface. This supports the earlier findingof a q2DEG at the NdNiO /STO (001) interface, which isabsent for perovskite films [19], and establishes it as a generalphenomenon in infinite-layer nickelate and cuprate filmson STO (001) . The occupation of the Ti d states varies ineach case, which reflects the different polar discontinuitiesof infinite-layer cuprates vs. nickelates at the interface toSTO (001) , and furthermore unravels substantial distinctionsbetween NdNiO and PrNiO vs. LaNiO films. The elec-tronic reconstruction is accompanied by ionic relaxations,specifically ferroelectric-like displacements of the Ti ionsin the topmost – Å of the STO substrate, that act asa fingerprint of the q2DEG formation. We demonstrateexplicitly that the depletion of the rare-earth d states, whichself-dope the bulk infinite-layer nickelates, enhances thesimilarity of nickelate and cuprate Fermi surfaces in filmgeometry, resulting in a single hole in the Ni and Cu d x − y orbitals. The hole density increases from the interface to thesurface due to electrostatic doping, which we find to be twiceas strong in cuprates as in nickelates, contrary to expectationsfrom the formal polarity mismatch. Finally, we show thatNdNiO films grown on a polar NdGaO (001) substrateexhibit depleted Nd d states in the film and a simultaneouslyquenched q2DEG in the substrate, which offers a routeto disentangle their contributions to superconductivity ininfinite-layer nickelates. a r X i v : . [ c ond - m a t . s up r- c on ] F e b II. METHODOLOGY
We performed first-principles calculations in the frameworkof density functional theory [25] (DFT) as implemented inthe Quantum ESPRESSO code [26]. The generalized gra-dient approximation was used for the exchange-correlationfunctional as parametrized by Perdew, Burke, and Ernzerhof(PBE) [27]. Where indicated, we compare with PBEsol re-sults, a functional that often renders improved structural prop-erties [28–30]. Higher-level methods are beyond the scope ofthe present work due to the large system sizes [30, 31]. Staticcorrelation effects were considered within the DFT + U for-malism [32, 33] employing U = 4 eV on Ni, Cu, and Ti sites,in line with previous work [9, 34–38]. We confirmed that ahigher value of U Cu = 6 . eV [39] leads to largely identicalresults.We model AB O /STO (001) in film geometry ( A = Pr,La, Ca, Sr; B = Ni, Cu) by using √ a × √ a supercellswith two transition metal sites per layer to account for octa-hedral rotations, strained to the STO substrate lattice param-eter a = 3 . Å. The symmetric slabs contain . MLof STO substrate and ML of infinite-layer nickelate orcuprate film on each side (the figures only show half of thesupercell). The vacuum region spans Å. Simulationsusing a NdGaO (001) substrate are carried out in analogy( a = 3 . Å). Wave functions and density were expandedinto plane waves up to cutoff energies of and Ry,respectively. Ultrasoft pseudopotentials [40] as successfullyemployed in previous work [35–38, 41–45], were used in con-junction with projector augmented wave datasets [46]. The Prand Nd f electrons are frozen in the core, similar to previousstudies involving Nd [4, 13, 19, 34]; their explicit treatmentleads to qualitatively similar results. We used a × × Monkhorst-Pack (cid:126)k -point grid [47] and mRy Methfessel-Paxton smearing [48] to sample the Brillouin zone. The ionicpositions were accurately optimized, reducing ionic forces be-low mRy / a.u. III. IONIC RESPONSE TO THE INTERFACE POLARITY
The optimized geometries of different 4-ML AB O filmson STO(001) are displayed in Fig. 1(a). Similar to the case of Table I. Structural data of the considered AB O /STO (001) systems,compared to NdNiO /STO (001) [19]. The film thickness d Film ismeasured from the B site positions in S and S − , spanning 4ML [cf. Fig. 1(a)]. The parameters ˜ z and ˜ d refer to the exponen-tial fit of the ferroelectric-like Ti displacements in the STO substrate[cf. Fig. 1(c)], as described in the text, and quantify how strong anddeep the electronic reconstruction affects the substrate.NdNiO PrNiO LaNiO CaCuO SrCuO Strain at a STO (%) − . − . − . . − . d Film (Å) .
50 13 .
68 14 .
08 13 .
44 14 . z (Å) − . − . − . − . − . d (Å) .
42 7 .
48 7 .
66 8 .
23 8 . CaCu SS − S − Sr Δ z A T i - O b o nd s ( Å ) Δ z B ( Å ) S S − S − Δ z A ( Å ) [100] [ ] (b)(c)(d) Film Substrate Expansion at surface and interfaceBuckling Pr Δ z B -0.4-0.200.20.4 Ferroelectric-likeTi displacements
PrNiO /SrTiO (001) LaNiO /SrTiO (001) CaCuO /SrTiO (001) SrCuO /SrTiO (001) (a) c PrNiO2 c LaNiO2 c CaCuO2 c SrTiO3 c SrCuO2
Figure 1. (a) Optimized geometry of different d infinite-layer AB O /STO (001) systems. The small red numbers denote the dis-tance between the surface B O layer and the subsurface A layer.(b) The apical A -site distances ∆ z A increase in the infinite-layerfilms from the interface to the surface. They are particularly en-hanced at the interface ( S − ), exceeding the STO bulk distance.The small horizontal dashed lines indicate bulk c reference values.(c) The B -O displacements ∆ z B = z B − z O reveal a surface buck-ling in each case, whereas buckling at the interface (in the oppositedirection) occurs only for the two nickelate systems. In the STOsubstrate, dark-blue curves represent a fit to an exponential function(see text and Table I). (d) The oscillating apical Ti-O bond lengthsare linked to the ∆ z Ti displacements and act as a fingerprint of theq2DEG formation. — In all panels, large colored symbols indicatePBE results, whereas small black symbols correspond to PBEsol val-ues for comparison. NdNiO ( a = 3 . , c = 3 . Å [4, 49]), the lattice parametersof bulk PrNiO ( a = 3 . , c = 3 . Å; DFT+ U ), LaNiO ( a = 3 . , c = 3 . Å [9, 50]), and SrCuO ( a = 3 . , c = 3 . Å [39, 51]) imply that these materials are subjectto compressive strain, if grown epitaxially on STO(001) ( a =3 . Å), whereas CaCuO ( a = 3 . , c = 3 . Å [39, 51]) L a y e r - r e s o l v e d d e n s i t y o f s t a t e s ( S t a t e s / e V ) NiO PrTiO SrO08 NiO LaTiO SrO
PrNiO /SrTiO (001) LaNiO /SrTiO (001)CaCuO /SrTiO (001) TiO SrO CuO Ca SrCuO /SrTiO (001) TiO SrO CuO Sr Energy (eV)0 1 2 3-4 -3 -2 -1 Energy (eV)0 1 2 3-4 -3 -2 -1
Oxygen d xy t d depleted d xy t d z + d xy (a) (b)(c) (d) L a y e r - r e s o l v e d d e n s i t y o f s t a t e s ( S t a t e s / e V ) L a y e r - r e s o l v e d d e n s i t y o f s t a t e s ( S t a t e s / e V ) L a y e r - r e s o l v e d d e n s i t y o f s t a t e s ( S t a t e s / e V ) Figure 2. The layer-resolved densities of states of the different AB O /STO (001) systems (cf. Fig. 1) show the q2DEG formation at theinterface due to the occupation of Ti d conduction band states. The band bending in the substrate due to polarity mismatch is more pronouncedfor nickelate films than for cuprate films (particularly for the valence band), whereas the emergent electric field in the films is approximatelytwice as strong in the cuprate films than in the nickelate films (as schematically indicated by red dashed lines; cf. Fig. 3). The distributionof the electron density (integrated from − . eV to E F ) visualizes the occupation of Ti d states that varies with the film composition (beingless pronounced for cuprate films), the orbital order at the Ti sites, and the presence (absence) of a hybrid d z interface state for nickelate(cuprate) films. The absence of electron density in the rare-earth layers (at the rare-earth sites and the corresponding apical oxygen vacancysites) highlights the 2D cuprate-like electronic structure emerging in the nickelate films. experiences tensile strain (Table I). Nevertheless, we observea vertical expansion in all films, as reflected in the apical A -site distances ∆ z A shown in Fig. 1(b). This expansion is notuniform, but increases continuously from the interface to thesurface. In particular directly at the interface, the distancesare enhanced; this result can be associated with the electro-static doping due to the polarity of the films, similar to thepreviously observed enhanced La-Sr distance across the n -type LaNiO /STO(001) interface ( ∼ . Å) [35, 52, 53]. TheSrCuO case highlights that this expansion at the interface isnot exclusively related to a chemical variation at the A site;surprisingly, the effect is even strongest in this system. No-tably, for cuprate films this ∆ z A expansion extends severallayers into the substrate, which is clearly not the case for thenickelate systems that show an abrupt transition to bulklikeapical Sr-Sr distances in STO. We find that PBE and PBEsolprovide qualitatively similar structural properties (Fig. 1). Thesmall intrinsic octahedral rotations of STO are removed nearthe interface, with the exception of the CaCuO film, and the B O squares in the infinite-layer films show almost no rota-tions around the c axis [Fig. 1(a)]. The cation-anion B -O displacements ∆ z B = z B − z O shown in Fig. 1(c) reveal a surface buckling in each case,whereas buckling at the interface (in the opposite direction)occurs exclusively for the nickelate systems. This indicatesthat the bucking is primarily impacted by the B -site element.In contrast, the distance between the surface B O layer andthe subsurface A layer, which is considerably contracted ineach case, correlates also with the ionic radius of the A siteelement [Fig. 1(a)].In the STO substrate, substantial ferroelectric-like displace-ments ∆ z B arise that are qualitatively similar for all consid-ered systems [Fig. 1(c)]. For NdNiO /STO(001), such dis-placements were shown to be indicative of the q2DEG forma-tion [19]. A fit to ∆ z B = ˜ z · exp( − d/ ˜ d ) renders the valuesgiven in Table I. Here, ˜ d provides insight how deep the elec-tronic reconstruction influences the ionic geometry in the STOsubstrate, which is larger for cuprate films than for nickelatefilms. In contrast, the maximal displacement ˜ z is ∼ . Ålarger in the nickelate cases. From these results, we esti-mate experimentally resolvable displacements (i.e., . Å > ∆ z B > . Å) in the topmost – Å of the STO substrate. Γ X M
Γ Γ
X M
Γ Γ
X M
Γ Γ
X M
Γ Γ
X M
Γ Γ
X M
Γ Γ
X M Γ P r N i O / S r T i O ( ) S d xy d z Ni Ti Ni Ni Ni Ti Ti Ti Ti d xz d yz Γ X M
Γ Γ
X M Γ (1/eV) d x -y d z , t S − S − S − S − S − S − S − S − d xy Ni d x -y Γ X M Γ -2-1.5-1-0.500.511.52 E n e r g y ( e V ) Bulk d z L a N i O / S r T i O ( ) C a C u O / S r T i O ( ) -2-1.5-1-0.500.511.52 E n e r g y ( e V ) -2-1.5-1-0.500.511.52 E n e r g y ( e V ) -2-1.5-1-0.500.511.52 E n e r g y ( e V ) S r C u O / S r T i O ( ) PrNiO LaNiO CaCuO SrCuO Cu Ti Cu Cu Cu Ti Ti Ti Ti Cu d xy d z d xy d xy Sur-face Inter-face
Figure 3. Band structure [ (cid:126)k -resolved densities of states, projected on Ni, Cu, and Ti d orbitals in different layers (from left to right)] of theconsidered AB O /STO (001) systems (cf. Fig. 1). Corresponding bulk panels are provided for comparison. The orbital characters are denoted.The figure highlights the emergent q2DEG due to occupation of dispersive interfacial Ti d states in the STO substrate (predominantly d xy states) and the modulation of the Ni/Cu d x − y states throughout the infinite-layer films. Exclusively for the nickelate films, an interfacestate can be observed that exhibits a hybrid rare-earth d z –Ni d z –Ti d z character. The finite displacements ∆ z B are also reflected in the dispro-portionation of the apical Ti-O bond lengths, which oscillatestrongly around the bulk value ( . Å) in Fig. 1(d).
IV. ELECTRONIC RECONSTRUCTION: CORRELATEDq2DEG FORMATION AND CUPRATE-LIKE FERMISURFACES
We now explore the implications of the polar disconti-nuities at the interface and the surface on the electronicstructure. As already suggested by the ionic relaxationsnear the interface [Fig. 1(c)], we find q2DEGs to emerge in the substrate for each case (Fig. 2), as reported earlierfor NdNiO /STO (001) [19]. All four ( AB O ) /STO (001) systems show a strong Ti d occupation at the interface, instark contrast with the paradigmatic (LAO) /STO(001) sys-tem which is just at the verge of a metal-insulator transi-tion [23]. Near the interface, each q2DEG is formed predomi-nantly by dispersive Ti d xy states, as observable in the layer-resolved band structures compiled in Fig. 3. This goes hand inhand with the ferroelectric-like Ti displacements [Figs. 1(c,d)]and resembles the situation in LAO/STO(001) [54, 55]. Theorbital order, which is also visible in the distribution of theelectron density (Fig. 2), persists within the topmost threelayers and then develops into a uniform occupation of the Table II. Band bending in the different AB O /STO (001) systems. The band energies (cid:15) are given relative to the Fermi energy and refer to the Γ point, where they are minimal (cf. Fig. 3). ∆ (cid:15) denotes the band bending experienced by the planar d x − y orbitals throughout the filmfrom the interface ( S − ) to the surface ( S ). We divide by the film thickness d Film (cf. Table I) to normalize. The interfacial Ti d xy energies( S − ) reflect how pronounced the emerging q2DEG is. The presence of a partially occupied rare-earth d z –Ni d z hybrid state in the bulk(the electron pocket at the Γ point), admixed with Ti d z in film geometry, distinguishes nickelates from cuprates (cf. Figs. 3 and 4).NdNiO [19] PrNiO LaNiO CaCuO SrCuO (cid:15) Ni/Cu d x − y in the bulk (eV) − . − . − . − . − . (cid:15) Ni/Cu d x − y in S (eV) − . − . − . − . − . (cid:15) Ni/Cu d x − y in S − (eV) − . − . − . − . − . (cid:15) Ni/Cu d x − y (eV) .
76 0 .
78 0 .
81 1 .
59 1 . (cid:15) Ni/Cu d x − y /d Film (meV / Å)
56 57 58 118 96 (cid:15) Ti d xy in S − (eV) − . − . − . − . − . (cid:15) d hybrid state in the bulk (eV) − . − . − . — — (cid:15) d hybrid state at the interface (eV) − . − . − . — — t g manifold. Notably, the infinite-layer compounds exhibita quite covalent nature in the B O layers, as reflected in thedistribution of the electron density (Fig. 2), while the Ti statesin the substrate are far more localized. Γ X M
Γ Γ
X M
Γ Γ
X M
Γ Γ
X M Γ P r N i O / S r T i O ( ) Pr Pr Pr Pr Pr Γ X M Γ -2-1.5-1-0.500.511.52 E n e r g y ( e V ) L a N i O / S r T i O ( ) -2-1.5-1-0.500.511.52 E n e r g y ( e V ) LaNiO La La La La La PrNiO N d N i O / S r T i O ( ) S Nd Nd Nd Nd (1/eV) S − S − S − d z -2-1.5-1-0.500.511.52 E n e r g y ( e V ) Bulk d z NdNiO (a) (b) Figure 4. (a) The rare-earth d states, which hole-dope theNiO layers in bulk NdNiO , PrNiO , and LaNiO due to elec-tron pockets (for instance, at the Γ point), (b) contribute to theFermi surface of NdNiO /STO (001) [19], PrNiO /STO (001) , andLaNiO /STO (001) only directly at the interface in the form of a hy-brid state. In the cuprates, the respective d states are located athigher energies [13]. Surprisingly, the q2DEG formation in STO (001) occurs de-spite the metallic character of the films that could screen thepolarity mismatch at the interface. Specifically, for a reducedpolarity mismatch at the interface, as present for instance inmetallic NdNiO /STO (001) with a (NdO) / (TiO ) inter-face stacking, no q2DEG forms [19].We find that the film composition tunes the manifestationof the q2DEG, reflected in the different band bending (localelectrostatic modification of the energy eigenvalues) of theTi d xy orbital, which we quantify in Table II. It is largestfor NdNiO [19] and PrNiO films ( − . and − . eV)and half as strong for SrCuO and CaCuO ( − . and − . eV), which is in line with the lower formal polaritymismatch in the cuprate case. The distinct band bending ofthe STO valence states observable in Fig. 2 indicates differ-ent band offsets of the present infinite-layer nickelates vs.cuprates.It is so far unresolved why NdNiO /STO (001) [1, 2]and PrNiO /STO (001) [3] exhibit superconductivity, whereassuch a phase is absent in LaNiO /STO (001) [1] despite a sim-ilar electronic structure of all three infinite-layer nickelatesin the bulk. Magnetic interactions with the rare-earth d/ f electrons have been suggested to possibly enter the mecha-nism [6, 18]. However, superconductivity could not be con-firmed experimentally in Sr-doped bulk NdNiO [17], whichraised a question about the role of the interface and the filmgeometry [19]. If we speculate that superconductivity is me-diated by the q2DEG, as it is the case in LAO/STO (001) [24],this would require notable differences in the q2DEG forNdNiO and PrNiO vs. LaNiO . Indeed, we observe thatthe Ti d xy band bending is about - larger for PrNiO and NdNiO than for LaNiO (Table II, Fig. 3). The dis-tinct carrier concentration implied by these differences in elec-trostatic doping could drive the system out of the supercon-ducting dome [2]. Further possible reasons for the absenceof superconductivity in LaNiO /STO (001) are an inhibitedq2DEG formation owing to incomplete reduction of the initialperovskite nickelate films in experiment [1], as predicted forNdNiO /STO (001) [19], or hydrogen intercalation followingthe topotactic reduction reaction [11].In bulk infinite-layer cuprates, a single hole occupies the PrNiO /SrTiO (001) LaNiO /SrTiO (001) CaCuO /SrTiO (001) SrCuO /SrTiO (001) B u l k L a N i O B u l k C a C u O B u l k S r C u O B u l k P r N i O Pr 5 d pockets Ni/Cu 3 d x -y Ti 3 d xy Ti 3 d xz/yz IF hybrid state X Γ M Figure 5. Fermi surfaces of AB O /STO (001) and the corresponding infinite-layer bulk compounds in comparable √ × √ cells. Particularlyfor the nickelate films, the Fermi surfaces are strongly reconstructed with respect to the bulk, owing to the depletion of the rare-earth d statesvisible as pockets around the Γ and Z points (cf. Fig. 4), which considerably enhances the similarity to cuprates. The remaining differenceconsists predominantly of the hybrid interface state. The illustration in the center disentangles the distinct contributions to the complex Fermisurface. The repetition of sheets associated with the Ti t g or the Ni/Cu d x − y states reflects the electrostatic modulation. planar Cu d x − y orbital [9, 13]. The situation is modi-fied in bulk nickelates due to two self-doping electron pockets(at the Γ and the A point, the latter corresponding to the Z point in the present geometry) that exhibit rare-earth d char-acter [Figs. 3 and 4(a)] [4, 5, 7–9, 13, 18]. In film geome-try, the Ni and Cu d z orbital remains completely occupied,while electrostatic doping induces a layer-wise modulation ofthe d x − y orbital occupation (Fig. 3; cf. Fig. 8 in the Ap-pendix). This is reflected in the band energies (cid:15) shown in Ta-ble II. The magnitude of the modulation throughout the film isexpressed by the difference of these band energies ∆ (cid:15) . Coun-terintuitively, it turns out to be approximately twice as strongin the cuprate films ( . , . eV) than in the nickelate films( . , . , . eV), even if normalized to the film thicknessand despite the higher polarity mismatch at the surface and theinterface in the nickelate case (Table II, Figs. 2 and 3).The involvement of the Nd d states in the Fermi surfaceand the superconductivity mechanism of NdNiO is currentlyintensely discussed [6, 14, 15]. In the bulk, the rare-earth d electron pocket around the Γ point is smaller for LaNiO than for PrNiO and NdNiO , and the states extend down to − . eV ( − . and − . eV) below the Fermi energy inthe former (latter) case [Table II, Fig. 4(a)]. In film geometry,however, we find the rare-earth d states to be almost entirelydepleted in all nickelate systems [Fig. 4(b)]. Exclusively atthe interface, they hybridize with Ni and particularly Ti d z orbitals, which enhances their band bending below the Fermienergy. Surprisingly, this effect is stronger for LaNiO films(bent down to − . eV) than for PrNiO and NdNiO films(bent down to − . and − . eV; Table II). We speculatethat the resulting interface state partially compensates the po-lar discontinuity at the interface for the nickelate films andthereby reduces the electrostatic modulation ∆ (cid:15) experiencedby the planar d x − y orbitals relative to the cuprate films (Ta-ble II).The Fermi surfaces of the different AB O /STO (001) sys-tems shown in Fig. 5 demonstrate how the electronic recon-struction enhances the similarity of nickelates and cuprates,owing to the depletion of the two rare-earth d electron pock- ets in the nickelate films. The remaining differences arelargely of quantitative nature and arise due to variations inthe q2DEG in the topmost STO(001) layers and the distinctdegree of modulation of the planar Ni and Cu d x − y or-bitals. As illustrated in Fig. 5, the four-pointed-star-shapedFermi surface sheets centered at the Γ point reflect the q2DEGemerging in the STO conduction band, specifically the Ti d xz/yz orbitals that cross the Fermi energy at a few layersdistance to the interface, whereas the Ti d xy orbitals give riseto circular sheets that are also centered at the Γ point [56, 57].The splitting of the Ti d xy and d xz/yz orbitals is inducedby the electrostatic doping and ionic relaxations at the inter-face. In the case of rare-earth nickelate films, the d z hybridinterface state is represented by a large circular sheet centeredat the Γ point, whereas the d electron pockets are empty andthus absent. The features at the Brillouin zone boundary arecontributed by the planar Ni and Cu d x − y orbitals.We complete the discussion of the polarity-driven elec-tronic reconstruction by contrasting the layer- and site-resolved charge differences as they arise for infinite-layernickelates vs. cuprates in film geometry with respect to thecorresponding bulk systems (Fig. 6). Both representative sys-tems PrNiO /STO (001) and CaCuO /STO (001) show a de-pletion of electrons near the surface and a concomitant accu-mulation in the interfacial Ti layers, which constitutes the cor-related q2DEG and rapidly decays into the substrate. The de-cay is paralleled by the decreasing ferroelectric-like displace-ments of the Ti ions reported above [Fig. 1(c)]. While theNi sites show a loss of electrons throughout the film, the Cusites exhibit a loss exclusively near the surface and a slightgain near the interface. Interestingly, the oxygen sublatticeresponds highly differently to the polar discontinuity in nick-elate vs. cuprate films: In the nickelate case, the oxygen siteslargely gain charge as opposed to the Ni sites, i.e., some elec-trons are transferred from Ni to oxygen within each NiO layer. In the cuprate case, the oxygen sites parallel the be-havior observed at the Cu sites, so that charge is redistributedexclusively between B O layers. This highlights the differ-ent degree of B d -O p hybridization in the two materials -0.3-0.2-0.100.10.20.3 PrNiO /SrTiO (001) C h a r g e d i ff . w r t . bu l k ( e − ) Nickelate Titanate
S S − S − S S − S − /SrTiO (001)Cuprate TitanateCu2×OTiInterface Interface Figure 6. Layer-resolved charge difference in the representative sys-tems PrNiO /STO (001) vs. CaCuO /STO (001) relative to the con-stituent bulk compounds, integrated at the Ni and Cu sites (darkblue), Ti sites (light blue), and in the corresponding basal oxygensublattice (red). The highly distinct response of the latter in nicke-lates vs. cuprates reveals an intra-layer charge transfer in the nicke-lates in addition to the common charge transfer from the surface tothe interface. classes. In the substrate, the oxygen sites always gain charge,particularly for CaCuO . The loss at the surface is roughlytwice as strong for CaCuO as for PrNiO , consistent with themuch larger electrostatic modulation (Table II, Figs. 2 and 3).Hence, we conclude that the charge redistribution in the sys-tems is not simply proportional to the formal polarity mis-match between the infinite-layer film and the nonpolar sub-strate, but unravels a complex interplay of the emergent inter-face electronic structure and the screening characteristics ofthe film. V. ROLE OF THE SUBSTRATE: NdNiO /NdGaO (001) While most experiments on superconducting infinite-layernickelates have been conducted on nonpolar STO (001) so far,further insight into the superconductivity mechanism couldbe gained by exchanging STO with a typical insulating sub-strate with naturally alternating formal charge of the consec-utive pseudocubic (001) layers, for instance, LaGaO (pseu-docubic lattice constant: . Å) or NdGaO ( . Å). Thedegree of compressive strain induced by these substrates iscomparable to that exerted by STO ( . Å), whereas thelattice constants of typical aluminates such as LAO ( . Å)are considerably smaller. Exemplarily, Fig. 7(a) shows theoptimized geometry and layer-resolved electronic structureof NdNiO /NdGaO (001) . In this system, the interfaceNd layer is closer in formal charge to the (NdO) lay-ers in the substrate, in contrast to the (SrO) layers in aSTO substrate. Hence, while the formal polarity mismatchat the Nd /(GaO ) − interface is even higher than at theSTO (001) interface, the infinite-layer film shows a com-parable electrostatic modulation. In contrast to STO, theNdGaO substrate exhibits strong a − a − c + octahedral ro-tations that induce modest c − rotations the NiO plaque-ttes near the interface. NiO buckling is observed exclu-sively at the surface, at variance with the nickelate films L a y e r - r e s o l v e d d e n s i t y o f s t a t e s ( S t a t e s / e V )
08 NiO NdGaO ×5 NdNiO /NdGaO (001)Energy (eV)0 1 2 3-4 -3 -2 -1 Ga ×5×5×5NdO NiNdOEnergy (eV)0 1 2 3-2 -1
NdONd
NdNiO /NdNiO /NdGaO (001)(a)(b) ×5×5×5×5 L a y e r - r e s o l v e d d e n s i t y o f s t a t e s ( S t a t e s / e V ) Figure 7. (a) In NdNiO /NdGaO (001) , the completely filled Ga d shell of the substrate leads to physics fundamentally different fromNdNiO /SrTiO (001) [19], characterized by the absence of the inter-facial q2DEG, but retaining the depleted Nd d states in the infinite-layer film. In the layer-resolved density of states, the GaO conduc-tion band states have been enhanced for better visibility. (b) In thecase of an oxidized interface layer, the band alignment changes from n - to p -type, at variance with NdNiO /SrTiO (001) which is always n -type [19]. grown on the STO (001) substrate (cf. Fig. 1). The com-pletely filled Ga d shell of the substrate leads to funda-mentally different behavior from NdNiO /SrTiO (001) [19],characterized by a quenched q2DEG, but retaining the de-pleted Nd d states, i.e., a cuprate-like electronic structure inthe nickelate film. The Fermi energy is located ∼ . eVbelow the conduction band of NdGaO , resulting in an n -type electronic structure. In the case of an oxidized inter-face layer [formally (NdNiO ) /(NdNiO ) /NdGaO (001) ,Fig. 7(b)], the band alignment changes from n - to p -type,and the Fermi energy is now located ∼ . eV above thevalence band of NdGaO . This situation is in sharp con-trast to NdNiO /SrTiO (001) with oxidized interface layer,which is n -type [19]. The oxygen vacancy formation energy Table III. Emergence of interfacial q2DEGs for different perovskiteand infinite-layer films on STO (001) and NdGaO (001) as a func-tion of the formal polarity mismatch at the interface.System Interface polarity q2DEGLaAlO /SrTiO (001) [22, 23] / yesNdNiO /SrTiO (001) [19] / noCaCuO /SrTiO (001) 2+ / yesSrCuO /SrTiO (001) 2+ / yesNdNiO /SrTiO (001) [19] / yesPrNiO /SrTiO (001) 3+ / yesLaNiO /SrTiO (001) 3+ / yesNdNiO /NdGaO (001) 3+ / − no E f = E Nd/GaO interface − E NdO/GaO interface + E O (oxygen-rich limit) amounts to . eV and is hence lower than inNdNiO /SrTiO (001) ( . eV [19]), which may facilitate acomplete reduction of the nickelate film during the topotacticreaction.Table III compiles results for the q2DEG formation in dif-ferent perovskite and infinite-layer systems (at 4 ML filmthickness) as a function of the formal polarity mismatch atthe interface and puts them into an interesting context. In theparadigmatic band insulator system LAO/STO (001) , a polar-ity mismatch of / is sufficient to drive the emergence ofa q2DEG. In contrast, NdNiO /STO (001) does not developa q2DEG despite having equal interface polarity, owing tometallic screening in the film. The further increased inter-face polarity in the infinite-layer cuprates ( / ) and nicke-lates ( / ) on STO (001) leads to the emergence of a verypronounced q2DEG despite the metallic screening present inparticular in the nickelates. Replacing the nonpolar STO sub-strate with polar NdGaO quenches the q2DEG entirely dueto the closed Ga d shell. VI. SUMMARY
The impact of interface polarity on the structuraland electronic properties of PrNiO /SrTiO (001),LaNiO /SrTiO (001), CaCuO /SrTiO (001), andSrCuO /SrTiO (001) was investigated by performingfirst-principles calculations in film geometry including aCoulomb repulsion term. Similar to NdNiO /SrTiO (001),polar discontinuity drives the emergence of a quasi-two-dimensional electron gas (q2DEG) at the interface in all casesdue to the occupation of the Ti d conduction band that isaccompanied by substantial ferroelectric-like displacementsof the Ti ions. Despite their comparable electronic structurein the bulk, the higher polarity mismatch at the interfaceof infinite-layer nickelates vs. cuprates to the nonpolarSrTiO (001) substrate enhances the q2DEG carrier density for the nickelate films. In addition, we found a strongdependence of the carrier density on the rare-earth ion in thenickelate films, being larger for PrNiO and NdNiO thanfor LaNiO . This difference in carrier density could affectthe superconducting properties of the q2DEG itself. On theother hand, the depletion of the self-doping rare-earth d states enhances the similarity of nickelate and cuprate Fermisurfaces in film geometry, except for a d - d hybrid interfacestate present for nickelates. The resulting single hole in theNi and Cu d x − y orbitals is modulated throughout theinfinite-layer films due to electrostatic doping, which turnsout to be twice as strong in cuprates as in nickelates, contraryto expectations from the formal polarity mismatch. Theseresults highlight similarities, but also fundamental differ-ences between infinite-layer nickelates and cuprates, andprovide clues as to why nickelate superconductivity is so farexclusively observed in film geometry. Finally, we exploredNdNiO films grown on a polar NdGaO (001) substrate,and showed that no q2DEG emerges at the interface, whilesimultaneously the Nd d states in the film are depleted. Thispromotes NdGaO (001) as interesting substrate that mayprovide deeper insight into the superconductivity mechanismin infinite-layer nickelates. VII. ACKNOWLEDGMENTS
This work was supported by the German Research Foun-dation (Deutsche Forschungsgemeinschaft, DFG) within theSFB/TRR 80 (Projektnummer 107745057), Project No. G3.Computing time was granted by the Center for ComputationalSciences and Simulation of the University of Duisburg-Essen(DFG Grants No. INST 20876/209-1 FUGG and No. INST20876/243-1 FUGG) and by the Leibniz-Rechenzentrum,Garching bei München (Grant No. pr87ro).
Appendix: Orbital contributions to the electronic structure
In order to disentangle the different orbital contributionsto the electronic structure shown in Fig. 3, Fig. 8 dis-plays a selection of orbital- and layer-resolved band struc-tures for the representative systems PrNiO /STO (001) andCaCuO /STO (001) . Similar to the bulk, the Ni and Cu d z and t g states (exemplarily, the d xy orbitals are shown) arecompletely occupied in both nickelate and cuprate films. Theresulting single hole in the Ni and Cu d x − y orbitals is mod-ulated throughout the infinite-layer films due to electrostaticdoping. The hybrid interface state formed by Ni d z , Ti d z ,and the rare-earth d z states appears exclusively for nickelatefilms. At the interface, the emerging q2DEG is constitutedpredominantly by Ti d xy states. [1] D. Li, K. Lee, B. Y. Wang, M. Osada, S. Crossley, H. R. Lee,Y. Cui, Y. Hikita, and H. Y. Hwang, Superconductivity in an infinite-layer nickelate, Nature , 624 (2019). -2-1.5-1-0.500.511.52Sur-face Inter-face S S − S − S − (1/eV) -2-1.5-1-0.500.511.52-2-1.5-1-0.500.511.52 d z d x - y d xy Cu TiCu Ti E n e r g y ( e V ) E n e r g y ( e V ) E n e r g y ( e V ) Γ X M
Γ Γ
X M
Γ Γ
X M
Γ Γ
X M Γ CaCuO /SrTiO (001)PrNiO /SrTiO (001)-2-1.5-1-0.500.511.52Sur-face Inter-face S S − S − S − (1/eV) -2-1.5-1-0.500.511.52-2-1.5-1-0.500.511.52 d z d x - y d xy Ni TiNi Ti E n e r g y ( e V ) E n e r g y ( e V ) E n e r g y ( e V ) Γ X M
Γ Γ
X M
Γ Γ
X M
Γ Γ
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