Electronic structure, self-doping, and superconducting instability in the alternating single-layer trilayer stacking nickelates ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}

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Electronic structure, self-doping, and superconducting instability in the alternating single-layer trilayer stacking nickelates ${La}_{3} {Ni}_{2} O_{7}$

Yang Zhang, Ling-Fang Lin, Adriana Moreo, Thomas A. Maier, and Elbio Dagotto

Phys. Rev. B 110, L060510 – Published 14 August 2024

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$Electronic structure, self-doping, and superconducting instability in the alternating single-layer trilayer stacking nickelates ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ (1)$

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$Electronic structure, self-doping, and superconducting instability in the alternating single-layer trilayer stacking nickelates ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ (2)$

Abstract

Motivated by the recently proposed alternating single-layer trilayer stacking structure for the nickelate ${La}_{3} {Ni}_{2} O_{7}$ , we comprehensively study this system using ab initio and random-phase approximation techniques. Our analysis unveils similarities between this novel ${La}_{3} {Ni}_{2} O_{7}$ structure and other Ruddlesden-Popper nickelate superconductors, such as a similar charge-transfer gap value and orbital-selective behavior of the $e_{g}$ orbitals. Pressure primarily increases the bandwidths of the Ni $e_{g}$ bands, suggesting an enhancement of the itinerant properties of those $e_{g}$ states. By changing the cell volume ratio $V / V_{0}$ from 0.9 to 1.10, we found that the bilayer structure in ${La}_{3} {Ni}_{2} O_{7}$ always has lower energy than the single-layer trilayer stacking ${La}_{3} {Ni}_{2} O_{7}$ . In addition, we observe a “self-doping” effect (compared to the average 1.5 electrons per $e_{g}$ orbital per site of the entire structure) from the trilayer to the single-layer sublattices and this effect will be enhanced by overall electron doping. Moreover, we find a leading $d_{x^{2} - y^{2}}$ -wave pairing state that is restricted to the single layer. Because the effective coupling between the single layers is very weak, due to the nonsuperconducting trilayer in-between, this suggests that the superconducting transition temperature $T_{c}$ in this structure should be much lower than in the bilayer structure.

$Electronic structure, self-doping, and superconducting instability in the alternating single-layer trilayer stacking nickelates ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ (3)$
$Electronic structure, self-doping, and superconducting instability in the alternating single-layer trilayer stacking nickelates ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ (4)$
$Electronic structure, self-doping, and superconducting instability in the alternating single-layer trilayer stacking nickelates ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ (5)$
$Electronic structure, self-doping, and superconducting instability in the alternating single-layer trilayer stacking nickelates ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ (6)$

Received 24 April 2024
Revised 15 July 2024
Accepted 31 July 2024

DOI:https://doi.org/10.1103/PhysRevB.110.L060510

Physics Subject Headings (PhySH)

Research Areas

Multiband superconductivityPairing mechanismsSuperconductivity

Physical Systems

High-temperature superconductorsNickelates

Techniques

Electron-correlation calculationsFirst-principles calculationsHubbard modelRandom phase approximationWannier function methods

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yang Zhang¹, Ling-Fang Lin¹, Adriana Moreo^1,2, Thomas A. Maier³, and Elbio Dagotto^1,2

¹Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
²Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
³Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

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Vol. 110, Iss. 6 — 1 August 2024

$Electronic structure, self-doping, and superconducting instability in the alternating single-layer trilayer stacking nickelates ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ (7)$

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$Electronic structure, self-doping, and superconducting instability in the alternating single-layer trilayer stacking nickelates ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ (8)$

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$Electronic structure, self-doping, and superconducting instability in the alternating single-layer trilayer stacking nickelates ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ (11)$

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$Electronic structure, self-doping, and superconducting instability in the alternating single-layer trilayer stacking nickelates ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ (12)$
Figure 1
(a)Schematic crystal structure of the conventional cells of the high-pressure $F m m m$ phase of 327-LNO (BL) and $P 4 / m m m$ phase of 327-LNO (SL-TL), respectively (green = La; gray = Ni; red = O). All crystal structures were visualized using the vesta code [59]. (b)Sketches of electronic states in the BL and SL-TL. The light blue (pink) horizontal lines represent $d_{3 z^{2} - r^{2}}$ ( $d_{x^{2} - y^{2}}$ ) states. The solid and open circles represent 1.0 and 0.5 electrons, respectively. The total population of $e_{g}$ electrons considered is $n = 3.0$ and 6.0 electrons, for BL with two sites and SL-TL with four sites, respectively. (c)The Ni $e_{g}$ orbitals projected band structures and density of states. The $d_{3 z^{2} - r^{2}}$ and $d_{x^{2} - y^{2}}$ orbitals are distinguished by the blue and red lines. (d)FS for the nonmagnetic state of the high-pressure $P 4 / m m m$ phase of the 327-LNO (SL-TL) structure at 16GPa. Note that the local $z$ axis is perpendicular to the ${NiO}_{6}$ plane towards the top O atom, while the local $x$ or $y$ axis is along the in-plane Ni-O bond directions.
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$Electronic structure, self-doping, and superconducting instability in the alternating single-layer trilayer stacking nickelates ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ (13)$
Figure 2
(a)Calculated energies of different structural phases of 327-LNO (SL-TL) and 327-LNO (BL), as a function of the ratio $V / V_{0}$ . Here, $V_{0}$ is the conventional-cell volume of the $P 4 / m m m$ phase of 327-LNO (SL-TL) at 16GPa. The $P 4 / m m m$ phase of 327-LNO (SL-TL) is taken as the energy of reference. (b), (c)The Ni $e_{g}$ orbitals projected band structure for the (b) $C m m m$ and (c) $F m m m$ phases, respectively.
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$Electronic structure, self-doping, and superconducting instability in the alternating single-layer trilayer stacking nickelates ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ (14)$
Figure 3
(a)Tight-binding band structure and (b)FS for the $P 4 / m m m$ phase of 327-LNO (SL-TL) at 16GPa. Here, an eight-band $e_{g}$ -orbital tight-binding model was considered including SL and TL hoppings (see the hopping file in the Supplemental Material [63]) with an overall filling of $n = 6$ (i.e., 1.5 electrons per site). (c)Crude sketches of the crystal-field splitting of the $e_{g}$ orbitals for different Ni sites. All the values are given in units of eV. (d)The total electron occupations and (e) different electronic densities of the $e_{g}$ orbitals for the different Ni sites vs the overall filling $n$ in the tight-binding model. The red line in (d)represents the average electronic Ni site occupancy.
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$Electronic structure, self-doping, and superconducting instability in the alternating single-layer trilayer stacking nickelates ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ (15)$
Figure 4
The RPA calculated leading superconducting singlet gap structure $g_{α} (k)$ for momenta $k$ on the FS of 327-LNO (SL-TL) at $n = 6.0$ and their pairing strength $λ$ : (a)Leading $d_{x^{2} - y^{2}}$ -wave state with $λ = 0.152$ , (b)subleading $d_{x y}$ -wave state with $λ = 0.112$ , (c) $g$ -wave state with $λ = 0.102$ . The sign of the gap structure $g_{α} (k)$ is indicated by the colors (orange = positive, blue = negative), and the gap amplitude by the point size. The RPA calculations used Coulomb interaction parameters $U = 0.5$ (intraorbital), $U^{'} = U / 2$ (interorbital), and $J = J^{'} = U / 4$ (Hund coupling and pair hopping, respectively) in units of eV. The hopping parameters are available in the Supplemental Material [63]. The dominant character of the Fermi-surface Bloch states arising from the SL (magenta) and TL (cyan) sublattices is shown in (d).
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