Compressive Strain Turns $s^{\pm}$ into $d$-Wave Pairing in One-unit-cell La$_3$Ni$_2$O$_7$ Thin Film Via Substrate-Induced Hole Doping

Abstract

Motivated by recent reports of ambient-pressure superconductivity in La$_3$Ni$_2$O$_7$ films grown on LaSrAlO$_4$, we investigate the superconducting instability in a one-unit cell thin film using {\it ab initio} and random-phase approximation techniques. Compared to the high-pressure bulk system, the ratio of inter-layer $d_{3z^2-r^2}$ hopping to intra-layer $d_{x^2-y^2}$ hopping is suppressed in the 1UC thin film, and the crystal-field splitting of the $e_g$ orbitals is increased. Our calculation indicates that spin-fluctuation-driven pairing correlations are weak for the stoichiometric case at ambient pressure, but increase significantly under hole doping. The leading pairing symmetry is also found to change by hole doping. Specifically, we obtain a leading $d_{x^2-y^2}$ pairing state at moderate hole doping, followed by a $d_{xy}$ state at higher doping. These states are driven by intra-band spin-fluctuation scattering {\it within} the $γ$ hole pocket centered around the M point, and arise primarily from states in the Ni layer {\it farther} from the substrate. These results strongly suggest that the thin-film superconducting samples are hole-doped and that pairing in this system predominantly arises in the layer, as opposed to the inter-layer pairing in the pressurized bulk system.

Figures (5)

• Figure 1: (a) Schematic of lattice modifications under the high-pressure and in-plane compressive-strain thin-film conditions. (c-d) Sketches of the Fermi surfaces for the high-pressure and compressive strain for hole-doping thin-films, including the signs of the superconducting order parameter. (c) is $s^{\pm}$ and (d) is $d_{x^2-y^2}$. The light pink dots in (d) denote nodes.
• Figure 2: (a) Schematic structural slab model and crystal structure (green = La; gray =Ni; red = O) of the 1UC thin film, with two BL blocks (four Ni layers) visualized via the VESTA code Momma:vesta. Note that the local $z$-axis is perpendicular to the NiO$_6$ plane toward the top O atom, while the local $x$ or $y$ axis is along the in-plane Ni-O bond directions. The in-plane lattice constants are fixed to those of the LSAO substrate ($a = b = 3.7557$ Å), and a vacuum layer of more than 20.0 Å is used to simulate the thin-film slab geometry. (b) Projected band structures for the 1UC thin film. The electronic structures are calculated within the local density approximation plus Hubbard $U$ and Hund’s coupling $J$ with the Liechtenstein formulation for the double-counting term Liechtenstein:prb. Here we use $U = 3.8$ eV and $J = 0.6$ eV, values obtained from the constrained random-phase approximation for La$_3$Ni$_2$O$_7$Christiansson:arxiv. (c-e) Tight-binding band structure and Fermi surface for the one BL (two Ni layers) model for the thin-film at (c-d) with $n = 3$, and (e) with $n = 2.8$, respectively. The hopping file can be found in the SM Supplemental.
• Figure 3: (a) The RPA calculated pairing strength $\lambda$ for different instability channels vs. electron density fillings in the compressive-strain BL model. (b,d) The RPA calculated leading superconducting singlet gap structures $g_\alpha({\bf k})$ for momenta ${\bf k}$ on the Fermi surfaces for $d_{x^2-y^2}$-wave and $d_{xy}$-wave with corresponding pairing strengths $\lambda$ for the case of the LSAO substrate at (b) $n = 2.75$ and (d) $n = 2.5$, respectively. (c) Gap structure in orbital space for $n = 2.75$ with the indexing: 1 = $d_{3z^2-r^2}$ orbitals from layer 1 (Ni1), 2 = $d_{x^2-y^2}$ orbitals from layer 1 (Ni1), 3 = $d_{3z^2-r^2}$ orbitals from layer 2 (Ni2), and 4 = $d_{x^2-y^2}$ orbitals from layer 2 (Ni2). The sign of $g_\alpha({\bf k})$ is indicated by colors (red = positive, blue = negative), and its amplitude by the color intensity. Here, we used Coulomb parameters $U=0.7$ eV RPA-U, with the ratios $U'=U/2$, and $J=J'=U/4$ already employed in previous literature Zhang:nc24Zhang:prb23-2. The calculation was performed at $T = 0.01$ eV.
• Figure 4: (a-b) The RPA calculated static spin susceptibility $\chi'({\bf q}, \omega=0)$ vs. $q_x$ and $q_y$ for the two-orbital 1BL model for $n=2.75$ and $n = 2.5$ respectively, and its orbital and layer contributions. (c) Spin patterns in real space for ${\bf q}$ = $(\pi/3, \pi/3)$ using a $6\times6$ cluster ($\pi/3$ is used instead of 0.35 for proper fit in the cluster), while a more detailed analysis for ${\bf q}$ = $(0.35\pi, 0.35\pi)$ and ${\bf q}$ = $(0.3\pi, 0.3\pi)$ is in the SM Supplemental. Dashed lines represent the waveforms along the two directions. (d) The layer contributions (Ni1: NiO$_2$ layer 1, Ni2: layer 2) to the Fermi-surface Bloch states for $n = 2.75$.
• Figure 5: (a) Tight-binding band structures of the thick film grown on an LSAO substrate, and (b) its corresponding Fermi surface at $n = 3.0$ (1.5 per site), respectively. The hopping files for this thick film are in separate files from the SM Supplemental.