Superconductivity and magnetism in bilayer nickelates: itinerant perspective

Abstract

We study superconductivity and magnetism in bilayer nickelates from an itinerant perspective. Starting from a tight binding fit to recent ARPES measurements on compressively strained thin films, we incorporate the standard set of onsite repulsive interactions among partially filled $e_g$ orbitals: intra-orbital $U$, inter-orbital $U'$, Hund's coupling $J_H$ and a pair hopping $J_P$. We obtain the effective pairing interaction by dressing these bare interactions with particle-hole fluctuations via the RPA. In the strong Hund's coupling regime, we find that $s$-wave superconductivity and $(π/2, π/2)$ SDW order are the favored ground states. With weaker Hund's coupling, we find that $d$-wave pairing and $(π, π)$ SDW are the leading ground states. Our results are qualitatively consistent with earlier DMRG studies, and point to the key role played by Hund's coupling in determining the nature of superconductivity and magnetism in this system.

Figures (7)

• Figure 1: Fermi surface of bilayer nickelate in the $k_x$-$k_y$ plane from Eq. \ref{['eq:H00']}, with color encoding the orbital weight. Here the central pocket is the $\alpha$-FS (bonding, $\nu_c = 0$), containing mainly contributions from the $d_{x^2-y^2}$ orbitals. The larger pocket surrounding $(\pi,\pi)$ is the $\beta$-FS (anti-bonding, $\nu_c = \pi$), and has equal contributions from both orbitals near the BZ boundary. The effective intra-pocket interaction $V^{\alpha\alpha}$ and $V^{\beta\beta}$, and the inter-pocket $V^{\alpha\beta}$ are pictorially shown here, see Fig. \ref{['fig:Valphabeta']} for details.
• Figure 2: (a) Phase diagram of the leading pairing symmetry in the parameter space $U'$-$U$-$J_H$. (b-e) Band basis projected gap function $\Delta(\bm{k})$ [see Eq. \ref{['eq:bandDelta']} and Appendix \ref{['app:lin_gap']}] obtained at different parameters indicated in the plots. The value on the color bar shows the relative magnitude of the gap function. (b)$d$-wave gap function in the $B_{1g}$ irrep with nodal points along the $\hat{x}\pm\hat{y}$ directions. (c)$s_\pm$-wave, (d) nodal $s$-wave and (e) conventional $s$-wave gap functions.
• Figure 3: Color maps of the effective interaction $[V_\text{eff}(\bm{k},\bm{p})]_{XX,XX}$ between $d_{x^2-y^2}$ orbitals in the $\bm{k}$-$\bm{p}$ plane. Since an equal number of points are sampled on the $\alpha$-FS and on the $\beta$-FS, each plot is divided into four equal-size blocks: the intra-pocket interaction $V^{\alpha\alpha}$ and $V^{\beta\beta}$ and the inter-pocket interaction $V^{\alpha\beta}=[V^{\beta\alpha}]^T$. (a) When all of the interactions are repulsive and the intra-pocket $V^{\alpha\alpha}, V^{\beta\beta}$ dominate, the system favors a $d$-wave. (b) Instead, when the inter-pocket $V^{\alpha\beta}$ dominates in a fully repulsive interaction, the system favors a $s_{\pm}$-wave. (c) When $V^{\alpha\alpha}$ and $V^{\beta\beta}$ are repulsive but $V^{\alpha\beta}$ is attractive, the system favors a nodal $s$-wave. (d) When all these four interactions are attractive, the system favors a conventional $s$-wave.
• Figure 4: Comparison of the RPA total spin susceptibility $\chi_S^\text{RPA}(\bm{q})$ and the bare total spin susceptibility $\chi_S^0(\bm{q})$, for $\bm{q}$ along the path $\Gamma$--X--M--$\Gamma$ in the BZ. $\chi_S^0(\bm{q})$ is shown in yellow. For $\chi_S^\text{RPA}(\bm{q})$, we fix $U$ and $U'$ and show two different values of $J_H$ in blue and orange.
• Figure 5: Diagrammatic representation of the microscopic interactions considered in Eq. \ref{['eq:interaction_app']}. We use red and blue coloring to denote the $d_{x^2-y^2}$ and $d_{z^2}$ orbitals respectively, while the spin indices are explicitly labeled. Depending on how the orbital and spin indices will be contracted, the total interaction can be equivalently written as $V_1$ or $V_2$. Here, the black thick line denotes the matrix propagator including both orbitals.