Triplon-mediated pairing and the superconducting gap structure in bilayer nickelates

Abstract

We investigate the superconducting gap structure in bilayer nickelates within a model where conduction bands of dx2-y2 symmetry coexist with localized d3z2-r2 spins. Strong interlayer coupling drives the local moments into a singlet ground state, whose virtual singlet-triplet excitations ("triplons") mediate the pairing interaction between conduction electrons. This yields interband s+- pairing, with opposite signs of the order parameter on the bonding beta and antibonding alpha bands. Our theory naturally explains two key experimental features: a larger gap on the alpha band despite its smaller density of states, and pronounced gap anisotropy arising from momentum-dependent nonlocal Kondo coupling. These results support triplon-mediated pairing as the microscopic origin of superconductivity in bilayer nickelates.

Figures (4)

• Figure 1: (a) On the $c$ axis bond connecting two layers 1 and 2, the localized $d_{3z^2\!-\!r^2}$ spins $S_1$ and $S_2$ interact via antiferromagnetic coupling $J_c=4t_c^2/U$ and form a spin-dimer with singlet ground state. Singlet-to-triplet excitation (dashed arrow) with energy $J_c$ is described by a boson creation operator $\boldsymbol{T}^{\dag}$. (b) In-plane hopping geometry between itinerant $d_{x^2\!-\!y^2}$ and local $d_{3z^2\!-\!r^2}$ orbitals. The opposite signs of $\pm t_{xz}$ along the $x$ and $y$ bonds generates $\eta_{\boldsymbol{k}}\!=\!\cos k_x \!-\!\cos k_y$ structure in momentum space. (c) In the virtual hopping process $d_{3z^2\!-\!r^2} \!\rightarrow\! d_{x^2\!-\!y^2}$, the $\langle z_1;z_2 \rangle$ dimer is left with a single $d_{3z^2\!-\!r^2}$ electron in the intermediate state, forming bonding $b$ and antibonding $a$ molecular orbitals with energies $E_b$ and $E_a$ below the Fermi level. Owing to the different excitation energies in the bonding $b\!\rightarrow\!\beta$ and antibonding $a\!\rightarrow\!\alpha$ hopping channels, the initially degenerate $\beta$ and $\alpha$ bands obtain different self-energy corrections and will thus split. (d) Illustration of the Kondo exchange process where virtual $t_{zx}$ hoppings generate on-site singlet-to-triplet transition (triplon $T^\dagger_1$ with $S_z=1$ is created in the case shown).
• Figure 2: (a) Antibonding $\alpha$ (blue) and bonding $\beta$ (red) band dispersions along $\Gamma(0,0)$---$\mathrm{X}(\pi,0)$---$\mathrm{M}(\pi,\pi)$ path, and (b) the corresponding Fermi surfaces in the Brillouin zone. The model parameters are $t_1=0.45$, $t_2 =-0.24$, $t_3=0.06$, $\epsilon_{\alpha}=0.4$, and $\epsilon_{\beta}=0.1$ (in units of eV). The chemical potential $\mu=-0.65$ eV is chosen to obtain the band fillings (per Ni ion) $n_{\alpha}=0.14$ and $n_{\beta}=0.31$ (as reported in ARPES study Sun25b).
• Figure 3: (a) Ratio $N_{\beta}/N_{\alpha}$ of the DOS at the Fermi level for $\alpha$ and $\beta$ bands of Fig. \ref{['fig:2']} as a function of electron density (per Ni) $n_c = n_\alpha + n_\beta$. (b) Ratio of superconducting gap amplitudes $\Delta_\alpha/\Delta_\beta$ as a function of $N_{\beta}/N_{\alpha}$, following from Eq. \ref{['eq:R']} at $\lambda=0.6$ and $0.3$. Dashed line $\sqrt{N_{\beta}/N_{\alpha}}$ shows $\lambda \rightarrow 0$ limit.
• Figure 4: (a) $\widetilde{N}/N$ ratio (i.e. density of states $\widetilde{N}$ weighted by $\eta_{\boldsymbol{k}}^2$ factor relative to $N$) as a function of electron density $n_c$ per Ni ion. (b) Superconducting gap values (relative to $\Delta_\alpha$ at $\theta=0$) at the $\alpha$ and $\beta$ Fermi surfaces as a function of angle $\theta$ [which is defined in Fig. 2(b)], calculated from Eqs. \ref{['eq:gap3']} and \ref{['eq:R']} with $n_c=0.45$, $\kappa=0.75$, and $\lambda=0.5$.