How a bilayer Nickelate superconducts: a Quantum Monte Carlo study

Abstract

Using determinant Quantum Monte Carlo, we investigate the interplay between doping, inter-layer tunneling and onsite Hund's coupling in stabilizing superconductivity (SC) in a two-orbital model for the bilayer Nickelate $\text{La}_3\text{Ni}_2\text{O}_7$. With realistic dispersion and for certain values of the interaction parameters, the auxiliary-field-decoupled fermion Hamiltonian has Kramers anti-unitary symmetries which guarantee the absence of a sign problem. The same anti-unitary symmetries can also be used to show there is a second instability towards $(π,π)$ exciton condensation in the strong interaction limit. We indicate the possible connection between this exciton order and the enigmatic density wave state observed in experiment, and clarify the decisive role played by the inter-layer tunneling in the competition between SC and exciton condensation. Finally, possible directions on how to enhance the SC transition temperature and stabilize the SC phase are also discussed.

Figures (4)

• Figure 1: (a) The spectral function $A(k,\omega)$ for $H_0$ with parameters from DFT calculation luo2023bilayer with an artificial width $\delta=0.02$ to indicate the band structure along high symmetry line for size $L=60$, the dashed line indicates the chemical potential $\mu=-0.2$ used for interacting case (c)(d). (b) Plot of $\lim_{\beta \to \infty}G(k,\tau=\beta/2)\sim A(k,\omega=0)$ with $L=\beta=60$. The color scale indicates the zero frequency spectral weight, where the bright region indicates the position of Fermi surface. (c) Spectral function $A(k,\omega)$ along high symmetry line derived from stochastic analytical continuation (SAC) sandvik1998stochasticbeach2004identifyingshao2023progress for interacting Hamiltonian with parameters $J_{xz}=0.4,L=8,T=0.05$. (d) The $G(k,\tau=\beta/2)$ with the same parameters as (c) showing the positions of single-particle excitation minima.
• Figure 2: (a) Finite-size crossing of Cooper pair correlation in $d_{x^2-y^2}$ orbital indicates $T_c\lesssim 0.06$ for interacting Hamiltonian with parameters $J_{xz}=0.4,\mu=-0.2,t_{zz}^{\perp}=-0.635$. (b) Spectral function from SAC of imaginary time correlation function $C(\tau)=\langle \Delta^{\dagger}(\tau)\Delta(0)\rangle$ for $L=8,T=0.05$ case. (c)(d) The same plot as (a) with different chemical potential $\mu=0$ and $\mu=-0.4$ respectively.
• Figure 3: (a) Finite-size crossing of Cooper pair correlation indicates $T_c\lesssim 0.06$ for interacting Hamiltonian with parameters $J_{xz}=0.4,\mu=-0.2,t^\perp_{zz}=0$. (b)(c) Finite-size crossing with the same parameters as in (a), except for $J_{xz}=0.2$ in (b) and $J_{xz}=0.1$ in (c). (d) Absence of SC with $t^\perp_{zz}=-0.635,J_{xz}=0.2$.
• Figure 4: Static structure factors for SC (a), EC (b) and SDW (c) with the same parameters as in Fig. \ref{['fig:FSBD']}(c)(d) and Fig. \ref{['fig:SC']}(a)(b).