Superconductivity in doped symmetric mass generation insulator: a quantum Monte-Carlo study

TL;DR

The study addresses superconductivity arising from doping a symmetric mass generation (SMG) insulator in a bilayer fermionic model with interlayer antiferromagnetic exchange and on-site Hubbard repulsion. Using a sign-problem-free quantum Monte Carlo (QMC) method, the authors obtain numerically exact results for ground-state properties at generic fillings. They find robust interlayer spin-singlet superconductivity upon doping the SMG phase, and the superconducting pairing is enhanced by increasing the Hubbard interaction $U$ and interlayer coupling $J$. These results establish a new paradigm for superconductivity driven by strong electronic correlations and offer guidance for experimental exploration of nickelate systems under pressure.

Abstract

Understanding unconventional superconductivity (SC) driven by strong electronic correlations is a central challenge in condensed matter physics. In this work, we employ sign-problem-free quantum Monte Carlo (QMC) simulations to systematically investigate a bilayer fermionic model featuring strong interlayer antiferromagnetic (AFM) exchange and on-site repulsive Hubbard interactions. This system serves as a prototypical model for realizing a symmetric mass generation (SMG) insulator. Our numerically exact results unambiguously demonstrate that robust superconducting pairing emerges upon doping the SMG phase. Remarkably, we find that the SC order is significantly enhanced by the repulsive Hubbard interaction. Given its potential relevance to the essential features of the high-$T_c$ superconductor $\mathrm{La}_{3}\mathrm{Ni}_{2}\mathrm{O}_{7}$ under pressure, our study establishes a new paradigm for superconductivity arising from a doped SMG parent state and provides key theoretical guidance for future experimental investigations.

Figures (6)

• Figure 1: (a) The ground-state phase diagram of the model in Eq. (\ref{['Eq1']}) versus interlayer Heisenberg interaction strength $J$ and doping concentration of holes $\delta_h$. Hubbard interaction strength is fixed at $U=0$. At half filling, the ground state is exciton condensation (EC) insulator when $J < 3.24$ and SMG insulator when $J>3.24$. Interlayer spin singlet SC emerges at finite doping level away from half filling. The colors indicate the static structure factor of SC. (b) At fixed $J=2.4$, the ground-state phase diagram of the model in Eq. (\ref{['Eq1']}) versus Hubbard interaction strength $U$ and doping concentration of holes. The superconducting pairing emerging at finite doping is enhanced by the repulsive Hubbard interaction.
• Figure 2: Evolution of SC with hole doping $\delta_h$ at $U=0$. Panels (a)--(c) show the interlayer SC structure factor $S_{\mathrm{sc}}$ and panels (d)--(f) show the superfluid stiffness $\rho_s$ as functions of $\delta_h$ for representative interlayer AFM Heisenberg interactions: $J=3.0$ [left column: (a, d)], $J=3.6$ [middle column: (b, e)], and $J=6.0$ [right column: (c, f)]. Results for different system sizes ($L=10, 12, 14$) illustrate finite-size scaling behavior. At half-filling ($\delta_h \to 0$), a phase transition occurs at $J \approx 3.24$. For $J < 3.24$, both $S_{\mathrm{sc}}$ and $\rho_s$ extrapolate to finite values as $\delta_h \to 0$, indicating a degenerate EC/SC ground state. In contrast, for $J > 3.24$, both quantities vanish as $\delta_h \to 0$, signaling the emergence of a SMG phase Li2023arXivSMG. Definitions of $S_{\mathrm{sc}}$ and $\rho_s$ are given in Eq. \ref{['SCstructure']} and Eq. \ref{['stiffness']}, respectively.
• Figure 3: The effect of Hubbard interaction on the ground state of model in Eq. (\ref{['Eq1']}). The model is sign-problem-free in QMC simulation for $|U|<\frac{3}{4}J$. (a) The correlation-length ratio as a function of Hubbard interaction strength $U$ with fixed $J=2.4$. The crossing point of $R_{\rm EC}$ for different system sizes indicates the phase transition from EC phase to SMG insulator occurring at $U \approx 0.65$. (b) The ground-state phase diagram of the model in Eq. (\ref{['Eq1']}) at half filling with varying $J$ and $U$. EC and SMG denote exciton condensation insulator and symmetric mass generation insulator, respectively.
• Figure 4: The effect of Hubbard interaction on the superconducting pairing in the model of Eq. (\ref{['Eq1']}) away from half filling. The structure factor of interlayer superconducting pairing versus doping level of hole $\delta_{\rm h}$ for different Hubbard interaction strength $U$ with fixed (a) $J=2.4$ (b) and $J=6$. The linear system size is fixed at $L=14$.
• Figure S1: The results of the SC static structure factor extrapolated to $L \rightarrow \infty$, where the parameters of (a)-(c) correspond to those of (a)-(c) in Fig.\ref{['Fig2']} in the main text, respectively. The finite extrapolated values indicate the existence of SC long-range order.