Dominant Excitonic Superconductivity in a Three-component Hubbard Chain

Abstract

Understanding superconductivity emerging from repulsive fermions remains a major challenge in condensed matter physics. In this paper, we investigate the pairing tendencies in a one-dimensional, three component repulsive Hubbard model, using the density matrix renormalization group method. At half-filling, the system exhibits density wave ground state due to strong Hubbard repulsions. Upon doping, we find that Cooper pairs can emerge, whose fluctuations predominate the long-range physics in the system across a wide parameter range. The effective attractions between Cooper pairs are mediated by the particle-hole fluctuations in the third non-pairing component, resembling an excitonic mechanism of superconductivity. The coexistence of multiple density waves and superconductivity at different fermion fillings is explored. We also present an analytical study of the pairing mechanism in both weak and strong coupling limits. Our results provide a new perspective for understanding and exploring unconventional superconductivities in strongly correlated fermionic systems.

Figures (10)

• Figure 1: Pair correlation function $\Phi(r)$ as a function of $r$ for a few different $U^{\prime} \equiv U_{13}$. Figure is plotted on a double-logarithmic scale. Dashed lines show fitting of $\Phi(r) \propto r^{-K_{SC}}$. Here $U \equiv U_{12} \equiv U_{23}= 4.0$ is fixed and average filling $n = 0.85$.
• Figure 2: Luttinger exponent $K_{sc}$ versus particle density $n$ at fixed $U=4.0$ and $U^{\prime}=0$. Inset provides a preliminary delineation of different phase regimes.
• Figure 3: Aggregated and spin-flavor resolved charge density distributions at half-filling. (a) For $U = 2.0$, (b) For $U = 4.0$. Here $U^{\prime} = 0$.
• Figure 4: Correlation functions at half-filling, plotted on a semi-logarithmic scale. (a)For $U = 2.0$, (b) For $U = 4.0$. Here $U^{\prime} = 0$. Dashed lines show exponential fits. Note that due to symmetry, $G_{1} (r) = G_{3} (r)$.
• Figure 5: Charge density distribution $n(r)$ for different $U$. Solid lines showing fitting curves obtained using Eq. \ref{['eq3']}. Here $n=0.85, U^{\prime} = 0$.