Spinon Singlet Pairing: Origin of $d$-Wave Sign Structure in a Partially-Filled Stripe

Abstract

Significant research advances have led to a consensus that the Fermi-Hubbard model and its extended variants are archetypical frameworks for elucidating the intertwined relationship between stripe orders and superconductivity in hole-doped high-$T_c$ materials. Notably, the Hubbard quantum simulator has recently achieved several remarkable breakthroughs, e.g., being cooled down to the cryogenic regime and enabling the observation of stable fluctuating stripes. However, the microscopic mechanism underlying the $d$-wave pairing of electrons in the presence of stripes at low temperatures remains poorly understood due to the intricate interplay between strongly correlated effects and non-negligible thermal fluctuations. Here, we conduct a close investigation of a partially-filled stripe in the representative $t$-$J$ and $t$-$t'$-$U$ models with both numerical and analytical methods. Analogous to quantum gas microscopy, the perfect sampling technique allows us to obtain the high-confidence-level statistics of the Fock basis states appearing in the ground-state wavefunction. In a novel physical paradigm, these data demonstrate that two spinons with opposite chiralities tend to pair spontaneously into a singlet state, thereby naturally giving rise to the $d$-wave pairing pattern. Then, using the updated effective theory of quantum colored string, we have reconstructed the wavefunction and have determined the nature of spinon pairing and its connection to the $d$-wave sign structure of pair-pair correlation. Furthermore, spinon singlet pairs enable the establishment of a long-range pair-pair correlation between the two stripes. Our work offers new insights into the microscopic physics of stripes and paves the way for further exploration of multi-stripe-mediated pairing mechanisms in the Fermi-Hubbard model.