Fermi-liquid-like phase driven by next-nearest-neighbor couplings in a lightly doped kagome-lattice t − J model

Due to the interplay between charge fluctuation and geometry frustration, the doped kagome-lattice Mott insulator is a fascinating platform to realize exotic quantum states. Through the state-of-the-art density matrix renormalization group calculation, we explore the quantum phases of the lightly doped kagome-lattice $t\text{\ensuremath{-}}J$ model in the presence of the next-nearest-neighbor electron hopping ${t}₂$ and spin interaction ${J}₂$. On the ${L}_y=3$ cylinder (${L}_y$ is the number of unit cells along the circumference direction), we establish a quantum phase diagram with tuning ${t}₂>0$ and ${J}₂>0$, showing an emergent Fermi-liquid-like phase driven by increased ${t}₂$ and ${J}₂$, at the neighbor of the previously identified charge density wave (CDW) phase. Compared with the CDW phase, the charge order is significantly suppressed in the Fermi-liquid-like phase, and most correlation functions are greatly enhanced with a power-law decay. In particular, we find the absence of hole pairing and a strong three-sublattice magnetic correlation. On the wider ${L}_y=4$ cylinder, this Fermi-liquid-like phase persists at low doping levels, strongly suggesting that this state might be stable in the two-dimensional kagome system.