Signatures of a gapless quantum spin liquid in the Kitaev material Na$_3$Co$_{2-x}$Zn$_x$SbO$_6$

The honeycomb-lattice cobaltate Na$_3$Co$_2$SbO$_6$ has recently been proposed to be a proximate Kitaev quantum spin liquid~(QSL) candidate. However, non-Kitaev terms in the Hamiltonian lead to a zigzag-type antiferromagnetic~(AFM) order at low temperatures. Here, we partially substitute magnetic Co$^{2+}$ with nonmagnetic Zn$^{2+}$ and investigate the chemical doping effect in tuning the magnetic ground states of Na$_3$Co$_{2-x}$Zn$_x$SbO$_6$. X-ray diffraction characterizations reveal no structural transition but quite tiny changes on the lattice parameters over our substitution range $0\leq x\leq0.4$. Magnetic susceptibility and specific heat results both show that AFM transition temperature is continuously suppressed with increasing Zn content $x$ and neither long-range magnetic order nor spin freezing is observed when $x\geq0.2$. More importantly, a linear term of the specific heat representing fermionic excitations is captured below 5~K in the magnetically disordered regime, as opposed to the $C_{\rm m}\propto T^3$ behavior expected for bosonic excitations in the AFM state. Based on the data above, we establish a magnetic phase diagram of Na$_3$Co$_{2-x}$Zn$_x$SbO$_6$. Our results indicate the presence of gapless fractional excitations in the samples with no magnetic order, evidencing a potential QSL state induced by doping in a Kitaev system.