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Dominant Kitaev Interaction and Field-induced Quantum Disordered Phase in the Cobaltate Na$_2$Co$_2$TeO$_6$

The identification of quantum spin liquid phases in Kitaev candidate materials remains a major experimental challenge. Since most Kitaev candidates develop antiferromagnetic (AFM) order at low temperatures, currently there are great interest on the field-induced magnetic disordered phase in these compounds, that are distinct from (partially) polarized states. Recently, a cobaltate Na$_2$Co$_2$TeO$_6$ has emerged as a promising Kitaev candidate with high-spin $t^{5}_{2g}e^2_g$ configuration and spin-orbit entangled $J_{\rm eff} = 1/2$ honeycomb lattice system. There are intensive studies on field-induced magnetic states and phase transitions under in-plane magnetic fields. In this study, we propose an intermediate disordered phase induced by an out-of-plane field along the $c$-axis, through high-field magnetization and magnetocaloric effect measurements. To explain the high-field behavior of Na$_2$Co$_2$TeO$_6$, we develop an effective $K$-$J$-$Γ$-$Γ^{\prime}$ spin model featuring a dominant AFM Kitaev interaction. This framework uncovers an intermediate quantum spin liquid phase, establishing the material as a unique platform for exploring Kitaev physics and field-induced quantum-disordered states.