Stacking disorder and thermal transport properties of $\alpha$-RuCl$_3$

$\alpha$-RuCl$_3$, a well-known candidate material for Kitaev quantum spin liquid, is prone to stacking disorder due to the weak van der Waals bonding between the honeycomb layers. After a decade of intensive experimental and theoretical studies, the detailed correlation between stacking degree of freedom, structure transition, magnetic and thermal transport properties remains unresolved. In this work, we reveal the effects of a small amount of stacking disorder inherent even in high quality $\alpha$-RuCl$_3$ crystals. This small amount of stacking disorder results in the variation of the magnetic ordering temperature, suppresses the structure transition and thermal conductivity. Crystals with minimal amount of stacking disorder have a T$_N>$7.4\,K and exhibit a well-defined structure transition around 140\,K upon cooling. For those with more stacking faults and a T$_N$ below 7\,K, the structure transition occurs well below 140\,K upon cooling and is incomplete, manifested by the diffuse streaks and the coexistence of both high temperature and low temperature phases down to the lowest measurement temperature. Both types of crystals exhibit oscillatory field dependent thermal conductivity and a plateau-like feature in thermal Hall resistivity in the field-induced quantum spin liquid state. However, $\alpha$-RuCl$_3$ crystals with minimal amount of stacking disorder have a higher thermal conductivity that pushes the thermal Hall conductivity to be closer to the half-integer quantized value. These findings demonstrate a strong correlation between layer stacking, structure transition, magnetic and thermal transport properties, underscoring the importance of interlayer coupling in $\alpha$-RuCl$_3$ despite the weak van der Waals bonding.