Comparative study of thermal transport properties in hexagonal boron nitride with different stacking orders

Recent studies have extensively explored the phonon heat transport properties of bulk hexagonal boron nitride ($h$-BN); however, the influence of stacking order on its thermal conductivity ($\kappa$) has received rare attention. In this work, we employ first-principles calculations to predict the thermal conductivity of $h$-BN with wurtize ($w$), AB, and ABC stacking. Our calculations show that $w$-BN possesses the highest thermal conductivity, with in-plane and out-of-plane values of 611 W/mK and 521 W/mK at room temperature (RT), respectively. In contrast, AB and ABC stacking exhibit comparable thermal conductivities, with RT in-plane (out-of-plane) values of 338 (5.8) and 357 (7.2) W/mK, respectively. Notably, four-phonon scattering is found to reduce the $\kappa$ of ABC and AB stacking by 9% and 13% at RT, while exerting non-negligible suppression on the $\kappa$ of $w$-BN only at high temperature. Through detailed mode-level analysis, we uncover that the lower thermal conductivity of AB and ABC stacking, compared to w-BN, stems from their stronger phonon anharmonicity, driven by weak interlayer van der Waals interactions. Furthermore, the calculated modal $\kappa$ reveals that the stacking sequence has opposite effects on the out-of-plane flexural acoustic phonons and other modes, and their competing effect noticeably weakens the difference in $\kappa$ between AB and ABC stacking phases. This work provides a fundamental understanding of the phonon thermal transport properties of bulk $h$-BN with different stacking orders and elucidates the roles of stacking order and higher-order anharmonicity in determining the thermal conductivity of van der Waals layered materials.