Coherent phonon transport in 2D layered $$\mathrm{Cu_3BHT}$$ metal organic frameworks

Two-dimensional metal-organic frameworks (2D MOFs) offer tunable interlayer coupling and low lattice stiffness, making them a compelling system for exploring stacking-dependent heat transport. In this work, we present a full ab initio investigation of lattice dynamics and thermal transport in copper benzenehexathiolate ([Formula: see text]), focusing on three distinct stacking arrangements: AA, AB, and C. Our phonon calculations show that AB is dynamically unstable, whereas the C phase is the thermodynamic ground state, lower in energy than AA by [Formula: see text] meV per formula unit, and features covalent Cu-S interlayer bonds that stiffen interlayer modes and enhance through-plane transport. Using Boltzmann transport (BTE-RTA) together with the Wigner formalism, we find that coherent phonon contributions are essential to capture the temperature dependence: they significantly raise κ and reduce the classical [Formula: see text] scaling to [Formula: see text] with [Formula: see text] in both AA and C configurations, evidencing a wave-like transport channel activated by near-degenerate, hybridized modes. These results identify stacking-controlled interlayer connectivity as a design lever for directional heat management in 2D MOFs, with potential implications where low lattice thermal conductivity is desirable.