Due to the rapid development of micro- and nano-manufacturing and electronic devices, heat transfer at the transition regime between radiation and conduction becomes increasingly important. Recent work has demonstrated the importance of nonlocal optical response and phonon tunneling. However, it remains unclear how the crystal orientation impacts them. In this work, we study this effect on heat transport across vacuum gaps between magnesium oxide (MgO) by nonequilibrium molecular dynamics (NEMD) simulation. At 5~Å~gaps, the overall thermal conductance exhibits 30% enhancement for [100] orientation versus [110] and [210], while becoming orientation-insensitive beyond 6~Å. When the gap size is extremely small, the crystal orientation significantly impacts the resonance frequencies of spectral thermal conductance which are quite close to those of unique surface phonon modes distinct from bulk counterparts. As the gap size gradually increases, the spectral thermal conductance gradually converges to the predicted results of fluctuation-electrodynamics (FE) theory in the long-wavelength approximation. Our findings reveal how surface phonon modes govern extreme near-field heat transfer across nanogap, providing insights for thermal management in electronic devices.

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