Atomic-scale order enables high thermal boundary conductance at $\beta$-Ga$_2$O$_3$/4H-SiC interfaces
Thermal boundary conductance (TBC) at dissimilar interfaces imposes a fundamental limit on electronic device performance, yet predicting and understanding heat transport across realistic, disordered boundaries remains elusive. Here, we develop a computational framework that combines machine-learned interatomic potentials with lattice dynamics to address the long-standing problem of how interfacial structure, from disordered to atomically sharp, affects thermal transport in the technologically important $\beta$-Ga$_2$O$_3$/4H-SiC heterostructure. By explicitly accounting for phonon wave-particle duality, we show that interfacial disorder introduces additional interfacial phonon modes that facilitate vibrational impedance matching between the two highly dissimilar crystals, yet it simultaneously disrupts interfacial phonon coherence and limits the potential heat-transport benefit. Our atomistic simulations further indicate that restoring atomic-scale order preserves coherence and yields markedly higher conductance. These insights motivate the controlled epitaxial growth of $\beta$-Ga$_2$O$_3$/4H-SiC heterostructures with systematically tuned interfacial order. Experimental measurements validate our predictions, achieving a record-high TBC of 231 MW m$^{-2}$ K$^{-1}$ at atomically sharp junctions. Beyond the immediate implications for $\beta$-Ga$_2$O$_3$-based power electronics, our results establish the preservation of interfacial phonon coherence as an effective strategy for mitigating thermal bottlenecks in mismatched systems.