The approach of solving the Boltzmann transport equation (BTE) is widely used to evaluate the thermal conductivity and screen low thermal conductivity materials for thermoelectric applications, where phonon transport is approximated as particlelike propagation. Phonon transport through a wavelike tunneling channel, as described by the Wigner transport equation (WTE), will have a notable effect in some two-dimensional (2D) materials due to the parabolic out-of-plane acoustic modes and lower phonon energy, which is usually neglected, inducing an underestimation of thermal conductivity. Here, we investigate the phonon transport of four representative 2D structures by the WTE approach. Both the low-symmetry unit cell with heavy atoms and the strong anharmonicity will lead to a higher contribution from the tunneling channel. The total lattice thermal conductivity of low-symmetry KAgSe is only 0.34 ${\mathrm{W}\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ at 800 K, of which 26% is contributed by the wavelike tunneling. The strong lattice anharmonicity of 2D InSe with lone-pair electrons induces wide phonon linewidths for both acoustic and optical phonon modes, suppressing the conductivity through particlelike propagation channel. The coherence conductivity through wavelike tunneling accounts for 58% of the total one at 800 K. Our work helps to gain a better understanding of the dual-channel phonon transport in complex 2D structures. The strong anharmonic acoustic modes are crucial to achieve ultralow lattice thermal conductivity.

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• Heat transfer
• Phonons
• Thermal conductivity
• Density functional calculations