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Finite Size Effects of Thermal Conductivity for One-Dimensional Mesoscopic Systems

The finite size effects of the thermal conductivity $κ$ have been studied in the phonon space. It is found that only a few phonon modes are selected to take part in the thermal transport when the size $L$ of the system is decreased. The amount of the selected phonon modes is proportional to the $L$. In this way, $κ$ decreases with the decreasing of $L$. Such mechanism for the size effect of $κ$ found in this work is beyond the Phonon-Boundary scattering. The exponent $α$ of the power law $κ\sim L^α$ has been fitted, showing that the exponent is not universal.