Super diffusive length dependent thermal conductivity in one-dimensional materials with structural defects: longitudinal to transverse phonon scattering leads to $\kappa \propto L^{1/3}$ law

Abstract

Structural defects in one-dimensional heat conductors couple longitudinal (stretching) and transverse (bending) vibrations. This coupling results in the scattering of longitudinal phonons to transverse phonons and backwards. We show that the decay rate of longitudinal phonons due to this scattering scales with their frequencies as ${\omega }^{3/2}$ within the long wavelength limit ($\omega \to 0$), which is more efficient scattering compared to the traditionally considered Rayleigh scattering within the longitudinal band (${\omega }^2$). This scattering results in temperature independent thermal conductivity depending on the size as $\kappa \propto L^{1/3}$ for sufficiently long materials. This predicted length dependence is observed in nanowires, though the temperature dependence is seen there possibly because of deviations from pure one-dimensional behavior. The significant effect of interaction of longitudinal phonons with transverse phonons is consistent with the earlier observations of a substantial suppression of thermal energy transport by kinks, obviously leading to such interaction, though anharmonic interaction can also be significant.

16 pages, 6 figures

References in corpus (19)

• Thermal conduction in classical low-dimensional lattices
• Quantized thermal conductance of dielectric quantum wires
• Anomalous heat conduction in one dimensional momentum-conserving systems
• Thermal conductance through molecular wires
• One-Dimensional van der Waals Quantum Materials -- State of the Art and Perspectives
• Heat Transport in Mesoscopic Systems
• Dynamic Correlators of Fermi-Pasta-Ulam Chains and Nonlinear Fluctuating Hydrodynamics
• Relaxation of classical many-body hamiltonians in one dimension
• Of Bulk and Boundaries: Generalized Transfer Matrices for Tight-Binding Models
• Mode-coupling theory and molecular dynamics simulation for heat conduction in a chain with transverse motions
• Thermal equilibrium of a macroscopic quantum system in a pure state
• Ultrahigh convergent thermal conductivity of carbon nanotubes from comprehensive atomistic modeling
• Wave scattering by discrete breathers
• Stochastic Simulation of Nonequilibrium Heat Conduction in Extended Molecule Junctions
• Hydrodynamic limit for a disordered harmonic chain
• Unsteady ballistic heat transport in a 1D harmonic crystal due to a source on an isotopic defect
• Comment on the calculation of forces for multibody interatomic potentials
• Maximum propagation speed and Cherenkov effect in optical phonon transport through periodic molecular chains
• Crucial effect of transverse vibrations on the transport through polymer chains

Cited by in corpus (1)

• Manning-type potential induced by kink scatterings with phonons in molecular chains with hyperbolic double-well substrates