Efficient linear scaling method for computing the thermal conductivity of disordered materials

Abstract

An efficient order$-N$ real-space Kubo approach is developed for the calculation of the thermal conductivity of complex disordered materials. The method, which is based on the Chebyshev polynomial expansion of the time evolution operator and the Lanczos tridiagonalization scheme, efficiently treats the propagation of phonon wave-packets in real-space and the phonon diffusion coefficients. The mean free paths and the thermal conductance can be determined from the diffusion coefficients. These quantities can be extracted simultaneously for all frequencies, which is another advantage in comparison with the Green's function based approaches. Additionally, multiple scattering phenomena can be followed through the time dependence of the diffusion coefficient deep into the diffusive regime, and the onset of weak or strong phonon localization could possibly be revealed at low temperatures for thermal insulators. The accuracy of our computational scheme is demonstrated by comparing the calculated phonon mean free paths in isotope-disordered carbon nanotubes with Landauer simulations and analytical results. Then, the upscalibility of the method is illustrated by exploring the phonon mean free paths and the thermal conductance features of edge disordered graphene nanoribbons having widths of $\sim$20 nanometers and lengths as long as a micrometer, which are beyond the reach of other numerical techniques. It is shown that, the phonon mean free paths of armchair nanoribbons are smaller than those of zigzag nanoribbons for the frequency range which dominate the thermal conductance at low temperatures. This computational strategy is applicable to higher dimensional systems, as well as to a wide range of materials.

References in corpus (18)

• Evolution of graphene growth on Cu and Ni studied by carbon isotope labeling
• Energy Dissipation and Transport in Nanoscale Devices
• Thermal Logic Gates: Computation with phonons
• Nonequilibrium Green's Function Approach to Phonon Transport in Defective Carbon Nanotubes
• Charge Transport in Disordered Graphene-Based Low Dimensional Materials
• Enhanced thermoelectric figure of merit in edge disordered zigzag graphene nanoribbons
• Electron- and phonon transport in silicon nanowires: an atomistic approach to thermoelectric properties
• Vibrational modes and low-temperature thermal properties of graphene and carbon nanotubes: A minimal force-constant model
• Sufficient conditions for thermal rectification in hybrid quantum structures
• Scaling theory put into practice: first-principles modeling of transport in doped silicon nanowires
• Vibrational properties of graphene nanoribbons by first-principles calculations
• Electronic transport in Si nanowires: Role of bulk and surface disorder
• Phonon transport in large scale carbon-based disordered materials: Implementation of an efficient order-N and real-space Kubo methodology
• Inelastic effects in electron transport studied with wave packet propagation
• The shape of disorder broadened Landau subbands in graphene
• Dynamical brittle fractures of nanocrystalline silicon using large-scale electronic structure calculations
• Reducing the thermal conductivity of carbon nanotubes below the random isotope limit
• Large-scale electronic structure theory for simulating nanostructure process

Cited by in corpus (5)

• Thermoelectric properties of finite graphene antidot lattices
• Linear Scaling Quantum Transport Methodologies
• Efficient linear-scaling quantum transport calculations on graphics processing units and applications on electron transport in graphene
• Electron and phonon transport in twisted graphene nanoribbons
• Approximating spectral densities of large matrices