Direct solution to the linearized phonon Boltzmann equation.

Area of Science:

• Condensed Matter Physics
• Materials Science
• Computational Physics

Background:

• Lattice thermal conductivity is crucial for heat transport in solids.
• Calculating thermal conductivity from first principles, especially frequency-dependent properties, remains challenging.
• Existing methods often struggle with accurately capturing phonon dynamics.

Purpose of the Study:

• To develop a novel ab initio method for calculating frequency-dependent lattice thermal conductivity.
• To obtain the first dynamical thermal conductivity results using this new approach.
• To validate the method by comparing predictions with experimental data for known materials.

Main Methods:

• Transformation of the frequency-dependent phonon Boltzmann equation into an integral equation.
• Simultaneous diagonalization of the collision kernel and symmetry crystal operator.
• Integration with density functional theory calculations.
• Application to carbon, silicon, and magnesium silicide.

Main Results:

• A spectral representation of lattice thermal conductivity valid at finite frequency was derived.
• The first ab initio dynamical thermal conductivity was successfully obtained.
• Static thermal conductivity was accurately reproduced as a special case.
• Excellent agreement was found between calculated and experimental static thermal conductivity for C, Si, and Mg2Si.

Conclusions:

• The developed method provides an accurate and robust way to compute lattice thermal conductivity, including its frequency dependence.
• This work opens new avenues for predicting and understanding thermal transport in materials from first principles.
• The approach is validated by its successful application to benchmark materials.