Phonon Linewidth and Thermal Conductivity

Second and third order irreducible derivatives must be computed first, as described here, and the second and third order force constants may then be used to predict the phonon linewidth using perturbation theory. The phonons and the linewidths can then be used to computed thermal conductivity with the relaxation time approximation.

Phonon Linewidth

Here we continue the NaCl example from before.

First, we need to prepare a configuration file config.yml for the pm-conductivity command:

#  config.yml
structure: xtal.yml
load_fi2: fi_order2.hdf5
load_fi3: fi_order3.hdf5
mesh: [11, 11, 11]
band:
  - ['0 0 0', '1/2 1/2 0']
  - ['-1/2 1/2 0', '0 0 0']
  - ['0 0 0', '1/2 1/2 1/2']
band_label:
  - $\Gamma$
  - X
  - $\Gamma$
  - L

where:

• xtal.yml contains structure of NaCl;

• fi_order2.hdf5 is the HDF5 data file for the FourierInterpolation class at second order, which contains the 2nd order force constants;

• fi_order3.hdf5 is the HDF5 data file for the FourierInterpolation class at third order, which contains the 3rd order force constants.

In this example, we use the FourierInterpolation object of a \(\hat{S}_{BZ}=4\hat{\mathbf{1}}\) FTG (i.e. a \(4 \times 4 \times 4\) supercell) at second order and the FourierInterpolation object of a \(\hat{S} _{BZ}=2\hat{\mathbf{1}}\) FTG (i.e. a \(2 \times 2 \times 2\) supercell) at third order. We interpolate the phonons and phonon interactions to the mesh of \(11\hat{\mathbf{1}}\), and compute the linewidth along the K-path \(\Gamma \to X \to \Gamma \to L\).

Execute the following command the compute the phonon linewidth:

pm-conductivity --config config.yml --save-gamma

Thermal Conductivity

Using the same NaCl example, we can prepare a configuration file config.yml similar to the one above:

# config.yml
structure: xtal.yml
load_fi2: fi_order2.hdf5
load_fi3: fi_order3.hdf5
mesh: [11, 11, 11]

Execute the following command the compute the thermal conductivity using relaxation time approximation (RTA):

pm-conductivity --config config.yml --save-kappa --mode RTA