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Phonon dispersion
phonon dispersion calculation in Quantum Espresso
Raman spectra

In Quantum Espresso, phonon dispersion is calculated using ph.x program, which is implementation of density functional perturbation theory (DFPT).

Here are the steps for calculating phonon dispersion:

(1) perform SCF calculation using pw.x

import CodeBlock from '@theme/CodeBlock'; import scf_GaAs_in from '!!raw-loader!/src/GaAs-phonon/pw.scf.GaAs.in';

{scf_GaAs_in}

We perform the SCF calculation:

mpirun -np 4 pw.x -i pw.scf.GaAs.in > pw.scf.GaAs.out

:::info

  1. Usually higher energy cutoff values are used for phonon calculation to get better accuracy.

  2. In case of two dimensional systems, use assume_isolated = '2D' in the SYSTEM namelist to avoid negative or imaginary acoustic frequencies near $\Gamma$ point. Read more here.

:::

(2) calculate the dynamical matrix on a uniform mesh of q-points using ph.x

import ph_GaAs_in from '!!raw-loader!/src/GaAs-phonon/ph.GaAs.in';

{ph_GaAs_in}

Run the calculation:

mpirun -np 4 ph.x -i ph.GaAs.in > ph.GaAs.out

The above calculation is computationally demanding. Our example calculation took about a whole day on a 2.6 GHz quad core processor.

:::info

You can restart an interrupted ph.x calculation with recover = .true. in the INPUTPH namelist. You can cleanly exit an ongoing calculation by creating an empty file with name {prefix}.EXIT.

:::

(3) perform inverse Fourier transform of the dynamical matrix to obtain inverse Fourier components in real space using q2r.x. Below is our input file:

import q2r_GaAs_in from '!!raw-loader!/src/GaAs-phonon/q2r.GaAs.in';

{q2r_GaAs_in}

mpirun -np 4 q2r.x -i q2r.GaAs.in > q2r.GaAs.out

(4) Finally, perform Fourier transformation of the real space components to get the dynamical matrix at any q by using matdyn.x.

import matdyn_GaAs_in from '!!raw-loader!/src/GaAs-phonon/matdyn.GaAs.in';

{matdyn_GaAs_in}

mpirun -np 4 matdyn.x -i matdyn.GaAs.in > matdyn.GaAs.out

We can now plot the phonon dispersion of GaAs:

import numpy as np
import matplotlib.pyplot as plt

data = np.loadtxt("../src/GaAs-phonon/GaAs.freq.gp")

nbands = data.shape[1] - 1
for band in range(nbands):
    plt.plot(data[:, 0], data[:, band], linewidth=1, alpha=0.5, color='k')
# High symmetry k-points (check matdyn.GaAs.in)
plt.axvline(x=data[0, 0], linewidth=0.5, color='k', alpha=0.5)
plt.axvline(x=data[20, 0], linewidth=0.5, color='k', alpha=0.5)
plt.axvline(x=data[40, 0], linewidth=0.5, color='k', alpha=0.5)
plt.axvline(x=data[60, 0], linewidth=0.5, color='k', alpha=0.5)
plt.xticks(ticks= [0, data[20, 0], data[40, 0], data[60, 0], data[-1, 0]], \
           labels=['L', '$\Gamma$', 'X', 'U,K', '$\Gamma$'])
plt.ylabel("Frequency (cm$^{-1}$)")
plt.xlim(data[0, 0], data[-1, 0])
plt.ylim(0, )
plt.show()
GaAs-phonon

:::tip

We may need to lower the value of conv_thr in scf calculation for more accurate result.

:::

Phonon Density of States

Input file for phonon DOS calculation:

import matdyn_dos_GaAs_in from '!!raw-loader!/src/GaAs-phonon/matdyn.dos.GaAs.in';

{matdyn_dos_GaAs_in}

Plot phonon DOS:

freq, dos, pdos_Ga, pdos_As = np.loadtxt("../src/GaAs-phonon/GaAs.dos", unpack=True)

plt.plot(freq, dos, c='k', lw=0.5, label='Total')
plt.plot(freq, pdos_Ga, c='b', lw=0.5, label='Ga')
plt.plot(freq, pdos_As, c='r', lw=0.5, label='As')
plt.xlabel('$\\Omega~(cm^{-1}$)')
plt.ylabel('Phonon DOS (state/cm$^{-1}/u.c.$)')
plt.legend(frameon=False, loc='upper left')
plt.xlim(freq[0], freq[-1])
plt.show()
GaAs-phonon-dos

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