Lattice dynamics and electron-phonon coupling calculations using non-diagonal supercells

TL;DR

This paper introduces a method using non-diagonal supercells for efficient lattice dynamics and electron-phonon coupling calculations, reducing computational costs and enabling large-scale convergence studies.

Contribution

It demonstrates that non-diagonal supercells can significantly lower computational costs in phonon and electron-phonon calculations compared to diagonal supercells.

Findings

Non-diagonal supercells reduce computational cost for phonon calculations.

Enables large-scale electron-phonon coupling calculations.

Provides convergence analysis for zero-point renormalization in diamond.

Abstract

We study the direct calculation of total energy derivatives for lattice dynamics and electron-phonon coupling calculations using supercell matrices with non-zero off-diagonal elements. We show that it is possible to determine the response of a periodic system to a perturbation characterized by a wave vector with reduced fractional coordinates $(m_1/n_1,m_2/n_2,m_3/n_3)$ using a supercell containing a number of primitive cells equal to the least common multiple of $n_1$, $n_2$, and $n_3$. If only diagonal supercell matrices are used, a supercell containing $n_1n_2n_3$ primitive cells is required. We demonstrate that the use of non-diagonal supercells significantly reduces the computational cost of obtaining converged zero-point energies and phonon dispersions for diamond and graphite. We also perform electron-phonon coupling calculations using the direct method to sample the vibrational Brillouin zone with grids of unprecedented size, which enables us to investigate the convergence of the zero-point renormalization to the thermal and optical band gaps of diamond.