Electron-phonon potential from supercells

The computation of the electron-phonon potential, ${\partial }_{\nu \mathbf{𝐪}}V(\mathbf{𝐫})$, is a prerequisite for the calculation of the electron-phonon matrix element:

$g_{mn\mathbf{𝐤},\nu \mathbf{𝐪}}\equiv ⟨{\psi }_{m\mathbf{𝐤}+\mathbf{𝐪}}|{\partial }_{\nu \mathbf{𝐪}}V|{\psi }_{n\mathbf{𝐤}}⟩.$

In the direct interpolation approach, ${\partial }_{\nu \mathbf{𝐪}}V$ is computed from a supercell calculation by means of Fourier interpolation while the Bloch orbitals, ${\psi }_{n\mathbf{𝐤}}(\mathbf{𝐫})$, are computed directly in the primitive cell. Naturally, this process involves multiple VASP calculations in different cells, which can introduce additional complexities compared to just a single execution of VASP. This page tries to give a high-level overview of the general workflow associated with electron-phonon calculations using the direct interpolation approach.

Finite displacements in the supercell

The electron-phonon potential is computed from finite atomic displacements in a sufficiently large supercell. In this case, sufficient means that the effects of an atomic displacement become negligible at about half the supercell size. Usually, converging the phonon frequencies is a good way of finding a supercell that is sufficiently large. Polar materials can exhibit long-range electrostatic interactions that go beyond reasonable supercell sizes. In this case, a correction scheme exists that explicitly treats the long-range dipole interactions and works with smaller cells. More information can be found on the theory page.