Electron-Phonon Coupling Matrix Symmetry
Posted: Mon Mar 02, 2026 1:10 pm
Hi,
I am trying to calculate the electron phonon coupling matrix between an electron at the cbm and acoustic phonons with a vector that has a fixed magnitude (q) while varying the polar and azimuthal angles (θ,φ) between 0 and π and 0 and 2π respectively. Essentially calculating the electron phonon coupling matrix on the surface of a sphere centred on the cbm with radius q. For FCC crystals like diamond and Si I would expect that for a fixed polar angle, varying the azimuthal angle would give values from the ep matrix 4 fold rotational symmetry as you sweep through the angle from 0 to 2π, however when I run the calculation for silicon this is not the case. Attached are two graphs that show this for q = 0.01, θ=3π/10 and q=0.01, θ=π/2. The full set of input and output files were too large to attach here so can be found at https://www.dropbox.com/scl/fo/ok8t2t1r ... 189sj&dl=0.
The phonon frequencies calculated along the same path show the expected symmetry and I see this symmetry in the phonon frequencies and electron-phonon coupling matrix when I run this calculation for diamond.
Please could someone help me work out what the problem is so that I can better understand what is happening for future calculations.
Patrick
I am trying to calculate the electron phonon coupling matrix between an electron at the cbm and acoustic phonons with a vector that has a fixed magnitude (q) while varying the polar and azimuthal angles (θ,φ) between 0 and π and 0 and 2π respectively. Essentially calculating the electron phonon coupling matrix on the surface of a sphere centred on the cbm with radius q. For FCC crystals like diamond and Si I would expect that for a fixed polar angle, varying the azimuthal angle would give values from the ep matrix 4 fold rotational symmetry as you sweep through the angle from 0 to 2π, however when I run the calculation for silicon this is not the case. Attached are two graphs that show this for q = 0.01, θ=3π/10 and q=0.01, θ=π/2. The full set of input and output files were too large to attach here so can be found at https://www.dropbox.com/scl/fo/ok8t2t1r ... 189sj&dl=0.
The phonon frequencies calculated along the same path show the expected symmetry and I see this symmetry in the phonon frequencies and electron-phonon coupling matrix when I run this calculation for diamond.
Please could someone help me work out what the problem is so that I can better understand what is happening for future calculations.
Patrick