EPW Forum

Dear experts,

Could you please tell me if the electron-phonon matrix elements are symmetrical in the following sense:
g(nk,n'k+q) = g(n'k+q,nk). n,n' - band indexes of the states, k - wavevector of the initial state, q - phonon wavevector.
In other words, if one reverses the scattering event are the elements still the same.
Could you also recommend an article where this is proven if you know one?

Another thing is if the scattering process that goes from a state at the Fermi level to another state at the Fermi level is symmetrical then what about those that connect occupied and unoccupied states? I mean the code takes a window around the Fermi level, and hence it includes occupied and unoccupied states. Now, if one looks at a scattering matrix element of a scattering process from an occupied to an unoccupied state it must be different from the matrix element for the reversed process ( since electron can be scattered to an unoccupied state, but cannot go to an occupied state), and for this case matrix elements should not be symmetrical right?

Best regards, Mikhail

Hej Mikhail,

to my knowledge, the only symmetry of the coupling constants that one can conclude (from the hermiticity of the Hamiltonian) is

g_{m n \nu} ( k , q ) = g_{n m \nu}^{*} ( k + q, -q).

I shadowly remember that I have read some further remarks on time-reversal-symmetry in one of Felicianos articles, but I don't remember which one by heart.

I hope this helps.

Med vänliga hälsningar
Sebastian Kalhöfer