Pockels calculation using anaddb

Hi all,

I am calculating the ionic Pockels response (see Eq 40 of Veithen, Gonze and Ghosez: https://journals.aps.org/prb/pdf/10.1103/PhysRevB.71.125107) of tetragonal BaTiO3. The phonon frequencies are all positive after acoustic sum rule correction (see anaddb.abo output attached). Nevertheless, the anaddb utility does not provide me with the Pockels tensor results (“EO tensor (pm/V) in Voigt notation”). I obtain NaN entries (see anaddb.abo output again).

My first question is why is that and how can I solve this issue?

My second question is tightly related to the first one. I tried calculating the Pockels ionic coefficients based on the anaddb.abo output. Starting from:

  • the first-order dielectric susceptibilities in [Bohr ^{-1} ]
  • the phonon eigendisplacements, I assume in [amu ^{-1/2} ] , and 1 amu = 1822.89 a.u. of mass in Abinit
  • the phonon eigenfrequencies in [cm ^{-1} ]
  • the Born effective charges in [e]
  • the dielectric tensor in [-]

I can calculate the raman susceptibilities \alpha_{ij}^m (Eq 28) and the mode polarities p_{m,\gamma} (Eq 41), and obtain the phonon frequencies directly from the output. In the a.u. unit system, the units of the ionic Pockels tensor should be: [Bohr ^{-1} ] * [amu ^{-1} ] * [e] * [cm ^{-2} ], which should eventually yield [m/V] (or commonly [pm/V])

My second question is thus: how to convert [cm ^{-2} ] from a.u. to SI in Abinit, in order to obtain the Pockels tensor in [pm/V]? My goal is to apply a similar conversion in Quantum Espresso, which uses a different eigenvector renormalization procedure and a different mass unit system than in Abinit.

You will find in attachement the anaddb.in and anaddb.abo files, as well as the derivative databases (merge.abo), its input (merge.abi), and the original DFPT calculation input for BaTiO3 (BTO.abi).

I am happy to share any further development/information if helpful,
Many thanks,

Virginie de Mestral
PhD student at ETHZ, Nano-TCAD group
anaddb.abi (747 Bytes)
anaddb.abo (48.2 KB)
BTO.abi (7.3 KB)
merge.abi (67 Bytes)
merge.abo (151.4 KB)