On the problems of born charge and non analytical correction in phonon and heat transport calculations

When calculating the phonon structure or heat transport properties of polar materials , In order to describe accurately in dispersion gamma point LO-TO The classification of , In the process of solving the dynamic matrix , Add the correction term of polar charge action to the dynamic matrix , As in many programs involving phonon calculation phononpy, alamode as well as shengbte And so on non-analytic correct , To achieve this correction , It is necessary to give the BORN Effective charge , That is, the tensor form of the equivalent charge in motion , Each atom is 3*3 Tensor , And dielectric constant ε tensor , The specific dynamic matrix is modified as follows ：

among ε by BORN Dielectric constant in the document ,Z Is the effective charge tensor of the corresponding atom . This BORN The document must pass DFPT Perturbation method calculation , Can pass QE or VASP Realization .

But there is usually a problem here , It involves the conversion of units in the implementation of the above formula , such as phononpy in , In the production BORN file , The first line is a unit Converted values , Yes VASP yes 14.399652 （ namely Ha*bohrbohr To eV*ang）, What is actually converted here is the unit of dielectric tensor ,born The charge is in e In units of , The international unit of dielectric constant is F/m, Atomic units are usually used in material calculations , namely 1/(eV*ang), In the correction of the above expression is 1/ε Dimension is eV*ang, So when phonon calculation defaults eV and ang In units , Dielectric function ( speculation VASP Use in the result Ha and Bohr) Put it into the above formula , If the above formula is used by default （ev*ang）, At this point, you need to do unit conversion , Equivalent to the above formula, you need to multiply by a conversion coefficient （2*13.6*0.529177）, just as phononpt What is needed in .

This also shows that VASP The calculated dielectric unit is （1/(Ha*Bohr）.

But yes. QE,phononpy Targeted at QE The force constant unit of is also adjusted , So the final conversion coefficient is only 2, Equivalent to Ha To Ry. This also shows that QE The unit of output dielectric constant and VASP identical , however QE The internal unit is usually Ry and Bohr, Aimed at GaN, Use them separately VASP and QE Calculate dielectric and BORN Effective charge , The result is ：

VASP:  Dielectric xx The value is 5.5429220    QE:  5.82133

VASP:  Ga Atomic effective charge xx value 2.5749225  QE: 2.570464

The comparison shows that , Considering the difference between lattice point and pseudopotential in calculation , The difference is very small , It is speculated that the unit of output dielectric of the two is the same , All for (1/(Ha*Bohr)).