# EffectiveMass

This page gives hints on how to perform an effective mass calculation with the ABINIT package.

## Introduction¶

The direct estimation of effective masses from DFT band curvature using topic_DFPT has been implemented within the linear response part of ABINIT [Laflamme2016]. This method avoids the use of finite differences to estimate these masses, which eliminates the associated numerical noise and convergence study. To compute the effective masses, one has to set the keyword efmas to 1 within a calculation of the derivative of ground-state wavefunctions with respect to wavevector (rfelfd = 1 or 2). The effective masses will then be computed for all k-points and bands present in the calculation. One can optionally specify the range of bands to be treated for each k-point with the keyword efmas_bands.

An additional feature of the effective mass implementation is the correct treatment of degenerate bands. Indeed, the concept of effective mass breaks down at degenerate band extrema since it is no longer possible to describe band curvature using a tensor [Luttinger1955], [Mecholsky2014]. However, using the concept of transport equivalent effective mass’‘ [Mecholsky2014] and its adaptation to the k.p framework, the implementation is able to provide the user with effective mass tensors which, while not describing the band curvature, describe accurately the contribution of the individual bands to transport properties.

The implementation supports both NCPP and PAW schemes.

Spin-polarized systems (nspden = 2) as well as spinors (nspinor = 2) can be treated, although the spin-orbit interaction can only be treated in the PAW case.

The treatment of degeneracies is limited to the extremal points of the band structure (which are the most relevant in any case).

By the way, the first derivative of the eigenenergies is also computed and printed during a d/dk calculation, and corresponds to the electronic velocity.

compulsory:

• efmas EFfective MASs
• rfelfd Response Function with respect to the ELectric FielD

basic:

• efmas_dirs EFfective MASs, DIRectionS to be calculated
• efmas_n_dirs EFfective MASs, Number of DIRectionS
• efmas_ntheta EFfective MASs, Number of points for integration w/r to THETA

useful:

expert:

• efmas_deg EFfective MASs, activate DEGenerate formalism

v7:

v8: