# Effective Mass calculations

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

##### Copyright (C) 2016-2017 ABINIT group (JLaflamme)

Mentioned in help_features#8.

### Table of content:

- 1. Introduction.
- 2. Related input variables.
- 3. Selected input files.
- 4. References.

### 1. Introduction.

The direct estimation of effective masses from DFT band curvature using 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 degenerescences 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.
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### 2. Related input variables.

Compulsory input variables:

... efmas [EFfective MASs]
... rfelfd [Response Function with respect to the ELectric FielD]

Basic input variables:

... 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 input variables:

... efmas_bands [EFfective MASs, BANDS to be treated.]
... efmas_calc_dirs [EFfective MASs, CALCulate along DIRectionS]
... efmas_deg [EFfective MASs, activate DEGenerate formalism]
... efmas_deg_tol [EFfective MASs, DEGeneracy TOLerance]
... efmas_dim [EFfective MASs, DIMension of the effective mass tensor]
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### 3. Selected input files.

WARNING : as of ABINITv8.6.x, the list of input files provided in the specific section of the topics Web pages is still to be reviewed/tuned. In some cases, it will be adequate, and in other cases, it might be incomplete, or perhaps even useless.
The user can find some related example input files in the ABINIT package in the directory /tests, or on the Web:

tests/v7/Input: t80.in t81.in
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### 4. References.

[Laflamme2016] J. Laflamme Janssen, Y. Gillet, S. Poncé, A. Martin, M. Torrent and X. Gonze, "Precise Effective Masses from Density Functional Perturbation Theory", Phys. Rev. B 93, 205147 (2016).
[Luttinger1955] J.M. Luttinger and W. Kohn, "Motion of Electrons and Holes in Perturbed Periodic Fields", Phys. Rev. 97, 869–883 (1955).
DOI: 10.1103/PhysRev.97.869.
[Mecholsky2014] N.A. Mecholsky, L. Resca, I.L. Pegg and M. Fornari, "Theory of band warping and its effects on thermoelectronic transport properties", Phys. Rev. B 89, 155131 (2014).
DOI: 10.1103/PhysRevB.89.155131.

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