mstar

Effective mass calculation with DFT using a perturbation theory. Currently supported codes:

• WIEN2k
• VASP

It is written in Fortran and intended for Linux OS

Current Version

Version Oct 13, 2021

Version Mar 24, 2021 (+gfortran compatibility)

Installation:

First clone the GitHub repository

$ git clone https://github.com/rubel75/mstar

WIEN2k compatibility note: The format of the case.mommat2 file has slightly changed in v20.1 to enable calculations for the number of bands greater than 9999. This mstar code is compatible with these changes (a new not fixed format). If you would like to use this code in conjunction with WIEN2k prior to v20.1, you need to comment/uncomment two lines in mstar/read_mommat_pij.f90 file making the following changes before compiling the code:

    READ(cline,'(3X,2I4,6E13.6,F13.8)',ERR=20) bii ,bjj, & !...
        p1_Re, p1_Im, p2_Re, p2_Im, p3_Re, p3_Im, dEij(bii,bjj)
    
    ! WIEN2k after May 2020 (the case.mommat2 file is not a fixed format)
    !READ(cline,*,ERR=30) bii ,bjj, & !...
    !    p1_Re, p1_Im, p2_Re, p2_Im, p3_Re, p3_Im, dEij(bii,bjj)

The makefile is set up for Intel Fortran compiler ifort and Intel MKL. (To compile with gfortran you need to uncoment corresponding FC, FCFLAGS, and FLFLAGS variables in the makefile). To compile, simply execute

$ cd mstar; make

Execution

First, you need to perform a standard SCF (self-consistent field) calculation and generate a file that contains optical matrix elements (case.mommat2[up/dn] in WIEN2k or WAVEDER in VASP). Tips on how to do this can be found at this Wiki page. Once the file is ready, execute

x mstar [-up/-dn] [-settol 1.0e-5] # if you use the version built into WIEN2k starting with v20.1

/path/to/mstar/mstar case.mommat2[up/dn] [1e-5] # if you use this GitHub version and WIEN2k (see the compatibility note above)

/path/to/mstar/mstar WAVEDER [1e-5] # VASP

Options:

• [-up/-dn] tells mstar to read case.mommat2[up/dn] files (needed for spin-polarized calculations or calculations with spin-orbit coupling).

• [-settol 1.0e-5] or [1e-5] is (optional) degeneracy energy tolerance [Ha], which is max dE for 2 states to be considered as degenerate (default value is 1.0e-6 Ha). Eigenvalues of states that are physically expected to be degenerate (for example light and heavy holes in GaAs at Gamma point) are not exactly the same for numerical reasons. If we treat them as non-degenerate states, a large error will occur due to the term p^2/dE when dE -> 0. These states need to be "bundled" together and treated as degenerate. It is recommended to inspect eigenvalues (in the case of GaAs it will be the top valence bands) and evaluate the energy difference dE between states that should be treated as degenerate. Then set the tolerance slightly greater than this value.

Output

minv_ij.dat - contains elements of the (m0/m*_ij) tensor for each k point and band.

minv_c.dat - conductivity effective mass (m0/m*_c).

minv_pr.dat - contains principal components of the inverse eff. mass tensor eig(m0/m*_ij).

minv_d.dat - density of states inverse effective mass m0/m*_d = m0/(m_1 *m_2 *m_3)**(1/3).

The file headers explain the content.

Documentation

For tutorials and tips on how to generate a file that contains optical matrix elements (case.mommat2[up/dn] in WIEN2k or WAVEDER in VASP), please refer to the Wiki page.

Examples of "real life" applications can be found in arXiv:2007.03816 [cond-mat.mtrl-sci]

Please communicate your feedback, support or feature requests via WIEN2k mailing list

Reference

If you find the results useful and publishable, we will appreciate citing the following paper:

• O. Rubel, F. Tran, X. Rocquefelte, and P. Blaha "Perturbation approach to ab initio effective mass calculations" Comp. Phys. Commun. 261, 107648 (2021).