Installation

DiracBilinears.jl can be installed with the Julia package manager:

julia -e 'import Pkg; Pkg.add("DiracBilinears")'

Usage

Spatial distribution

The following files are required:

• seedname.scf.in (The input file for scf calculation.)
• seedname.nscf.in (The input file for nscf calculation.)

Before evaluation of the bilinears, you need to perform DFT calculations by Quantum ESPRESSO to obtain the Bloch functions.

QE/bin/pw.x < seedname.scf.in > seedname.scf.out
QE/bin/pw.x < seedname.nscf.in > seedname.nscf.out

To compute the spatial distribution of electron chirality, use the following commands:

using DiracBilinears
τz = calc_density(calc="τz", qedir="$outdir/seedname.save")

Here, qedir should be set to the output directory from the Quantum ESPRESSO calculation, which contains the Bloch wave functions. The variable $outdir corresponds to the directory specified in the nscf input file. You can select the physical quantity to calculate by specifying the calc option. The available options are listed in the table below.

You can generate the xsf file for XCrySDen plot after the calc_density() calculation:

write_density(τz; qedir=QEDIR, savefile=FILENAME)

The file extension of FILENAME must be set to ".xsf".

Wannier matrix element

The following files are required:

• seedname.scf.in (The input file for scf calculation.)
• seedname.pw2wan.in (The input file for pw2wannier90.x.)
• seedname.win.ref (The reference file for generating the input file of Wannier90.)
• conf.toml (The configuration file for wan2respack.)

For the Wannier matrix elements, you first need to perform DFT calculations using Quantum ESPRESSO to obtain the Bloch functions. You can do this by running:

QE/bin/pw.x < seedname.scf.in > seedname.scf.out

After completing the scf calculation, you can generate the Wannier functions using Wannier90 and wan2respack (for more information, see the GitHub page of wan2respack). First, run:

python Wan2respack/bin/wan2respack.py -pp conf.toml

This command will generate an input file seedname.nscf_wannier.in. In this file, please replace calc="scf" with calc="nscf". Next, calculate the Wannier functions by running:

QE/bin/pw.x < seedname.nscf_wannier.in > seedname.nscf_wannier.out
Wanier90/wannier90.x -pp seedname
QE/bin/pw2wannier90.x < seedname.pw2wan.in > seedname.pw2wan.out
Wanier90/wannier90.x seedname
python Wan2respack/bin/wan2respack.py conf.toml

To compute the matrix elements, you need to specify the paths of two directories, "dir-wfn-full" (referred to as WFNDIR) and "dir-wan" (referred to as WANDIR). These directories are generated by the wan2respack calculation. To calculate the matrix elements of electron chirality, use the following commands:

using DiracBilinears
rs, degen = calc_rgrid(rfile=FILENAME)
τz = calc_wannier_matrix(calc="τz", rgrid=rs, wfndir=WFNDIR, wandir=WANDIR)

Please set rfile to the input file of Wannier90 or the input file of scf calculation. You can choose the type of calc from the table shown below.

The Wannier matrix elements can be saved to a text file using the following command:

write_wannier_matrix(τz, rs; savefile=FILENAME)