6: Copper — Fermi surface¶

Outline: Obtain MLWFs to describe the states around the Fermi-level in copper
Directory: tutorials/tutorial06/ Files can be downloaded from here
Input Files
- copper.scf The pwscf input file for ground state calculation
- copper.nscf The pwscf input file to obtain Bloch states on a uniform grid
- copper.pw2wan Input file for pw2wannier90
- copper.win The wannier90 input file
Run pwscf to obtain the ground state of copper
Terminal
```
pw.x < copper.scf > scf.out
```
Run pwscf to obtain the Bloch states on a uniform k-point grid
Terminal
```
pw.x < copper.nscf > nscf.out
```
Run wannier90 to generate a list of the required overlaps (written into the copper.nnkp file).
Terminal
```
wannier90.x -pp copper
```
Run pw2wannier90 to compute the overlap between Bloch states and the projections for the starting guess (written in the copper.mmn and copper.amn files).
Terminal
```
pw2wannier90.x < copper.pw2wan > pw2wan.out
```
Run wannier90 to compute the MLWFs.
Terminal
```
wannier90.x copper
```

Inspect the output file copper.wout.

Use Wannier interpolation to obtain the Fermi surface of copper. Rather than re-running the whole calculation we can use the unitary transformations obtained in the first calculation and restart from the plotting routine. Add the following keywords to the copper.win file:
Input file
```
restart = plot

fermi_energy = [insert your value here]

fermi_surface_plot = true
```
and re-run wannier90. The value of the Fermi energy can be obtained from the initial first principles calculation. wannier90 calculates the band energies, through Wannier interpolation, on a dense mesh of k-points in the Brillouin zone. The density of this grid is controlled by the keyword fermi_surface_num_points. The default value is 50 (i.e., 50\(^3\) points). The Fermi surface file copper.bxsf can be viewed using XCrySDen, e.g.,
Terminal
```
xcrysden --bxsf copper.bxsf
```

Plot the interpolated bandstructure. A suitable path in k-space is

Input file

begin kpoint_path
G 0.00 0.00 0.00 X 0.50 0.50 0.00
X 0.50 0.50 0.00 W 0.50 0.75 0.25
W 0.50 0.75 0.25 L 0.00 0.50 0.00
L 0.00 0.50 0.00 G 0.00 0.00 0.00
G 0.00 0.00 0.00 K 0.00 0.50 -0.50
end kpoint_path

Further ideas¶

Compare the Wannier interpolated bandstructure with the full pwscf bandstructure. Obtain MLWFs using a denser k-point grid. To plot the bandstructure you can use the pwscf tool bands.x or the small FORTRAN program available at http://www.tcm.phy.cam.ac.uk/~jry20/bands.html.
Investigate the effects of the outer and inner energy windows on the interpolated bands.
Instead of extracting a subspace of seven states, we could extract a nine dimensional space (i.e., with \(s\), \(p\) and \(d\) character). Examine this case and compare the interpolated bandstructures.