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.

Note

We encourage you to attempt this tutorial on your own first, but a worked solution is available here.