How to Calculate and Visualize a Fermi Surface

by Dmitrii Nabok & Caterina Cocchi for exciting carbon

Purpose: Here, it will be shown how you can use exciting to calculate and visualizethe Fermi surface of gold .

### Fermi surface 3D plot

A general input file for generating the Fermi surface of gold should look like this:

```<input>

<title>Gold</title>

<structure speciespath="\$EXCITINGROOT/species" autormt="true">
<crystal scale="7.707">
<basevect> 0.5  0.5  0.0 </basevect>
<basevect> 0.5  0.0  0.5 </basevect>
<basevect> 0.0  0.5  0.5 </basevect>
</crystal>
<species speciesfile="Au.xml">
<atom coord="0.0 0.0 0.0"/>
</species>
</structure>

<groundstate
do="fromscratch"
xctype="GGA_PBE_SOL"
rgkmax="8.0"
ngridk="8 8 8"
nempty="10"
stype="Methfessel-Paxton 1"
swidth="0.01"
>
</groundstate>

<properties>
<fermisurfaceplot nstfsp="6">
<plot3d>
<box grid="40 40 40" >
<origin coord="0 0 0"/>
<point  coord="1 0 0"/>
<point  coord="0 1 0"/>
<point  coord="0 0 1"/>
</box>
</plot3d>
</fermisurfaceplot>
</properties>

</input>
```

Make sure to set \$EXCITINGROOT to the correct exciting root directory in the speciespath attribute using the command

````\$ SETUP-excitingroot.sh`
```

Assuming that you are already familiar with the groundstate block in the input file, we now focus on the properties block:

```...
<properties>
<fermisurfaceplot nstfsp="6">
<plot3d>
<box grid="40 40 40" >
<origin coord="0 0 0"/>
<point  coord="1 0 0"/>
<point  coord="0 1 0"/>
<point  coord="0 0 1"/>
</box>
</plot3d>
</fermisurfaceplot>
</properties>
...
```

The element fermisurfaceplot triggers the calculation of the Fermi surface. The value of the attribute nstfsp indicates the number of bands which are considered to compute the Fermi surface. In this case we choose 6, which also corresponds to the default value for this attribute (see Input Reference). By specifying the element plot3d we are generating a 3D representation of the Fermi surface. For a complete description of the functionality of this element and of its sub-elements refer to the How to visualize Kohn-Sham states.

Execute exciting. An output file FERMISURF.bxsf is generated. It is already suitable for visualization with XCrySDen, by typing:

````\$ xcrysden --bxsf FERMISURF.bxsf >/dev/null 2>&1 &`
```

As a result of the visualization, one should obtain the something similar to the following figure:
##### Exercise
• Plot the Fermi surface for silver and aluminum. Analyze the band structure using the BARGraph tool in XCrySDen. How many bands contribute to the Fermi surface for Ag? How many for Al?