Bands, DOS, and the Fermi surface
*********************************

BAND DOS Fermi surface Spin-orbit coupling

In this tutorial we consider a metallic system for which the spin-
orbit effect is important.

The system under study is cubic TlBi. As both Tl and Bi are heavy
elements we use the Spin-Orbit level for relativity. As this is a
metal we also take a look at the fermi surface.


Step 1: Load the geometry
=========================

Here we will use the standard geometry as it is available from
**AMSinput**.

   Start **AMSinput**
   Search for TlBi  [image: Search][image]
   Click on the only hit under "Crystals"

The editor should now show the atoms of the first unit cell as well as
the lattice vectors:

   [image]


Step 2: Calculation
===================

With the system loaded it is time to setup the calculation

   In the **Main** panel:
   **Relativity → Spin-Orbit**
   Tick "Yes" next to **Calculate PDOS** and **Calculate band structure**

   [image]

   In the **Properties → Band Structure** panel:
   Tick **Calculate Fermi surface**

   [image]

   (Optionally) In the **Details → Expert BAND** panel:
   Search for FermiSurface
   Scroll down to where you see the keywords shown in a black rectangle in the image below
   Set **KInteg for symmetric grid** to 9, providing a more smooth Fermi surface compared to the default of 5 for this system.

   [image]

   **File → Save As...**
   Save e.g. under "BandsDosFermiSurface.ams"

Now run the calculation with **File → Run**.  This calculation may
take a few minutes.

Note:

  The results shown here have been calculated with k-space quality
  good. This is normally recommended for metallic systems. In this
  case, however, the band structure is almost unaffected.


Step 3: Inspecting the results
==============================

After the calculation is complete, open the results with **SCM → Band
Structure**

   [image]

In the picture the default ranges for the DOS axis have been changed
to better see the partial DOS contributions.

   Try to get a similar picture
   Try the scroll wheel when hovering over the x-axis (scale x-axis)
   Try the scroll wheel when hovering over the y-axis (scale y-axis)
   Try dragging the picture (shift the origin)

Once you have achieved this there are a few interesting things to
observe. First of all you see a list of angular momentum labels. While
normally these are "s,p,d,f", now there are more choices due to the
spin-orbit coupling. All levels (except for s) have been split in two.
For instance the p shell is split into a p1/2 and a p3/2 level. This
is true both for the "fat band" coloring of the band structure curves,
and the (partial) dos contributions.

You can also see that the fermi level (horizontal black line) crosses
some bands, and we are dealing with a metal.

Another interesting thing is that in the left most panel the Fermi
surface is shown.

   Try to zoom in the Brillouin Zone area with the scroll wheel
   Rotate the Fermi surface by clicking and dragging

All the three the parts, from left to right: Fermi surface, Band
Structure and DOS are related.

The DOS at a certain energy can be regarded as a sum of the band
structure plot, counting the crossings at that energy. The purple
colored peak at -18 eV is clearly caused by the equally purple band.

   [image]

So both the bands and DOS at this energy have mostly a d3/2 character.
This band has very little dispersion, and it is almost core like. A
bit higher in energy we find the d5/2 band which is more diffuse and
shows more dispersion. It also mixes a bit with s functions.

The fermi surface is an implicit surface defined by where any band has
an energy exactly equal to the fermi energy. From the central panel we
can see that on the path from Gamma to R there are three bands
crossing the fermi level. Two are colored green, and hence of the P3/2
character, while the other one is blue, and of the P1/2 character.

   [image]

   Convince yourself that in the Fermi surface picture there are indeed three crossings on the Gamma to R line.
