Fermi Surfaces

XCrysDen can plot Fermi surfaces if presented with a .bxsf file. From version 2.34, c2x can generate such files. An alternative visualisation program, which can also read .bxsf files, is FermiSurfer. It is used in the Quantum Espresso example below.

XCrysDen needs band eigenvalues on a regular grid across the whole unit cell, and the grid must include the origin. DFT codes generally use symmetry to reduce the number of kpoints at which they need to perform calculations, and so the main work of c2x is to take eigenvalues from a reduced set of kpoints and to use the symmetry operations to regenerate the full grid.

High quality Fermi surfaces need a fine grid, and thus many k-points. Arguably this is best achieved through sophisticated interpolation schemes, such as that used by Wannier90. However, there is still some utility in cruder approaches...

Most DFT codes can find the electronic groundstate using a (relatively) small number of kpoints, and then freeze the resulting charge density, and hence potential, and calculate eigenvalues more rapidly using this frozen potential.

Note that c2x makes no attempt to re-order bands to take account of crossings. However, if one is considering the Fermi surface formed by all bands together, this is of no consequence at all.

Note also that if XCrysDen shows a window which looks like

XCrysDen Window

Then the window has become confusingly truncated, and one should resize it by pulling down the bottom considerably. (Click on the above image for the extended version.)

Al Fermi surface

Fermi surface of Aluminium

ScB2 Fermi surface

Fermi surface of Scandium Boride