Eigenstate occupancy arrays

[Quantamania]

How are the array data for eigenstate occupancy generated?  This choice only has one parameter and generates arrays for all of the Bloch eigenstates, including virtual ones.  In my results for graphene and mixed h-BN/graphene bilayers in supersized cells, I find that nearly all of the numbers in the occupied orbital arrays are 2, but one of the values differs significantly from all of the others (by as much as 0.025-0.03 qe).  This does not happen with monolayer h-BN, as it is an insulator.  Does this particular value have any meaning?

[Anders Blom]

The function to compute eigenstate occupations for bulk systems is not very useful, since it uses the SCF k-point sampling. If you are really interested in the occupation of a particular eigenstate (n,k) where n is the band index and k the wave vector, just compute its energy E via the band structure functionality and apply the Fermi distribution.

[Quantamania]

Thanks for the reply.

In the example of graphene, I have an array of numbers at eigenstate #3 (its HOMO).  In this array, all of the numbers except for one, are 2.  The lone outlier is around 1.97 qe, and the band energy for this eigenstate is around 0.0001 eV below the Fermi energy.  Only at K (1/3, 1/3, 0) does this condition arise for graphene.  These results were obtained using an electron temperature of 300 K (for the Fermi-Dirac distribution).  With the other eigenstates that are occupied, I do not find an outlier k-point value anywhere.

What is the physical meaning of a single k-point showing significantly less eigenstate occupancy than other k-points adjacent to it?

[Anders Blom]

This is just a numerical thing, and nothing to be concerned about. This is the only state which is really close to the Fermi level, and thus the only one which can deviate from two, really. I'm guessing it's not entirely that all occupations in the array are 2, there will be many zeros too. These might however on closer inspection have a small positive part if you print them with enough decimals, and they will add up to 0.03 (if you consider all k-points) to balance the 1.97, to keep the total charge an integer. States below the Fermi energy only have exact occupation 2 at zero temperature.

I don't quite understand your reference to the k-point being (1/3,1/3,0). With Monkhorst sampling it is unlikely you hit exactly this point unless you use thousands of k-points.

[zh]

Plot the band structures of graphene and monolayer BN along the high symmetry directions, and also mark the Fermi level with transverse line in these plots. Then you can easily find out which eigenvalue for each interested k-point is occupied or unoccupied.