In my DFT calculations of sodium bismuth titante (Na0.5Bi0.5TiO3-NBT) (primitive unit cell with 10 atoms), I found discontinuity in the band structure at Gamma point (High symmetry K-point). When compared my results with others, they got this discontinuity at Z point (other high symmetry K-point). Here, I am posting this question to know about what is the cause of discontinuity in the band structure ? If it is occurring at Gamma point, how can I demonstrate whether my compound is direct or indirect band gap material ?
Short answer: bug(s) in at least one of the codes you are using, which might be the code used for plotting.
Dear Behnam Farid,
I am using quantum espresso for my DFT calculations. The codes and input files used are working good for other similar systems.
Can you please elaborate your answer more ? If the bug (s) is causing this discontinuity, can I know where it is exactly from ??
Thank you and waiting for your acknowledgement.
Santosh Kumar Behara : Irrespective of the type of package you are using, and irrespective of how well this package does for other systems, the energy bands close to the Γ point make no sense. From my past experience (several decades ago, when one wrote one's own codes) I do know that because of some approximations that one can implement in the calculation of the pseudopotentials (to bypass use of computationally costly hyperbolic sine and cosine functions in the calculations), calculations are prone to go wrong in particular in the vicinity of the Γ point. Be it as it may, since I have no expertise with espresso, the particulars of the error at hand should be considered by someone who has experience with this package.
Ps. The problem can also be due to use of different cut-off energies in approaching the Γ point from different directions. For instance, the bands in the direction of Z-Γ could be converged in regard to the cut-off energy, and those in the direction of F-Γ not. Having said that, I do wonder why the discontinuities are so pronounced even in the low-lying bands; these converge earliest as functions of the cut-off energy.
Dear Santosh,
Band can never be discontinuous at Gamma point or any high symmetry point. There is something very seriously wrong in your energy level calculation. May be you increase the plane wave-vector K cutoff further and plot again. Make sure that you have used enough real mesh cutoff as well during your charge density calculation.
Dear Santosh,
This doesn't look right at all, I can't see how this bandstructure could make sense even if your cut-off energy and k-point grid (for the ground state) were under-converged. I suppose if you had a really low cut-off energy, at the zone edges you might find the basis set loses a significant number of states (since the cut-off is on |G+k|^2 and at the edge k is quite large, ~G/2) -- but this should be a very small effect on the computed eigenenergies.
Did you definitely compute all the states across the Brillouin zone with the same parameters? Do you have the same number of states at each k-point? Have you looked at the optical matrix elements (essentially dE/dk) to see if they are sensible?
If you send me your input geometry (atomic positions, lattice and, ideally, k-point sampling and the k-points for your band-structure) I'll try it with my own code (CASTEP) and see if I can reproduce the issue. Which XC functional are you using?
All the best,
Phil Hasnip
(CASTEP developer)
Dear Philip James and Behnam Farid,
Thank you for your valuable suggestions and inputs. Myself, I resolve this issue by taking suitable high symmetry k-points in the bands.x calculation.
I did all these calculations in quantum-espresso code.
Thanks once again for your discussions.
Santosh Kumar Behara : You are welcome. It would have been interesting to know the cause of the problem: what error, whether by you or by the code, had given rise to the problem?
Dear Behnam Farid,
Manually, I choose wrong Irreducible Brillouin Zone (IBZ) path (high symmetry K-points) for my rhombohedral crystal structure. So, I got this error. After that, I allow my quantum espresso code to choose automatic right IBZ path for rhombohedral cell. This sort out my actual computational problem.
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