This is a rather interesting case. How large are the super cells you used? and what was the k-pointset used in both cases? Were they Gamma-centered or not? How well are you energies converged with regard to the k-pointset? 30meV is not that much.

Futhermore it would also be interesting to show the k-point path used, A,H,K,L,M have not that much meaning, and from the second bandstructure I think you also took lines orthogonal to the plane of the MoS2.

First suggestions would be: 

* provide some additional information (the actual K-points file of you band calculation?, I think A and G may be the same points)

* check if your energies are sufficiently converged (

Clearly your kpoint nomenclature is jumbled. These are two realizations of the very same system; as it is an insulator, even with different scf grids you should not see major changes. Of course such things do happen, but under perturbation. In graphene under shear+tensile strain you do see that, besides a tiny gap opening, the Dirac points move away from the zone corners. 

Thanks, Danny and Darshana! It’s an interesting case indeed.

Please find the POSCAR and the KPOINT files for both the cases appended below. Yes, geometry optimization using a 25x25x1 Gamma-centred k-mesh had preceded the static band structure calculations. EDIFF=1E-6 and a vacuum thickness of 16 Å has been used in the calculations. Band structures have been plotted with respect to the Fermi energy obtained using “grep E-fermi OUTCAR”.

Thanks again.

Slide 1

___________________________________________________________________

MoS2 sheet

1.00000000000000

3.1899999999999999 0.0000000000000000 0.0000000000000000

-1.5950000000000000 2.7626210000000002 0.0000000000000000

0.0000000000000000 0.0000000000000000 19.0000000000000000

Mo S

1 2

Direct

0.6666659999999993 0.3333340000000007 0.5014170000000036

0.3333330000000032 0.6666669999999968 0.4192464800507724

0.3333330000000032 0.6666669999999968 0.5835875199492276

___________________________________________________________________

KPOINTS

___________________________________________________________________

Kpoints along high symmetry lines

30 ! 30 intersections

Line-mode

rec

0.500 0.000 0.000 ! M

0.000 0.000 0.000 ! Gamma

0.000 0.000 0.000 ! Gamma

0.333 0.333 0.000 ! K

0.333 0.333 0.000 ! K

0.500 0.000 0.000 !M

___________________________________________________________________

Slide 2

___________________________________________________________________

MoS2-3x2

1.00000000000000

9.5699996947999999 0.0000000000000000 0.0000000000000000

0.0000000000000000 11.0504999160999997 0.0000000000000000

0.0000000000000000 0.0000000000000000 19.0000000000000000

Mo S

12 24

Direct

0.0000000000000000 0.1666712707109269 0.5000000000000000

0.1666643199088551 0.4166745088183256 0.5000000000000000

0.3333356800911449 0.1666745088183256 0.5000000000000000

0.5000000000000000 0.4166712707109269 0.5000000000000000

0.6666643489088538 0.1666745088183256 0.5000000000000000

0.8333356510911462 0.4166745088183256 0.5000000000000000

0.0000000000000000 0.6666712997109258 0.5000000000000000

0.1666643199088551 0.9166745378183244 0.5000000000000000

0.3333356800911449 0.6666745378183244 0.5000000000000000

0.5000000000000000 0.9166712997109258 0.5000000000000000

0.6666643489088538 0.6666745378183244 0.5000000000000000

0.8333356510911462 0.9166745378183244 0.5000000000000000

0.0000000000000000 0.3333287786091873 0.3959072294920014

0.1666667352985219 0.0833280353585152 0.3959061980588797

0.0000000000000000 0.3333287786091873 0.6040927415079997

0.1666667352985219 0.0833280353585152 0.6040937729411214

0.3333332647014780 0.3333280423585123 0.3959061980588797

0.5000000000000000 0.0833287716091903 0.3959072294920014

0.3333332647014780 0.3333280423585123 0.6040937729411214

0.5000000000000000 0.0833287716091903 0.6040927415079997

0.6666667642985208 0.3333280423585123 0.3959061980588797

0.8333332357014792 0.0833280353585152 0.3959061980588797

0.6666667642985208 0.3333280423585123 0.6040937729411214

0.8333332357014792 0.0833280353585152 0.6040937729411214

0.0000000000000000 0.8333287496091885 0.3959072294920014

0.1666667352985219 0.5833280133585134 0.3959061980588797

0.0000000000000000 0.8333287496091885 0.6040927415079997

0.1666667352985219 0.5833280133585134 0.6040937729411214

0.3333332647014780 0.8333280133585134 0.3959061980588797

0.5000000000000000 0.5833287496091885 0.3959072294920014

0.3333332647014780 0.8333280133585134 0.6040937729411214

0.5000000000000000 0.5833287496091885 0.6040927415079997

0.6666667642985208 0.8333280133585134 0.3959061980588797

0.8333332357014792 0.5833280133585134 0.3959061980588797

0.6666667642985208 0.8333280133585134 0.6040937729411214

0.8333332357014792 0.5833280133585134 0.6040937729411214

___________________________________________________________________

KPOINTS

___________________________________________________________________

Kpoints along high symmetry lines

30 ! 30 intersections

Line-mode

rec

0.000 0.000 0.500 ! A

0.000 0.000 0.000 ! Gamma

0.000 0.000 0.000 ! Gamma

0.500 0.000 0.000 !M

0.500 0.000 0.000 !M

0.500 0.000 0.500 !L

0.500 0.000 0.500 !L

0.000 0.000 0.500 ! A

0.000 0.000 0.500 ! A

0.333 0.333 0.500 ! H

0.333 0.333 0.500 ! H

0.333 0.333 0.000 ! K

0.333 0.333 0.000 ! K

0.000 0.000 0.000 ! Gamma

___________________________________________________________________

Thanks, Prof. Vincenzo, for sharing the facts about perturbed graphene, when it is under tensile/shear strain. Interestingly, on unperturbed MoS2, we observe significant changes in the band structure simply upon changing the supercell symmetry.

Yes, geometry optimization using a 25x25x1 Gamma-centred k-mesh had preceded the static band structure calculations. EDIFF=1E-6 and a vacuum thickness of 16 Å has been used in the calculations. Band structures have been plotted with respect to the Fermi energy obtained using “grep E-fermi OUTCAR”.

In good practice you will need 3 calculations:

1) relaxation

2) static SCF

3) BANDS/DOS calculation

(this is because there are some inconsistencies in the CHGCAR/CONTCAR of VASP for a relaxation)

[--> check out the VASP manual, or my tutorial: http://dannyvanpoucke.be/students/ ]

Your Fermi-level you should get from your DOSCAR file (line 6, value 4, for a non-spin polarized calculation, for a spin polarized one, check the DOS) from a DOS calculation or the SCF (NOT the bandstructure calculation)

Regarding your structures: If I am correct, your S atoms stick out of the C-plane by 1.5A in the Z direction in the first case, while they stick 2A aout of the surface in the second case...this is clearly not the same system, so ofcourse you will get a different bandstructure.

Danny

PS: not being into the MoS2 business, are you sure the S should stick out? As it is a graphene topology?

Thanks very much, Dr. Danny.

Yes, in the MoS2 monolayer nanosheet, the S atoms stick out of the central Mo-plane on either side. This graphene-like structure is well documented [Ref: the attached paper (file: Published.pdf) and the references therein]. In the slides, the top view of the sheet has been shown.  

We have been following all those three steps in calculating the band structures.

The E_F obtained using “grep E-fermi OUTCAR” is found to be the same as the one occurring in line 6, value 4 in the DOSCAR file.

Please find two files attached herewith. The band structure in Slide 1, sent earlier, agrees with the Fig. 2 of archived.pdf file. While in Published.pdf, the band structure (Fig. 2) has been plotted for a different supercell symmetry and the corresponding set of k points.

The differences in the band structures in the two slides is attributable to the differences in the two structures (S atoms sticking out of the central Mo-plane by different proportions in the two structures differing in symmetry).

We will do a recheck with the same structure for the two different supercell symmetries.

Thanks again.

Best Regards,

"The E_F obtained using “grep E-fermi OUTCAR” is found to be the same as the one occurring in line 6, value 4 in the DOSCAR file."

I that is the case, the top of your valence band should coincide with the Fermi level. If that is not the case, you did not find the valence-band maximum, so you can not state to have found the (in)direct band gap.

Thanks, Dr. Danny. 

I'm aware. I understand. However, what we have been getting for the optimized structure in Slide 1 is as follows.

E_F from DOSCAR = -1.95999992 eV

E_F from “grep E-fermi OUTCAR” = -1.96 eV

The script bandgap.pl in vtstscripts-895 finds the bottom of the conduction band at the k-point K at energy -0.7657 eV. While it locates the top of the valence band at the Gamma point at energy -2.3990 eV. It overlooks the k-point K (infinitesimally close to the valence band edge) at energy -2.4127 eV, which is nearly degenerate with the Gamma point. The energy difference between these two k points at the valence band edge is 0.0140 eV.

Therefore, 

Indirect band gap calculated between Gamma and K = 1.633 eV

Direct band gap calculated between the two K’s = 1.6475 eV

Darshana,

The structures in slides 1 and 2 are basically the same with minor differences, as pointed out by Dr. Danny. In slide 1 supercell, both the x and y directions are zig-zag and therefore, equivalent. While the x and the y directions are zig-zag and arm-chair respectively in the structure on Slide 2. 

So I can correctly conclude that the Efermi indicated in your slides is just placed at a wrong position(in both pictures). Are you doing spin-polarized calculations?

Secondly, I would not call the differences between the structures minor, especially if they lead to such different band-structures. Now I am getting rather confused with your original question. You have two rather different geometries, and one of them gives good agreement with experiments, while the other does not. Assuming the experiment does not know which geometry they are looking at, this means you now have an initial computational model for the experimental system. Your second structure, is nice, but has no  relation to the experimental system. What you could do now is (for example) simulate STM images of both structures and compare to the experimental STM images of the system.

Using odd sized k-grid and ISMEAR=-5 has corrected the position of E_F.

Tetrahedron method is recommended for semiconductors and insulators for small supercells. While odd sized k-mesh is more efficient for n > 8.

Please find the attached file. 

Gamma-centred  23x23x5 and 21x13x5 k-mesh have been used respectively for the structures in Slides 1 and 2, corresponding to a k spacing of 0.1 1/Ang.    

E_F for both the slides are found to coincide.

I will be happy to calculate/simulate the STM images. 

Sorry for the differences in the earlier structures. I should have provided the optimized CONTCAR files.