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Hi,

I want to calculate the band structure of a 2D material with an applied electric field in the z-direction. First, I aim to verify if I can reproduce the original band structure with zero electric field applied. To do this, I used the following INCAR file for scf calculation:

ISTART = 0
ICHARG = 2
LORBIT = 11

ISMEAR = 1
SIGMA = 0.03
ENCUT = 400

LSORBIT = .TRUE.
LMAXMIX = 4
ISPIN = 1
SAXIS = 0 0 1
MAGMOM = 9*0

ALGO = Normal
AMIX = 0.1
BMIX = 0.00001
EDIFF = 1E-7

EFIELD = 0.8
IDIPOL = 3
LDIPOL = .TRUE.
DIPOL = 0.00 0.00 0.50

However, this did not reproduce my original results. Could you please help me resolve this issue?

Finally, I would like to calculate the band structure with an applied electric field of 0.8 eV perpendicular to the monolayer.

Could you elaborate please? Can you provide the two sets of input files that you used to produce the two different outputs? If the calculation is very expensive to run, please try to reproduce the effect in a simple cell.

The INCAR file that you provided has already an electric field so I would not expect it to yield the same results as one without.

Hello,

Thank you for your quick response, and I apologize for the confusion. I have set 'EFIELD = 0.0' in the above INCAR file. Here's a detailed explanation of my process:

1. I started with the following INCAR file for the self-consistent field (SCF) calculation of a unit cell of 2D NbSe₂. This gave the correct band structure after non-SCF calculations:

ISTART = 0
ICHARG = 2
LORBIT = 11

ISMEAR = 1
SIGMA = 0.03
ENCUT = 400

LSORBIT = .TRUE.
LMAXMIX = 4
ISPIN = 1
SAXIS = 0 0 1
MAGMOM = 9*0

ALGO = Normal
AMIX = 0.1
BMIX = 0.00001
EDIFF = 1E-7

For the band structure calculation, I defined the desired K-path (M-K-Γ-K’-M’) and modified only the following two flags, leaving everything else unchanged from the initial INCAR file:

ISTART = 1
ICHARG = 11

2. Next, I aimed to calculate the band structure of 2D NbSe₂ with an applied electric field perpendicular to the plane. Before applying a finite electric field, I first attempted to reproduce the original band structure with zero electric field, using the same K-path and following INCAR file for SCF calculation:

ISTART = 0
ICHARG = 2
LORBIT = 11

ISMEAR = 1
SIGMA = 0.03
ENCUT = 400

LSORBIT = .TRUE.
LMAXMIX = 4
ISPIN = 1
SAXIS = 0 0 1
MAGMOM = 9*0

ALGO = Normal
AMIX = 0.1
BMIX = 0.00001
EDIFF = 1E-7

EFIELD = 0.0
IDIPOL = 3
LDIPOL = .TRUE.
DIPOL = 0.00 0.00 0.50

After the SCF calculation, I carried out the band structure calculation, modifying only the same two flags as in case 1, and keeping the rest of the parameters unchanged with the same K-path:

ISTART = 1
ICHARG = 11

However, the results were not same as case 1, and the output showed random curves that were clearly incorrect. Could you advise on what might be wrong with this approach?

3. Finally, I intend to calculate the band structure with an electric field of 0.8 eV/Å applied perpendicular to the monolayer. Could you guide me through the correct steps for this calculation?

Thank you in advance for your help.

If you compute a surface, you should (almost) always apply electrostatic corrections (IDIPOL/LDIPOL) even if you do not want to apply an electric field. Without these VASP will remove any dipole from your cell to achieve a continuous potential, i.e., any system that would have a dipole will be incorrectly described. By activating the corrections, VASP is free to include a discontinuity in the potential so that a dipole can form.

So for your calculation, I would predict that the first calculation has a different electronic configuration because VASP rearranged the electrons such that they cancel out any dipole the ions induce. In the second calculation, you allow for a nonzero dipole moment. You can run

grep dipolmoment OUTCAR

to check that. If this output is nonzero than only the second approach is correct.

Could you please outline the steps for applying an external electric field to a 2D material in the z-direction? I have found the following flags—are there any additional flags that I need to specify to incorporate this effect:

EFIELD = 0.8
IDIPOL = 3
LDIPOL = .TRUE.
DIPOL = 0.00 0.00 0.50

Also, do I need to perform relaxation calculations with these flags before the SCF calculations, or is that unnecessary?

Yes these flags are correct assuming your surface normal is in z direction. DIPOL is not required, VASP will determine automatically where to put the divergence but you can avoid possible issues by setting it manually. Just make sure to have the correct position.

Additionally you may want to look into WRT_POTENTIAL to visualize the potential or LVACPOTAV to get a better plot of the averaged potential.

Regarding relaxation it depends what you want to simulate. If it is a short field pulse like light where the atoms would not have time to adjust not relaxing the structure would be appropriate. If the field is permanent the atoms would relax in reality then computing without relaxation is an approximation that may or may not be justified.