Dear VASP users and developers,
I am investigating the effect of an out-of-plane external electric field on the van Hove singularities of bilayer WTe2.
My main observation is that the energy position of a prominent van Hove singularity, located at approximately 0.482 eV above the Fermi level, remains almost unchanged when the applied electric field is increased from 0 to 0.5 eV/Å. More generally, the calculated DOS curves with and without the electric field are nearly identical within the energy range from −1 to 1 eV relative to the Fermi level.
I would like to understand whether this insensitivity of the van Hove singularity is physical or is caused by my computational setup.
Structure
My system is a freestanding bilayer WTe2 slab with approximately 25 Å of vacuum along the \(z\) direction. The two layers are related by a mirror plane in the zero-field structure. The POSCAR is
Code: Select all
double layer WTe2 with 25 Angstrom vacuum
1.00000000000000
6.3147687911999997 0.0000000000000000 0.0000000000000000
0.0000000000000000 3.4924850464000001 0.0000000000000000
0.0000000000000000 0.0000000000000000 37.1424511712979000
W Te
4 8
Direct
0.8192838689305688 0.7500000000000000 0.3896283284005936
0.1805168977468270 0.2500000000000000 0.3950315050160000
0.1805168827468293 0.2500000000000000 0.6049690276618290
0.8192838689305688 0.7500000000000000 0.6103721807289790
0.0790958088588738 0.7500000000000000 0.4479115959754843
0.5733355090055099 0.2500000000000000 0.4323619199776256
0.4268879895381232 0.7500000000000000 0.3526481351558931
0.9208800229200804 0.2500000000000000 0.3365421399452359
0.9208799629200826 0.2500000000000000 0.6634578600547641
0.4268879595381279 0.7500000000000000 0.6473518404838330
0.5733355090055099 0.2500000000000000 0.5676380321138499
0.0790957568588766 0.7500000000000000 0.5520883796642591
I used the PAW-PBE potentials for W and Te.
Calculation Procedure
For each electric-field strength, my calculation procedure was:
1) A self-consistent static calculation was performed using a Γ-centered 6 * 12 * 1 k-mesh.
2) A non-self-consistent DOS calculation was then performed using ICHARG = 11 and a Γ-centered 24*48*1 k-point mesh.
3) For the zero-field calculation, LDIPOL was enable and EFIELD was set to zero.
4) For non-zero EFIELD, a CHGCAR from the zero EFIELD calculation was used, and ICHARG = 1 was set.
5) no SOC is included. The field is applied along z axis.
6) The Fermi energy is set as zero.
INCAR file for the non-self-consistent DOS calculation
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SYSTEM = bilayer_WTe2_DOS
# Fixed charge density from the preceding SCF calculation
ICHARG = 11 # for SCF this is 1 or 0
# Electronic structure
ENCUT = 450
EDIFF = 1E-6
PREC = Accurate
LREAL = .FALSE.
NELM = 200
# Static calculation
NSW = 0
# Occupations and DOS
ISMEAR = -5
SIGMA = 0.2
LORBIT = 11
EMIN = -2.0
EMAX = 2.0
NEDOS = 2000
# Parallelization
KPAR = 4
NCORE = 6
# Mixing
AMIX = 0.2
BMIX = 0.0001
AMIN = 0.02
# External electric field
LDIPOL = .TRUE. # always enable
IDIPOL = 3
DIPOL = 0.5 0.5 0.5
EFIELD = 0.10 # set to 0 for zero EFIELD calc.
ISYM = -1 # symmetry disabled
Results
Despite increasing the electric field from 0 to 0.5 eV/Å, I observe very little change in the total DOS near the Fermi level. In particular, the position of my target van Hove singluarity located at 0.482 eV remains at nearly the same energy for all tested field strengths.
I also observe a field-induced dipole moment. For example, for EFIELD = 0.10 eV/Å, the OUTCAR contains:
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DIPCOR: dipole corrections for dipol
dipolmoment 0.000000 0.000000 0.173630 electrons x Angstroem
dipol+quadrupol energy correction -0.003330 eV
The calculated dipole moment increases with the applied field and appears to saturate near 0.173 electron Å at approximately EFIELD = 0.10 eV/Å. Therefore, the charge density appears to respond to the field, but the position of the van Hove singularity relative to the Fermi level changes very little. The attached figure compares the DOS in the range from −1 to 1 eV. The same energy and DOS scales are used for all fields.
Questions
1. Are EFIELD, LDIPOL, IDIPOL, and DIPOL being used correctly for this freestanding bilayer slab?
2. Should the electric field be included self-consistently in a separate SCF calculation for every field strength before performing the ICHARG = 11 DOS calculation?
3. Is it physically reasonable for the van Hove singularity at approximately 0.482 eV above the Fermi level to remain almost unchanged, even though the induced dipole moment increases with the field?
4. This is not about electric field, but does using an odd or even number of k points matter (in terms of determining van Hove singularity from Fermi surface calculations)?
I am using VASP 6.5.1.
Thank you very much for your help.
Best regards,
Fan Wu