Density functional theory calculations on the
diamond nitrogen-vacancy center
Robin Löfgren, Ravinder Pawar, Sven Öberg and J. Andreas Larsson
Applied Physics, Division of Materials Science, Department of Engineering Sciences and Mathematics, Luleå University of Technology, SE-971 87
Luleå, Sweden
The diamond NV-center
NV-center in bulk diamond, supercell calculations
• Color center containing atomic nitrogen
and a vacancy, situated on neighbouring
vacancy positions.
• Formed by irradiation (creating
negative state is the most well researched
and promising
• Exhibits a zero-phonon line at 1.945 eV
under optical excitation
• The process of optical excitation and
decay results in a preferential occupation
of the Sz = 0 ground state level
NV−N
NV−
1.51
Looking at how the transition energy between
the v and e electronic levels are affected by
placing the donor nitrogen at different distances from the NV-center, as well as different
orientations with respect to the C3 symmetry
axis.
1.5
1.49
1.48
1.47
1.46
1.45
1.56
1.54
1.52
1.5
1.44
7
8
9
10
N−N distance (Å)
11
5
12
6
7
8
N−N distance (Å)
9
10
Figure 5: Transition energy between v and e levels for
N-NV configuration in 512 atom supercell
Figure 2: Transition energy between v and e levels for
NV-N configuration in 512 atom supercell
• Have long spin lattice lifetime
N−NV
NV−
1.58
Transition energy v−e (eV)
• Can be in a neutral or negative state. The
Calculations on the diamond NV-center
placed in a supercell, with a substitutional nitrogen placed a distance from the NV-center,
acting as an electron donor.
Transition energy v−e (eV)
vacancies), followed by annealing (make
vacancies move to nitrogens)
1.52
• The two previous properties makes the
NV-center a promising candidate for
quantum information applications
Our research
• Calculations on supercells and slabs
• Comparing the hybrid HSE06 potential
with the GGA potential PBE
• Interested in applications like a qubit close
• Vienna
ab Initio Simulation Package
(VASP)
• PAW PBE potentials
• Gamma centered k-point grid
• 512 & 216 atom supercells
Symmetry br.
NV−
Transition energy v−e (eV)
changing external conditions
Computational method:
Transition energy v−e (eV)
• Looking at how properties change by
1.58
1.56
1.54
1.52
1.5
1.48
1.46
to a surface, and the NV-center as a
sensor close to a surface
1.62
Side v−e1
1.6
NV−
Side v−e2
1.58
1.56
1.54
1.52
1.5
20
30
40
50
60
Angle from C axis (degrees)
1.48
70
3
3
Figure 3: Transition energy between v and e levels for
symmetry breaking in 216 atom supercell
Distance to donor nitrogen in a
supercell
E
3
E
varying the distance to the electron
donator nitrogen
ms = +-1
ms = 0
2
2
u v e 1w
u2v1e3
5
6
7
N−N distance (Å)
8
9
10
Figure 6: Transition energy between v and e levels for
side configuration in 512 atom supercell. Splitting of
e-levels occurs because of the symmetry breaking
1
• How the electronic levels shift when
4
3
A2
3
groundstate: u2v2e2
E excited state associated with ZPL: u2v1e3
1
• At what distance the NV-center is
C3 axis
”destroyed” (shifting more than 20
percent)
ZPL = 1.945 eV
• Placing donor N on the C3 symmetry axis
or perpendicular (on the side) to C3.
3
Different types of surfaces and
terminations
• (001), (110) and (111) oriented surfaces
A2
V
ms = +-1
u 2 v2 e 2
ms = 0
Figure 4: The groundstate 3A2, the excited state 3E,
and the ZPL corresponding to the v-e transition
Figure 1: Energy levels belonging to the NV-center
Figure 7: The diamond NV-center
investigated
• Terminations include H, F, OH and clean
• Reconstructed surfaces
Surfaces, slab calculations
• Putting a molecule on surface
Table 1: PBE Energies (eV), large diamond slabs with NV defect
HSE06 vs PBE
• DFT underestimates the bandgap
• Using HSE06 to widen the bandgap
• Experimental bandgap of bulk diamond is
5.4 eV
• PBE gives 4.171 eV
Figure 8: (100), (110), and (111) surfaces
• HSE06 gives 5.268 eV
Conclusions and future work
Workfunction: Φ = E vac − f
• N-N distance influence transition energies
• Need to use HSE06 instead of PBE
• Study the NV-center interaction with
0
other diamond defects beside N
Workfunction (eV)
different functionalizations of the surface
Acknowledgements
• Swedish Research Council
• Swedish National Infrastructure for
Computing (SNIC)
I
HPC2N
I
PDC
I
NSC
Electrostatic Potential (eV)
• Study how the NV-center interact with
-5
-10
-15
-20
0
50
Distance (Å)
100
Surface
Termination N-N dist. (Å)
100,
Clean
4.2979
360 atoms,
5.0486
20 layers
8.8741
H term.
4.2979
5.0486
8.8741
F term.
4.2979
5.0486
8.874
110,
Clean
4.374
384 atoms,
5.052
14 layers
9.108
H term.
4.374
5.052
9.108
F term.
4.374
5.052
9.108
111,
Clean
4.950
384 atoms,
6.322
14 layers
7.695
H term.
4.950
6.322
7.695
F term.
4.950
6.322
7.695
Figure 9: Workfunction for a small 16-carbon atom F-terminated
(110)-slab
References
H. Pinto, R. Jones, D.W. Palmer, J.P. Goss, Amit K. Tiwari, P.R. Briddon, Nick G. Wright, Alton B. Horsfall, M.J Rayson, S. Öberg, Phys. Rev. B 86 045313 (2012)
H. Pinto, R. Jones, D.W. Palmer, J.P. Goss, P.R. Briddon, S. Öberg, Phys. Status Solidi A 208 No. 9 2045-2050 (2011)
J.A. Larsson, P. Delaney, Phys. Rev. B 77 165201 (2008)
Energy gap v-e
3.150
3.052
3.076
3.700
3.922
3.6392
1.501
1.466
1.377
1.547
1.497
1.418
2.613
2.541
2.572
4.2432
4.2584
3.7304
1.525
1.419
1.314
1.667
1.540
1.458
2.948
2.918
2.919
3.494
3.775
3.755
1.636
1.419
1.427
1.723
1.413
1.427
Workfunction (up) Workfunction (down)
1.896
2.881
1.894
2.892
1.858
2.901
2.023
1.965
2.441
1.810
1.992
1.997
3.084
2.393
2.866
2.615
2.281
3.155
2.367
2.367
2.345
2.377
2.410
2.410
1.931
2.048
2.016
1.948
2.200
1.803
3.128
2.623
2.840
2.841
2.191
3.379
4.839
4.780
4.769
4.782
4.764
4.944
1.445
1.565
1.308
1.348
1.391
1.431
4.409
5.859
5.183
6.080
5.143
6.012