default_nv_model
- default_nv_model(nitrogen_isotope=None, carbon_atom_indices=None, static_field_strength=0.05, interaction=True, **kwargs)
Create a default central spin model based on a nitrogen-vacancy center. The electron spin of the nitrogen-vacancy center is added by default as
'e'. \(^{13}\text{C}\) nuclear spins can be added via thecarbon_atom_indicesargument. The positions of the nuclear spins are used to determine the hyperfine tensors, based on the Ivády Group’s hyperfine dataset.- Parameters:
nitrogen_isotope (
int|None) – Atomic number of the nitrogen isotope (optional, should be14or15).carbon_atom_indices (
List[tuple] |None) – List of (\(n_1\), \(n_2\), \(n_3\), \(n_4\)) tuples.static_field_strength (
float) – Strength of the static field (in \(\text{T}\))interaction (
bool) – Whether interaction is presented or not.**kwargs (
dict) – Additional keyword arguments passed to thedefault_rotating_frame()function, which is responsible for defining the rotating frame.
- Return type:
- Returns:
Default model.
- Raises:
SimphonyError – If invalid nitrogen isotope is given. If invalid carbon nuclear spin indices are given.
Note
The Hamiltonian describes the default NV model (note that our convention for nuclear spin gyromagnetic ratios is different from the standard convention):
\[\begin{split}H =& \underbrace{\gamma_{e} \mathbf{B} \cdot \mathbf{S} + D S_z^2}_{\text{electron}} + \underbrace{\gamma_{N} \mathbf{B} \cdot \mathbf{I}_{N} + P I_{N,z}^2 + \mathbf{S} \cdot \mathbf{A}_{N} \cdot \mathbf{I}_{N}}_{\text{nitrogen}} \\ &+\underbrace{\sum_{i}{\gamma_{C} \mathbf{B} \cdot \mathbf{I}_{C}^{(i)} + \mathbf{S} \cdot \mathbf{A}_{C}^{(i)} \cdot \mathbf{I}_{C}^{(i)}}}_{\text{carbon(s)}},\end{split}\]where the parameters are the follows:
Spin
Parameter
Symbol
Value
Electron (\(S=1\))
Gyromagnetic ratio
\(\gamma_e\)
\(28.0331\,\text{GHz/T}\) [1]
Zero-field splitting
\(D\)
\(2.872\,\text{GHz}\) [1]
Nitrogen-14 (\(I=1\))
Gyromagnetic ratio
\(\gamma_{N}\)
\(-3.07771\,\text{MHz/T}\) [2]
Quadrupole splitting
\(P\)
\(-5.01\,\text{MHz}\) [1]
Hyperfine perpendicular
\(A_{N\perp}\)
\(-2.70\,\text{MHz}\) [1]
Hyperfine parallel
\(A_{N\parallel}\)
\(-2.14\,\text{MHz}\) [1]
Nitrogen-15 (\(I=1/2\))
Gyromagnetic ratio
\(\gamma_{N}\)
\(4.31727\,\text{MHz/T}\) [2]
Hyperfine perpendicular
\(A_{N\perp}\)
\(3.65\,\text{MHz}\) [1]
Hyperfine parallel
\(A_{N\parallel}\)
\(3.03\,\text{MHz}\) [1]
Carbon-13 (\(I=1/2\))
Gyromagnetic ratio
\(\gamma_C\)
\(-10.7084\,\text{MHz/T}\) [2]
References:[1] Felton et al., Phys. Rev. B 79, 075203 (2009)[2] CRC Handbook of Chemistry and Physics, sec. 11-4 (97th edition)Hint
The carbon atom indices specify the position of a carbon atom as:
\[\text{carbon atom position} = n_1 \cdot \mathbf{a}_1 + n_2 \cdot \mathbf{a}_2 + n_3 \cdot \mathbf{a}_3 + n_4 \cdot \boldsymbol{\tau},\]where \(\mathbf{a}_1\), \(\mathbf{a}_2\) and \(\mathbf{a}_3\) are the primitive lattice vectors, \(\mathbf{0}\) and \(\boldsymbol{\tau}\) are the positions of the atoms inside the primitive cell, furthermore \(n_1\), \(n_2\), \(n_3\) (integers) and \(n_4\) (\(0\) or \(1\)) are the carbon nuclear spin indices. Our convention is:
\[ \begin{align}\begin{aligned}\mathbf{a}_1 &= a_\text{CC}\cdot ( 0, 2\sqrt{2}/3, 4/3 ),\\\mathbf{a}_2 &= a_\text{CC}\cdot ( -\sqrt{6}/3, -\sqrt{2}/3, 4/3 ),\\\mathbf{a}_3 &= a_\text{CC}\cdot ( \sqrt{6}/3, -\sqrt{2}/3, 4/3 ),\\\boldsymbol{\tau} &= (\mathbf{a}_1 + \mathbf{a}_2 + \mathbf{a}_3) / 4 = a_\text{CC}\cdot ( 0, 0, 1 )\end{aligned}\end{align} \]where \(a_\text{CC} = 0.1545 \text{ nm}\) is the carbon-carbon distance. The nitrogen occupies the \(\boldsymbol{\tau}\) position, while the missing carbon atom corresponds to the \(\mathbf{0}\) lattice point.