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 nitrogen-vacancy center. Electron spin of the nitrogen-vacancy center is added by default as 'e'. \(^{13}\text{C}\) nuclear spins can be added by the carbon_atom_indices argument.

Parameters:

  • nitrogen_isotope (int | None) – Atomic number of the nitrogen isotope (optional, should be 14 or 15).

  • 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 the default_rotating_frame() function, which is responsible for defining the rotating frame.

Return type:

Model

Returns:

Default model.

Raises:

SimphonyError – If invalid nitrogen isotope is given. If invalid carbon nuclear spin indices are given.

Note

The carbon atom indices define a carbon spin vector as

\[\text{carbon atom vector} = n_1 \cdot \mathbf{a}_1 + n_2 \cdot \mathbf{a}_2 + n_3 \cdot \mathbf{a}_3 + n_4 \cdot \boldsymbol{\tau},\]

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.