tbplas.CachedSample
- class tbplas.CachedSample(directory: str = 'sample')
Sample with attributes loaded from disk.
- _directory
directory within which the data is saved
- Type:
str
- _attr
dictionary containing the key-value type attributes
- Type:
dict
Note
There are two cases where we need to save/load the sample. Most of the time we are just doing post-processing, and need only the essential attributes of the sample. We may also load the sample for another full TBPM run. For the former case, the attributes are loaded during initialization and reloaded in init_*. For the latter case, the attributes and arrays are loaded in init_*.
- __init__(directory: str = 'sample') None
- Parameters:
directory – directory within which the data is saved
Methods
__init__([directory])apply_magnetic_field(intensity[, gauge])Apply magnetic field perpendicular to xOy-plane to -z direction via Peierls substitution.
Get all array attributes for sending to C++ extensions. :return: name tuple with orb_eng, orb_pos, hop_ind, hop_eng, lat_vec, dr and sc0_lat_vec as attributes.
init_array([force_init])Interface for initializing the arrays.
init_hop([force_init])Reserved for compatibility.
init_orb_eng([force_init])Reserved for compatibility.
init_orb_pos([force_init])Reserved for compatibility.
plot([fig_name, fig_size, fig_dpi, ...])Plot lattice vectors, orbitals, and hopping terms to axes.
Reset all arrays.
Attributes
Get the total number of hopping terms of the sample.
Get the total number of orbitals of the sample.
Get lattice vectors of the first supercell. :return: (3, 3) float64 array Cartesian coordinates of lattice vectors in NM.
Get origin of the first supercell. :return: (3, ) float64 array Cartesian coordinates of origin in NM.
- __init__(directory: str = 'sample') None
- Parameters:
directory – directory within which the data is saved
- apply_magnetic_field(intensity: float, gauge: int = 0) None
Apply magnetic field perpendicular to xOy-plane to -z direction via Peierls substitution.
- The gauge-invariant Peierls phase from R_i to R_j is evaluated as
exp[-1j * |e|/(2*h_bar*c) * (R_i - R_j) * (A_i + A_j)]
- or
exp[1j * |e|/(2*h_bar*c) * (R_j - R_i) * (A_j + A_i)]
For the reference, see eqn. 10-11 of ref [1] and eqn. 19-20 of ref [2]. Be aware that ref [1] uses |e| while ref [2] uses e with sign.
- For perpendicular magnetic pointing to +z, we have A = (-By, 0, 0). Then
(R_j - R_i) * (A_j + A_i) = -B * (y_j + y_i) * (x_j - x_i)
However, there isn’t the minus sign in the source code of TBPLaS. This is because we are considering a magnetic field pointing to -z.
Note that the above formulae use Gaussian units. For SI units, the speed of light vanishes. This is verified by checking the dimension under SI units:
[e]/[h_bar] = IT/(L^2 M T^-1) = L^-2 M^-1 I T^-2 [R][A] = L * (M T^-2 I^-1 L) = L^2 M I^-1 T^-2
which cancel out upon multiplication. Similarly, under Gaussian units we have: [e]/[c*h_bar] = L^(-3/2) M^(-1/2) T [R][A] = L^(3/2) M^(1/2) T which also cancel out upon multiplication.
The analysis also inspires to calculate the scaling factor in SI units as:
|e/2h_bar| = 759633724404755.2
However, we use nm for lengths. So the scaling factor should be divided by 1e18, yielding 0.0007596337244047553. That is exactly the magic number pi / 4135.666734 = 0.0007596339008078771 in the source code of TBPLaS.
Reference: [1] https://journals.aps.org/prb/pdf/10.1103/PhysRevB.51.4940 [2] https://journals.jps.jp/doi/full/10.7566/JPSJ.85.074709
- Parameters:
intensity – magnetic B field in Tesla
gauge – gauge of vector potential of the magnetic field to -z 0 for (By, 0, 0), 1 for (0, -Bx, 0), 2 for (0.5By, -0.5Bx, 0)
- Returns:
None
- get_array() namedtuple
Get all array attributes for sending to C++ extensions. :return: name tuple with orb_eng, orb_pos, hop_ind, hop_eng, lat_vec,
dr and sc0_lat_vec as attributes
- init_array(force_init: bool = False) None
Interface for initializing the arrays.
If any array is empty, build all arrays from scratch. Otherwise, build them when force_init is True.
- Parameters:
force_init – whether to force initializing the arrays from scratch even if they have already been initialized
- Returns:
None
- init_hop(force_init: bool = False) None
Reserved for compatibility. Use init_array instead.
- init_orb_eng(force_init: bool = False) None
Reserved for compatibility. Use init_array instead.
- init_orb_pos(force_init: bool = False) None
Reserved for compatibility. Use init_array instead.
- plot(fig_name: str = None, fig_size: Tuple[float, float] = None, fig_dpi: int = 300, with_orbitals: bool = True, with_cells: bool = True, with_conj: bool = False, orb_color: Callable[[ndarray], List[str]] = None, hop_as_arrows: bool = True, hop_eng_cutoff: float = 1e-05, hop_color: str = 'r', view: str = 'ab') None
Plot lattice vectors, orbitals, and hopping terms to axes.
- Parameters:
fig_name – file name to which the figure will be saved
fig_size – width and height of the figure
fig_dpi – resolution of the figure file
with_orbitals – whether to plot orbitals as filled circles
with_cells – whether to plot borders of primitive cells
with_conj – whether to plot conjugate hopping terms as well
orb_color – function for coloring the orbitals
hop_as_arrows – whether to plot hopping terms as arrows
hop_eng_cutoff – cutoff for showing hopping terms
hop_color – color of hopping terms
view – kind of view point, should be in ‘ab’, ‘bc’, ‘ca’, ‘ba’, ‘cb’, ‘ac’
- Returns:
None
- reset_array() None
Reset all arrays. :return: None
- __weakref__
list of weak references to the object
- property num_hop: int
Get the total number of hopping terms of the sample. :return: total number of hopping terms
- property num_orb: int
Get the total number of orbitals of the sample. :return: total number of orbitals
- property sc0_lat_vec: ndarray
Get lattice vectors of the first supercell. :return: (3, 3) float64 array
Cartesian coordinates of lattice vectors in NM
- property sc0_origin: ndarray
Get origin of the first supercell. :return: (3, ) float64 array
Cartesian coordinates of origin in NM