# Reference¶

## Model Class¶

class tbmodels.Model(*, on_site: Optional[Sequence[float]] = None, hop: Optional[Dict[Tuple[int, …], Any]] = None, size: Optional[int] = None, dim: Optional[int] = None, occ: Optional[int] = None, pos: Optional[Sequence[Sequence[float]]] = None, uc: Optional[numpy.ndarray] = None, contains_cc: bool = True, sparse: bool = False)[source]

A class describing a tight-binding model. It contains methods for modifying the model, evaluating the Hamiltonian or eigenvalues at specific k-points, and writing to and from different file formats.

Parameters
• on_site – On-site energy of the states. This is equivalent to having a hopping within the same state and the same unit cell (diagonal terms of the R=(0, 0, 0) hopping matrix). The length of the list must be the same as the number of states.

• hop – Hopping matrices, as a dict containing the corresponding lattice vector R as a key.

• size – Number of states. Defaults to the size of the hopping matrices, if such are given.

• dim – Dimension of the tight-binding model. By default, the dimension is guessed from the other parameters if possible.

• occ – Number of occupied states.

• pos – Positions of the orbitals, in reduced coordinates. By default, all orbitals are set to be at the origin, i.e. at [0., 0., 0.].

• uc – Unit cell of the system. The unit cell vectors are given as rows in a dim x dim array

• contains_cc – Specifies whether the hopping matrices and on-site energies are given fully (contains_cc=True), or the complex conjugate should be added for each term to obtain the full model. The on_site parameter is not affected by this.

• sparse – Specifies whether the hopping matrices should be saved in sparse format.

__add__(model: tbmodels._tb_model.Model) → tbmodels._tb_model.Model[source]

__mul__(x: float) → tbmodels._tb_model.Model[source]

Multiplies hopping terms by x.

__neg__() → tbmodels._tb_model.Model[source]

Changes the sign of all hopping terms.

__rmul__(x: float) → tbmodels._tb_model.Model[source]

Multiplies hopping terms by x.

__sub__(model: tbmodels._tb_model.Model) → tbmodels._tb_model.Model[source]

Substracts one model from another by substracting all hopping terms.

__truediv__(x: float) → tbmodels._tb_model.Model[source]

Divides hopping terms by x.

add_hop(overlap: complex, orbital_1: int, orbital_2: int, R: Sequence[int])[source]

Adds a hopping term with a given overlap (hopping strength) from orbital_2 ($$o_2$$), which lies in the unit cell pointed to by R, to orbital_1 ($$o_1$$) which is in the home unit cell. In other words, overlap is the matrix element $$\mathcal{H}_{o_1,o_2}(\mathbf{R}) = \langle o_1, \mathbf{0} | \mathcal{H} | o_2, \mathbf{R} \rangle$$.

The complex conjugate of the hopping is added automatically. That is, the matrix element $$\langle o_2, \mathbf{R} | \mathcal{H} | o_1, \mathbf{0} \rangle$$ does not have to be added manually.

Note

This means that adding a hopping of overlap $$\epsilon$$ between an orbital and itself in the home unit cell increases the orbitals on-site energy by $$2 \epsilon$$.

Parameters
• overlap – Strength of the hopping term (in energy units).

• orbital_1 – Index of the first orbital.

• orbital_2 – Index of the second orbital.

• R – Lattice vector pointing to the unit cell where orbital_2 lies.

Warning

The positions given in the constructor of Model are automatically mapped into the home unit cell. This has to be taken into account when determining R.

add_hoppings_kwant(kwant_sys)[source]

Sets the on-site energies and hopping terms for an existing kwant system to those of the Model.

Note

The TBmodels - Kwant interface is experimental. Use it with caution.

add_on_site(on_site: Sequence[float])[source]

Adds on-site energy to the orbitals. This adds to the existing on-site energy, and does not erase it.

Parameters

on_site – On-site energies. This must be a sequence of real numbers, of the same length as the number of orbitals

change_unit_cell(*, uc: Optional[Sequence[Sequence[float]]] = None, offset: Sequence[float] = 0, 0, 0, cartesian: bool = False) → tbmodels._tb_model.Model[source]

Return a model with a different unit cell of the same volume.

Creates a model with a changed unit cell - with a different shape and / or origin. The new unit cell must be compatible with the current lattice, and have the same volume.

Parameters
• uc – The new unit cell shape. Lattice vectors are given as rows in a (dim x dim) matrix. If no unit cell is given, the current unit cell shape is kept.

• offset – The position of the new unit cell origin, relative to the old one.

• cartesian – Specifies if the offset and unit cell are in cartesian or reduced coordinates. Reduced coordinates are with respect to the old unit cell.

construct_kdotp(k: Sequence[float], order: int)[source]

Construct a k.p model around a given k-point. This is done by explicitly evaluating the derivatives which make up the Taylor expansion of the k.p models.

This method can currently only construct models using convention 2 for the Hamiltonian.

Parameters
• k – The k-point around which the k.p model is constructed.

• order – The order (sum of powers) to which the Taylor expansion is performed.

eigenval(k: Union[Sequence[float], Sequence[Sequence[float]]]) → Union[numpy.ndarray, List[numpy.ndarray]][source]

Returns the eigenvalues at a given k point, or list of k-points.

Parameters

k – The k-point at which the Hamiltonian is evaluated. If a list of k-points is given, a corresponding list of eigenvalue arrays is returned.

fold_model(*, new_unit_cell: Sequence[Sequence[float]] = None, unit_cell_offset: Sequence[float] = 0, 0, 0, position_tolerance: float = 0.001, unmatched_position_threshold: float = inf, orbital_labels: Sequence[Hashable] = None, target_indices: Optional[Sequence[int]] = None, check_cc: bool = True, check_uc_volume: bool = True, uc_volume_tolerance: float = 1e-06, check_orbital_ratio: bool = True) → tbmodels._tb_model.Model[source]

Returns a model with a smaller unit cell. Orbitals which are related by a lattice vector of the new unit cell are “folded” into a single orbital. This is the inverse operation of the supercell construction.

Note

This function is currently experimental, and its interface may still change without warning.

Parameters
• new_unit_cell – The unit cell of the new model. Note that this unit cell must lie completely within the old unit cell.

• unit_cell_offset – Position (in cartesian coordinates) at which the new unit cell is based.

• position_tolerance – Tolerance used when determining if a position mapped into the new unit cell is the same as an existing orbital position.

• unmatched_position_threshold – Threshold above which orbital positions that do not have a matching position in the new model are ignored. The threshold is defined as cartesian distance from the new unit cell origin.

• orbital_labels – A list of labels for the orbitals of the current model. This is needed to distinguish between orbitals of the same position when mapping them to the new orbitals.

• target_indices – Optional list of indices (in the current model) of the orbitals which lie within the new unit cell. This can be used as a check that the new orbitals are the expected ones.

• check_cc – Flag to determine whether the hoppings should be checked for being perfect complex conjugates. This check can fail if the model does not have exact translation symmetry w.r.t. the new unit cell. If set to false, hoppings are averaged to be complex conjugates.

• check_uc_volume – Flag to determine if the unit cell volume should decrease by the same factor as the number of orbitals.

• uc_volume_tolerance – Absolute tolerance when checking if the unit cell volume change is consistent with the change in number of orbitals.

• check_orbital_ratio – Flag to determine if the ratio of individual orbital labels should be checked to be the same as the initial ratio. If this is set to False, the resulting model will always have occ=None.

classmethod from_hdf5(hdf5_handle, **kwargs) → tbmodels._tb_model.Model[source]

Deserializes the object stored in HDF5 format.

classmethod from_hdf5_file(hdf5_file: str, **kwargs) → tbmodels._tb_model.Model[source]

Returns a Model instance read from a file in HDF5 format.

Parameters
• hdf5_file – Path of the input file.

• kwargsModel keyword arguments. Explicitly specified keywords take precedence over those given in the HDF5 file.

classmethod from_hop_list(*, hop_list: Iterable[Tuple[complex, int, int, Tuple[int, …]]] = , size: Optional[int] = None, **kwargs) → tbmodels._tb_model.Model[source]

Create a Model from a list of hopping terms.

Parameters
• hop_list

List of hopping terms. Each hopping term has the form [t, orbital_1, orbital_2, R], where

• t: strength of the hopping

• orbital_1: index of the first involved orbital

• orbital_2: index of the second involved orbital

• R: lattice vector of the unit cell containing the second orbital.

• size – Number of states. Defaults to the length of the on-site energies given, if such are given.

• kwargs – Any Model keyword arguments.

classmethod from_wannier_files(*, hr_file: str = None, wsvec_file: Optional[str] = None, xyz_file: Optional[str] = None, win_file: Optional[str] = None, h_cutoff: float = 0.0, ignore_orbital_order: bool = False, pos_kind: str = 'wannier', distance_ratio_threshold: float = 3.0, **kwargs) → tbmodels._tb_model.Model[source]

Create a Model instance from Wannier90 output files.

Parameters
• hr_file – Path of the *_hr.dat file. Together with the *_wsvec.dat file, this determines the hopping terms.

• wsvec_file – Path of the *_wsvec.dat file. This file determines the remapping of hopping terms when use_ws_distance is used in the Wannier90 calculation.

• xyz_file – Path of the *_centres.xyz file. This file is used to determine the positions of the orbitals, from the Wannier centers given by Wannier90.

• win_file – Path of the *.win file. This file is used to determine the unit cell.

• h_cutoff – Cutoff value for the hopping strength. Hoppings with a smaller absolute value are ignored.

• ignore_orbital_order – Do not throw an error when the order of orbitals does not match what is expected from the Wannier90 output.

• pos_kind – Determines how positions are assinged to orbitals. Valid options are wannier (use Wannier centres) or nearest_atom (map to nearest atomic position).

• distance_ratio_threshold – [Applies only for pos_kind=’nearest_atom’] The minimum ratio between the second-nearest and nearest atom below which an error will be raised.

• kwargsModel keyword arguments.

classmethod from_wannier_folder(folder: str = '.', prefix: str = 'wannier', **kwargs) → tbmodels._tb_model.Model[source]

Create a Model instance from Wannier90 output files, given the folder containing the files and file prefix.

Parameters
• folder – Directory containing the Wannier90 output files.

• prefix – Prefix of the Wannier90 output files.

• kwargs – Keyword arguments passed to from_wannier_files(). If input files are explicitly given, they take precedence over those found in the folder.

hamilton(k: Union[Sequence[float], Sequence[Sequence[float]]], convention: int = 2) → numpy.ndarray[source]

Calculates the Hamilton matrix for a given k-point or list of k-points.

Parameters
• k – The k-point at which the Hamiltonian is evaluated. If a list of k-points is given, the result will be the corresponding list of Hamiltonians.

• convention – Choice of convention to calculate the Hamilton matrix. See explanation in the PythTB documentation . Valid choices are 1 or 2.

classmethod join_models(*models: tbmodels._tb_model.Model) → tbmodels._tb_model.Model[source]

Creates a tight-binding model which contains all orbitals of the given input models. The orbitals are ordered by model, such that the resulting Hamiltonian is block-diagonal.

Parameters

models – Models which should be joined together.

property reciprocal_lattice

An array containing the reciprocal lattice vectors as rows.

remove_long_range_hop(*, cutoff_distance_cartesian: float = None)None[source]

Remove hoppings whose range is longer than the given cutoff.

Parameters

cutoff_distance_cartesian – Cartesian distance between the two orbitals above which the hoppings are removed.

remove_small_hop(cutoff: float)None[source]

Remove hoppings which are smaller than the given cutoff value.

Parameters

cutoff – Cutoff value below which a hopping is removed.

set_sparse(sparse: bool = True)[source]

Defines whether sparse or dense matrices should be used to represent the system, and changes the system accordingly if needed.

Parameters

sparse – Flag to determine whether the system is set to be sparse (True) or dense (False).

slice_orbitals(slice_idx: List[int]) → tbmodels._tb_model.Model[source]

Returns a new model with only the orbitals as given in the slice_idx. This can also be used to re-order the orbitals.

Parameters

slice_idx – Orbital indices that will be in the resulting model.

supercell(size: Sequence[int]) → tbmodels._tb_model.Model[source]

Generate a model for a supercell of the current unit cell.

Parameters

size – The size of the supercell, given as integer multiples of the current lattice vectors

symmetrize(symmetries: , full_group: bool = False) → Model[source]

Returns a model which is symmetrized w.r.t. the given symmetries. This is done by performing a group average over the symmetry group.

Parameters
• symmetries – Symmetries which the symmetrized model should respect.

• full_group – Specifies whether the given symmetries represent the full symmetry group, or only a subset from which the full symmetry group is generated.

to_hdf5(hdf5_handle)[source]

Serializes the object to HDF5 format, attaching it to the given HDF5 handle (might be a HDF5 File or Dataset).

to_hdf5_file(hdf5_file)

Saves the object to a file, in HDF5 format.

Parameters

hdf5_file (str) – Path of the file.

to_hr()str[source]

Returns a string containing the model in Wannier90’s *_hr.dat format.

Note

The *_hr.dat format does not contain information about the position of the atoms or the shape of the unit cell. Consequently, this information is lost when saving the model in this format.

Warning

The *_hr.dat format does not preserve the full precision of the hopping strengths. This could lead to numerical errors.

to_hr_file(hr_file: str)None[source]

Writes to a file, using Wannier90’s *_hr.dat format.

Parameters

hr_file – Path of the output file

Note

The *_hr.dat format does not contain information about the position of the atoms or the shape of the unit cell. Consequently, this information is lost when saving the model in this format.

Warning

The *_hr.dat format does not preserve the full precision of the hopping strengths. This could lead to numerical errors.

to_kwant_lattice()[source]

Returns a kwant lattice corresponding to the current model. Orbitals with the same position are grouped into the same Monoatomic sublattice.

Note

The TBmodels - Kwant interface is experimental. Use it with caution.

## Helper functions¶

This module contains a helper function to create a list of hoppings from a given matrix (matrix_to_hop()).

tbmodels.helpers.matrix_to_hop(mat: Sequence[Sequence[complex]], orbitals: Optional[Sequence[int]] = None, R: Sequence[int] = 0, 0, 0, multiplier: float = 1.0) → List[List[Union[complex, int, numpy.ndarray]]][source]

Turns a square matrix into a series of hopping terms.

Parameters
• mat – The matrix to be converted.

• orbitals – Indices of the orbitals that make up the basis w.r.t. which the matrix is defined. By default (orbitals=None), the first len(mat) orbitals are used.

• R – Lattice vector for all the hopping terms.

• multiplier – Multiplicative constant for the hopping strength.

tbmodels.io.save(obj, hdf5_file)

Save TBmodels objects to a HDF5 file. Compatible with all types registered through fsc.hdf5_io.

tbmodels.io.load(file_path)[source]

Load TBmodels objects from an HDF5 file. Compatible with all types registered through fsc.hdf5_io.

## Command line interface¶

### tbmodels¶

tbmodels [OPTIONS] COMMAND [ARGS]...


Options

--version

Show the version and exit.

#### eigenvals¶

Calculate the energy eigenvalues for a given set of k-points (in reduced coordinates). The input and output is given in an HDF5 file.

tbmodels eigenvals [OPTIONS]


Options

-i, --input <input>

File containing the input model (in HDF5 format).

-k, --kpoints <kpoints>

File containing the k-points for which the eigenvalues are evaluated.

-o, --output <output>

Output file for the energy eigenvalues.

-v, --verbose

#### parse¶

Parse Wannier90 output files and create an HDF5 file containing the tight-binding model.

tbmodels parse [OPTIONS]


Options

-f, --folder <folder>

Directory containing the Wannier90 output files.

-p, --prefix <prefix>

Common prefix of the Wannier90 output files.

--pos-kind <pos_kind>

Which position to use for the orbitals.

Options

wannier|nearest_atom

--distance-ratio-threshold <distance_ratio_threshold>
--sparsity <sparsity>

Write the model in sparse format. By default, the format of the input model is used.

Options

sparse|dense|as_input

-v, --verbose
-o, --output <output>

Path of the output file.

#### slice¶

Create a model containing only the orbitals given in the SLICE_IDX.

tbmodels slice [OPTIONS] [SLICE_IDX]...


Options

-i, --input <input>

File containing the input model (in HDF5 format).

-o, --output <output>

Output file for the sliced model.

--sparsity <sparsity>

Write the model in sparse format. By default, the format of the input model is used.

Options

sparse|dense|as_input

-v, --verbose

Arguments

SLICE_IDX

Optional argument(s)

#### symmetrize¶

Symmetrize tight-binding model with given symmetry group(s).

tbmodels symmetrize [OPTIONS]


Options

-i, --input <input>

File containing the input model (in HDF5 format).

-o, --output <output>

Output file for the symmetrized model.

-s, --symmetries <symmetries>

File containing symmetry_representation.SymmetryGroup objects (in HDF5 form).

-f, --full-group, --no-full-group

Full group: The full symmetry group is given in the symmetries. No full group: The symmetries only contain a generating subset of the full group. Overrides the option given in the symmetries file (if any).

--sparsity <sparsity>

Write the model in sparse format. By default, the format of the input model is used.

Options

sparse|dense|as_input

-v, --verbose

## k.p Model class¶

class tbmodels.kdotp.KdotpModel(taylor_coefficients: Mapping[Tuple[int, …], Any])[source]

A class describing a k.p model.

Parameters

taylor_coefficients

A mapping containing the taylor coefficients of the k.p model. The keys are tuples which describe the power of the k-vector components, and the values are the corresponding matrices.

Example:

(1, 0, 2): [[1, 0], [0, -1]] describes k_x * k_z**2 * sigma_z

## Exceptions¶

Defines custom exceptions to be used in TBmodels. The main purpose of these custom exceptions is their use in the CLI. Custom exceptions are formatted in the CLI in a way that makes error parsing simple.

exception tbmodels.exceptions.TbmodelsException(message: str, exception_marker: tbmodels.exceptions.ExceptionMarker)[source]

Custom exception class for TBmodels errors. This class should be used only for exception with a well-known cause, not for unexpected “crashes”. For example, it can be used for malformed or incompatible inputs, truncated or missing input files, and similar errors.

Errors which use this exception class will be formatted in the CLI as:

Error: [<exception marker name>] <error message>

exit_code = 3
format_message()[source]
class tbmodels.exceptions.ExceptionMarker[source]

Base class for markers to be used with TbmodelsException exceptions.

Note

The exception marker names are considered a public interface and will not be changed in a minor release (although new ones can be added). The values of the exception markers however are informational only, and should not be relied upon.

class tbmodels.exceptions.ParseExceptionMarker[source]

Exception markers for errors which can occur while parsing a tight-binding model.

AMBIGUOUS_NEAREST_ATOM_POSITIONS = 'The nearest atom to use for position parsing is ambiguous.'
INCOMPLETE_WSVEC_FILE = 'The seedname_wsvec.dat file is empty or incomplete.'
class tbmodels.exceptions.SymmetrizeExceptionMarker[source]

Exception markers for errors which can occur while symmetrizing a tight-binding model.

INVALID_SYMMETRY_TYPE = 'The type of the given symmetries object is incorrect.'
POSITIONS_NOT_SYMMETRIC = 'The model positions do not respect the given symmetry.'