sisl.io.tbtrans.tbtprojncSileTBtrans

class sisl.io.tbtrans.tbtprojncSileTBtrans(filename, mode='r', lvl=0, access=1, *args, **kwargs)

Bases: tbtncSileTBtrans

TBtrans projection file object

Plotting

plot	Plotting functions for the tbtprojncSileTBtrans class.
plot.geometry(*args[, ...])	Calls read_geometry and creates a GeometryPlot from its output.
plot.pdos([geometry, ...])	Creates a PDOSData object and then plots a PdosPlot from it.

Methods

ADOS(elec_mol_proj[, E, kavg, atoms, ...])	Projected spectral density of states (DOS) (1/eV)
Adensity_matrix(elec_mol_proj, E[, kavg, ...])	Projected spectral function density matrix at energy E (1/eV)
BDOS([elec, E, kavg, sum, norm])	Bulk density of states (DOS) (1/eV).
DOS([E, kavg, atoms, orbitals, sum, norm])	Green function density of states (DOS) (1/eV).
Eindex(E[, method])	Return the closest energy index corresponding to the energy E
a2p(atoms)	Return the pivoting orbital indices (0-based) for the atoms, possibly on an electrode
a_down(elec[, bulk])	Down-folding atomic indices for a given electrode
a_elec(elec)	Electrode atomic indices for the full geometry (sorted)
atom_ACOHP(E[, elec, kavg, isc, orbitals, uc])	Atomic COHP curve of the spectral function
atom_ACOOP(E[, elec, kavg, isc, orbitals, uc])	Atomic COOP curve of the spectral function
atom_current([elec, elec_other, activity, ...])	Atomic current of atoms, a scalar quantity quantifying how much currents flows through an atom
atom_transmission(E[, elec, activity, kavg, ...])	Atomic transmission at energy E of atoms, a scalar quantity quantifying how much transmission flows through an atom
base_directory([relative_to])	Retrieve the base directory of the file, relative to the path relative_to
bloch(elec)	Bloch-expansion coefficients for an electrode
bond_current([elec, elec_other, kavg, isc, ...])	Bond current between atoms (sum of orbital currents)
bond_transmission(E[, elec, kavg, isc, ...])	Bond transmission between atoms at a specific energy
btd([elec])	Block-sizes for the BTD method in the device/electrode region
chemical_potential(elec)	Return the chemical potential associated with the electrode elec
close()
dir_file([filename, filename_base])	File of the current Sile
eigenstate(molecule[, k, all])	Return the eigenstate on the projected molecule
electron_temperature(elec)	Electron bath temperature [Kelvin]
eta([elec])	The imaginary part used when calculating the self-energies in eV (or for the device
info([molecule])	Information about the calculated quantities available for extracting in this file
iter([group, dimension, variable, levels, root])	Iterator on all groups, variables and dimensions.
kT(elec)	Electron bath temperature [eV]
kindex(k)	Return the index of the k-point that is closests to the queried k-point (in reduced coordinates)
mu(elec)	Return the chemical potential associated with the electrode elec
n_btd([elec])	Number of blocks in the BTD partioning
na_down(elec)	Number of atoms in the downfolding region (without device downfolded region)
no_down(elec)	Number of orbitals in the downfolding region (plus device downfolded region)
no_e(elec)	Number of orbitals in the downfolded region of the electrode in the device
norm([atoms, orbitals, norm])	Normalization factor depending on the input
o2p(orbitals[, elec])	Return the pivoting indices (0-based) for the orbitals, possibly on an electrode
orbital_ACOHP(elec_mol_proj, E[, kavg, isc, ...])	Orbital COHP analysis of the projected spectral function
orbital_ACOOP(elec_mol_proj, E[, kavg, isc, ...])	Orbital COOP analysis of the projected spectral function
orbital_current([elec, elec_other, kavg, ...])	Orbital current originating from elec as a sparse matrix
orbital_transmission(E, elec_mol_proj, ...)	Transmission at energy E between orbitals originating from elec
pivot([elec, in_device, sort])	Return the pivoting indices for a specific electrode (in the device region) or the device
pivot_down(elec)	Pivoting orbitals for the downfolding region of a given electrode
projections(molecule)	List of projections on molecule
read(*args, **kwargs)	Generic read method which should be overloaded in child-classes
read_data(*args, **kwargs)	Read specific type of data.
read_geometry(*args, **kwargs)	Returns Geometry object from this file
read_lattice()	Returns Lattice object from this file
reflection([elec, kavg, from_single])	Reflection into electrode elec
sparse_atom_to_vector(Dab)	Reduce an atomic sparse matrix to a vector contribution of each atom
sparse_orbital_to_atom(Dij[, uc, sum_dup])	Reduce a sparse matrix in orbital sparse to a sparse matrix in atomic indices
sparse_orbital_to_scalar(Dij[, activity])	Atomic scalar contribution of atoms for a sparse orbital matrix
sparse_orbital_to_vector(Dij[, uc, sum_dup])	Reduce an orbital sparse matrix to a vector contribution of each atom
transmission(elec_mol_proj_from, ...[, kavg])	Transmission from mol_proj_elec_from to mol_proj_elec_to
transmission_bulk([elec, kavg])	Bulk transmission for the elec electrode
transmission_eig(elec_mol_proj_from, ...[, kavg])	Transmission eigenvalues from elec_mol_proj_from to elec_mol_proj_to
vector_current([elec, elec_other, kavg, ...])	Vector for each atom being the sum of bond currents times the normalized bond vector between the atoms
vector_transmission(E[, elec, kavg, isc, ...])	Vector for each atom being the sum of bond transmissions times the normalized bond vector between the atoms
write(*args, **kwargs)	Generic write method which should be overloaded in child-classes
write_tbtav(*args, **kwargs)	Convert this to a TBT.AV.nc file, i.e. all k dependent quantites are averaged out.

Attributes

E	Sampled energy-points in file
a_buf	Atomic indices (0-based) of device atoms
a_dev	Atomic indices (0-based) of device atoms (sorted)
atom_COHP
atom_COOP
base_file	File of the current Sile
cell	Unit cell in file
current
current_parameter
density_matrix
elecs	List of electrodes
fano
file	File of the current Sile
geom	Same as geometry, but deprecated
geometry	The associated geometry from this file
k	Sampled k-points in file
kpt	Sampled k-points in file
lasto	Last orbital of corresponding atom
molecules	List of regions where state projections may happen
nE	Number of energy-points in file
na	Returns number of atoms in the cell
na_b	Number of atoms in the buffer region
na_buffer	Number of atoms in the buffer region
na_d	Number of atoms in the device region
na_dev	Number of atoms in the device region
na_u	Returns number of atoms in the cell
ne	Number of energy-points in file
nk	Number of k-points in file
nkpt	Number of k-points in file
no	Returns number of orbitals in the cell
no_d	Number of orbitals in the device region
no_u	Returns number of orbitals in the cell
noise_power
o_dev	Orbital indices (0-based) of device orbitals (sorted)
orbital_COHP
orbital_COOP
shot_noise
wk	Weights of k-points in file
wkpt	Weights of k-points in file
xa	Atomic coordinates in file
xyz	Atomic coordinates in file

ADOS(elec_mol_proj, E: EType | None = None, kavg=True, atoms=None, orbitals=None, sum: bool = True, norm: NormType = 'none')

Projected spectral density of states (DOS) (1/eV)

Extract the projected spectral DOS from electrode elec on a selected subset of atoms/orbitals in the device region

\[\mathrm{ADOS}_\mathfrak{el}(E) = \frac{1}{2\pi N} \sum_{i\in \{I\}} [\mathbf{G}(E)|i\rangle\langle i|\Gamma_\mathfrak{el}|i\rangle\langle i|\mathbf{G}^\dagger]_{ii}(E)\]

where \(|i\rangle\) may be a sum of states. The normalization constant (\(N\)) is defined in the routine norm and depends on the arguments.

Parameters:

• elec_mol_proj (str or tuple) – originating projected spectral function (<electrode>.<molecule>.<projection>)

• E (float or int, optional) – optionally only return the DOS of atoms at a given energy point

• kavg (bool, int or array_like, optional) – whether the returned DOS is k-averaged, an explicit k-point or a selection of k-points

• atoms (array_like of int or bool, optional) – only return for a given set of atoms (default to all). NOT allowed with orbital keyword

• orbitals (array_like of int or bool, optional) – only return for a given set of orbitals (default to all) NOT allowed with atoms keyword

• sum – whether the returned quantities are summed or returned as is, i.e. resolved per atom/orbital.

• norm – how the normalization of the summed DOS is performed (see norm routine).

Adensity_matrix(elec_mol_proj, E: EType, kavg=True, isc=None, orbitals=None, geometry: Geometry | None = None)

Projected spectral function density matrix at energy E (1/eV)

The projected density matrix can be used to calculate the LDOS in real-space.

The \(\mathrm{LDOS}(E, \mathbf r)\) may be calculated using the density routine. Basically the LDOS in real-space may be calculated as

\[\boldsymbol\rho_{\mathbf A_{\mathfrak{el}}}(E, \mathbf r) = \frac{1}{2\pi}\sum_{ij}\phi_i(\mathbf r)\phi_j(\mathbf r) \Re[\mathbf A_{\mathfrak{el}, ij}(E)]\]

where \(\phi\) are the real-space orbitals. Note that the broadening used in the TBtrans calculations ensures the broadening of the density, i.e. it should not be necessary to perform energy averages over the density matrices.

Parameters:

• elec_mol_proj (str or tuple) – the projected electrode of originating electrons

• E – the density matrix corresponding to the energy.

• kavg (bool, int or array_like, optional) – whether the returned density matrix is k-averaged, an explicit k-point or a selection of k-points

• isc (array_like, optional) – the returned density matrix from unit-cell ([None, None, None]) to the given supercell, the default is all density matrix elements for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].

• orbitals (array-like or dict, optional) – only retain density matrix elements for a subset of orbitals, all other are set to 0.

• geometry – geometry that will be associated with the density matrix. By default the geometry contained in this file will be used. However, then the atomic species are probably incorrect, nor will the orbitals contain the basis-set information required to generate the required density in real-space.

Returns:

DensityMatrix (the object containing the Geometry and the density matrix elements)

BDOS(elec: str | int = 0, E: str | float | None = None, kavg=True, sum: bool = True, norm: Literal['none', 'atom', 'orbital', 'all'] = 'none') → ndarray

Bulk density of states (DOS) (1/eV).

Extract the bulk DOS from electrode elec.

\[\mathrm{BDOS}_\mathfrak{el}(E) = -\frac{1}{\pi} \Im\mathbf{G}(E)\]

This returns the density of states for the full (Bloch-expanded) electrode. When norm is ‘none’, the DOS is the full DOS for all electrode atoms (fully expanded), if you want to get the DOS for the minimal (un-expanded) electrode unit-cell, then divide by np.prod(tbt.bloch(elec)). When norm is anything else, it will be normalised to the number of atoms/orbitals in the electrode.

Parameters:

• elec – electrode where the bulk DOS is returned

• E – optionally only return the DOS of atoms at a given energy point

• kavg (bool, int, optional) – whether the returned DOS is k-averaged, or an explicit (unweighed) k-point is returned

• sum – whether the returned quantities are summed or returned as is, i.e. resolved per atom/orbital.

• norm – whether the returned quantities are summed over all orbitals or normed by number of orbitals in the electrode. Currently one cannot extract DOS per atom/orbital.

See also

DOS

the total density of states (including bound states)

ADOS

the spectral density of states from an electrode

DOS(E: str | float | None = None, kavg=True, atoms=None, orbitals=None, sum: bool = True, norm: Literal['none', 'atom', 'orbital', 'all'] = 'none') → ndarray

Green function density of states (DOS) (1/eV).

Extract the DOS on a selected subset of atoms/orbitals in the device region

\[\mathrm{DOS}(E) = -\frac{1}{\pi N} \sum_{i\in \{I\}} \Im \mathbf{G}_{ii}(E)\]

The normalization constant (\(N\)) is defined in the routine norm and depends on the arguments.

Parameters:

• E – optionally only return the DOS of atoms at a given energy point

• kavg (bool, int, optional) – whether the returned DOS is k-averaged, or an explicit (unweighed) k-point is returned

• atoms (array_like of int or bool, optional) – only return for a given set of atoms (default to all). NOT allowed with orbitals keyword. If True it will use all atoms in the device. False is equivalent to None.

• orbitals (array_like of int or bool, optional) – only return for a given set of orbitals (default to all) NOT allowed with atoms keyword. If True it will use all orbitals in the device. False is equivalent to None.

• sum – whether the returned quantities are summed or returned as is, i.e. resolved per atom/orbital.

• norm – how the normalization of the summed DOS is performed (see norm routine)

See also

ADOS

the spectral density of states from an electrode

BDOS

the bulk density of states in an electrode

Eindex(E: Etype, method: Literal['nearest', 'above', 'below'] = 'nearest')

Return the closest energy index corresponding to the energy E

Parameters:

• E – if int, return it-self, else return the energy index which is closests to the energy. For a str it will be parsed to a float and treated as such.

• method – how non-equal values should be located. * nearest takes the closests value * above takes the closests value above E. * below takes the closests value below E.

a2p(atoms)

Return the pivoting orbital indices (0-based) for the atoms, possibly on an electrode

This is equivalent to:

>>> p = self.o2p(self.geometry.a2o(atom, True))

Will warn if an atom requested is not in the device list of atoms.

Parameters:

atoms (array_like or int) – atomic indices (0-based)

a_down(elec: str | int, bulk: bool = False)

Down-folding atomic indices for a given electrode

Parameters:

• elec – electrode to retrieve indices for

• bulk – whether the returned indices are only in the pristine electrode, or the down-folding region (electrode + downfolding region, not in device)

a_elec(elec: str | int)

Electrode atomic indices for the full geometry (sorted)

Parameters:

elec – electrode to retrieve indices for

atom_ACOHP(E: str | float, elec: str | int = 0, kavg=True, isc=None, orbitals=None, uc: bool = False) → csr_matrix

Atomic COHP curve of the spectral function

Parameters:

• E – the atomic COHP corresponding to the energy.

• elec – the electrode of the spectral function

• kavg (bool, int, optional) – whether the returned COHP is k-averaged, or an explicit (unweighed) k-point is returned

• isc (array_like, optional) – the returned COHP from unit-cell ([None, None, None]) to the given supercell, the default is all COHP for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].

• orbitals (array-like or dict, optional) – only retain COHP matrix elements for a subset of orbitals, all other are set to 0.

• uc – whether the returned COHP are only in the unit-cell. If True this will return a sparse matrix of shape = (self.na, self.na), else, it will return a sparse matrix of shape = (self.na, self.na * self.n_s). One may figure out the connections via sc_index.

See also

orbital_COOP

orbital resolved COOP analysis of the Green function

atom_COOP

atomic COOP analysis of the Green function

orbital_ACOOP

orbital resolved COOP analysis of the spectral function

atom_ACOOP

atomic COOP analysis of the spectral function

orbital_COHP

orbital resolved COHP analysis of the Green function

atom_COHP

atomic COHP analysis of the Green function

orbital_ACOHP

orbital resolved COHP analysis of the spectral function

atom_ACOOP(E: str | float, elec: str | int = 0, kavg=True, isc=None, orbitals=None, uc: bool = False) → csr_matrix

Atomic COOP curve of the spectral function

The atomic COOP are a sum over all orbital COOP:

\[\mathrm{COOP}_{IJ} = \sum_{i\in I}\sum_{j\in J} \mathrm{COOP}_{ij}\]

This is a shorthand for calling orbital_ACOOP and sparse_orbital_to_atom in order.

Parameters:

• E – the atomic COOP corresponding to the energy.

• elec – the electrode of the spectral function

• kavg (bool, int, optional) – whether the returned COOP is k-averaged, or an explicit (unweighed) k-point is returned

• isc (array_like, optional) – the returned COOP from unit-cell ([None, None, None]) to the given supercell, the default is all COOP for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].

• orbitals (array-like or dict, optional) – only retain COOP matrix elements for a subset of orbitals, all other are set to 0.

• uc – whether the returned COOP are only in the unit-cell. If True this will return a sparse matrix of shape = (self.na, self.na), else, it will return a sparse matrix of shape = (self.na, self.na * self.n_s). One may figure out the connections via sc_index.

See also

orbital_COOP

orbital resolved COOP analysis of the Green function

atom_COOP

atomic COOP analysis of the Green function

orbital_ACOOP

orbital resolved COOP analysis of the spectral function

orbital_COHP

orbital resolved COHP analysis of the Green function

atom_COHP

atomic COHP analysis of the Green function

orbital_ACOHP

orbital resolved COHP analysis of the spectral function

atom_ACOHP

atomic COHP analysis of the spectral function

atom_current(elec: str | int = 0, elec_other: str | int = 1, activity: bool = True, kavg=True, isc=None, orbitals=None) → ndarray

Atomic current of atoms, a scalar quantity quantifying how much currents flows through an atom

The atomic current is a single number specifying a figure of the magnitude current flowing through each atom. It is thus not a quantity that can be related to the physical current flowing in/out of atoms but is merely a number that provides an idea of how much current this atom is redistributing.

The atomic current may have two meanings based on these two equations

\[\begin{split}\mathbf j_I^{|a|} &=\frac 12 \sum_{\{J\}} \Big| \sum_{i\in I}\sum_{j\in J} \mathbf J_{ij} \Big| \\ \mathbf j_I^{|o|} &=\frac 12 \sum_{i\in I}\sum_{j\in\{J\}} \big| J_{ij} \big|\end{split}\]

\[\]

If the activity is requested (activity=True) \(\mathbf j_I^{\mathcal A} = \sqrt{\mathbf j_I^{|a|} \mathbf j_I^{|o|} }\) is returned.

If activity=False \(\mathbf j_I^{|a|}\) is returned.

For geometries with all atoms only having 1-orbital, they are equivalent.

Generally the activity current is a more rigorous figure of merit for the current flowing through an atom. More so than than the summed absolute atomic current due to the following reasoning. The activity current is a geometric mean of the absolute bond current and the absolute orbital current. This means that if there is an atom with a large orbital current it will have a larger activity current.

Parameters:

• elec – the originating electrode

• elec_other – this electrode determines the other chemical potential. As such the orbital currents does not reflect the current going from elec to elec_other!

• activity – True to return the activity current, see explanation above

• kavg (bool, int, optional) – whether the returned orbital current is k-averaged, or an explicit (unweighed) k-point is returned

• isc (array_like, optional) – the returned bond currents from the unit-cell ([None, None, None]) to the given supercell, the default is all orbital currents for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].

• orbitals (array-like or dict, optional) – only retain orbital currents for a subset of orbitals.

Examples

>>> Jij = tbt.orbital_current(0, 1, what="all") # orbital current originating from electrode ``0``
>>> Ja = tbt.sparse_orbital_to_scalar(Jij)

Notes

Calculating the current between two electrodes with the same chemical potential will return a matrix filled with 0’s since there is no bias window.

The currents does not reflect the current going from elec_from to elec_other!

See also

orbital_transmission

energy resolved transmission between orbitals

orbital_current

bias window integrated transmissions

bond_transmission

energy resolved transmissions between atoms

bond_current

bias window integrated transmissions (orbital current summed over orbitals)

vector_transmission

an atomic field transmission for each atom (Cartesian representation of bond-transmissions)

vector_current

an atomic field current for each atom (Cartesian representation of bond-currents)

atom_transmission

energy resolved atomic transmission for each atom (scalar representation of bond-transmissions)

atom_transmission(E: str | float, elec: str | int = 0, activity: bool = True, kavg=True, isc=None, orbitals=None) → ndarray

Atomic transmission at energy E of atoms, a scalar quantity quantifying how much transmission flows through an atom

The atomic transmission is a single number specifying a figure of the magnitude transmission flowing through each atom. It is thus not a quantity that can be related to the physical transmission flowing in/out of atoms but is merely a number that provides an idea of how much this atom is redistributing.

The atomic transmission may have two meanings based on these two equations

\[\begin{split}T_I^{|a|} &=\frac 12 \sum_{\{J\}} \Big| \sum_{i\in I}\sum_{j\in J} \mathbf T_{ij} \Big| \\ T_I^{|o|} &=\frac 12 \sum_{i\in I}\sum_{j\in\{J\}} \big| T_{ij} \big|\end{split}\]

\[\]

If the activity is requested (activity=True) \(T_I^{\mathcal A} = \sqrt{T_I^{|a|} T_I^{|o|} }\) is returned. If the activity current is requested (activity=True)

If activity=False \(T_I^{|a|}\) is returned.

For geometries with all atoms only having 1-orbital, they are equivalent.

Generally the activity is a more rigorous figure of merit for the transmission flowing through an atom. More so than than the summed absolute atomic transmission due to the following reasoning. The activity transmission is a geometric mean of the absolute bond transmission and the absolute orbital transmission. This means that if there is an atom with a large orbital transmission it will have a larger activity.

Parameters:

• E – the atomic transmission corresponding to the energy.

• elec – the originating electrode

• activity – True to return the activity, see explanation above

• kavg (bool, int, optional) – whether the returned atomic transmissions are k-averaged, or an explicit (unweighed) k-point is returned

• isc (array_like, optional) – the returned transmissions from the unit-cell ([None, None, None]) to the given supercell, the default is all orbital transmissions are used for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].

• orbitals (array-like or dict, optional) – only retain orbital currents for a subset of orbitals.

Examples

>>> Jij = tbt.orbital_transmission(-1., what"all") # transmission @ E=-1 eV from electrode ``0``
>>> Ja = tbt.sparse_orbital_to_scalar(Jij)

See also

orbital_transmission

energy resolved transmission between orbitals

orbital_current

bias window integrated transmissions

bond_transmission

energy resolved transmissions between atoms

bond_current

bias window integrated transmissions (orbital current summed over orbitals)

vector_transmission

an atomic field transmission for each atom (Cartesian representation of bond-transmissions)

vector_current

an atomic field current for each atom (Cartesian representation of bond-currents)

atom_current

the atomic current for each atom (scalar representation of bond-currents)

base_directory(relative_to='.')

Retrieve the base directory of the file, relative to the path relative_to

bloch(elec: str | int)

Bloch-expansion coefficients for an electrode

Parameters:

elec – bloch expansions of electrode

bond_current(elec: str | int = 0, elec_other: str | int = 1, kavg=True, isc=None, what: str = 'all', orbitals=None, uc: bool = False) → csr_matrix

Bond current between atoms (sum of orbital currents)

Short hand function for calling orbital_current and sparse_orbital_to_atom.

The bond currents are a sum over all orbital currents:

\[J_{IJ} = \sum_{i\in I}\sum_{j\in J} J_{ij}\]

Parameters:

• elec – the electrode of originating electrons

• elec_other – this electrode determines the other chemical potential. As such the orbital currents does not reflect the current going from elec to elec_other!

• kavg (bool, int, optional) – whether the returned bond current is k-averaged, or an explicit (unweighed) k-point is returned

• isc (array_like, optional) – the returned bond currents from the unit-cell ([None, None, None]) (default) to the given supercell. If [None, None, None] is passed all bond currents are returned.

• what ({"all"/"both"/"+-"/"inout", "+"/"out", "-"/"in"}) – If +/out is supplied only the positive currents are used (going out) for -/in, only the negative currents are used (going in), else return both. Please see discussion in orbital_current.

• orbitals (array-like or dict, optional) – only retain currents for a subset of orbitals before calculating bond current Passed directly to orbital_current.

• uc – whether the returned currents are only in the unit-cell (supercell currents will be folded to their unit-cell equivalents). If True this will return a sparse matrix of shape = (self.na, self.na), else, it will return a sparse matrix of shape = (self.na, self.na * self.n_s). One may figure out the connections via sc_index.

Examples

>>> Jij = tbt.orbital_current(0, 1, what="out") # orbital current originating from electrode ``0``
>>> Jab1 = tbt.sparse_orbital_to_atom(Jij)
>>> Jab2 = tbt.bond_current(0, 1, what="out")
>>> Jab1 == Jab2
True

Notes

Calculating the current between two electrodes with the same chemical potential will return a matrix filled with 0’s since there is no bias window.

The currents does not reflect the current going from elec_from to elec_other!

See also

orbital_transmission

energy resolved transmission between orbitals

orbital_current

bias window integrated transmissions

bond_transmission

energy resolved transmissions between atoms

vector_transmission

an atomic field transmission for each atom (Cartesian representation of bond-transmissions)

vector_current

an atomic field current for each atom (Cartesian representation of bond-currents)

atom_transmission

energy resolved atomic transmission for each atom (scalar representation of bond-transmissions)

atom_current

the atomic current for each atom (scalar representation of bond-currents)

bond_transmission(E: str | float, elec: str | int = 0, kavg=True, isc=None, what: str = 'all', orbitals=None, uc: bool = False) → csr_matrix

Bond transmission between atoms at a specific energy

Short hand function for calling orbital_transmission and sparse_orbital_to_atom.

The bond transmissions are a sum over all orbital transmissions

\[T_{IJ}(E) = \sum_{i\in I}\sum_{j\in J} T_{ij}(E)\]

Parameters:

• E – the bond transmission corresponding to the energy.

• elec – the electrode of originating electrons

• kavg (bool, int, optional) – whether the returned bond transmissions is k-averaged, or an explicit (unweighed) k-point is returned

• isc (array_like, optional) – the returned transmissions from the unit-cell ([None, None, None]) (default) to the given supercell. If [None, None, None] is passed all transmissions are returned.

• what ({"all"/"both"/"+-"/"inout", "+"/"out", "-"/"in"}) – If +/out is supplied only the positive transmissions are used (going out) for -/in, only the negative transmissions are used (going in), else return both. Please see discussion in orbital_transmission.

• orbitals (array-like or dict, optional) – only retain transmissions for a subset of orbitals before calculating bond transmissions Passed directly to orbital_transmission.

• uc – whether the returned transmissions are only in the unit-cell (supercell bonds will be folded to their unit-cell equivalents). If True this will return a sparse matrix of shape = (self.na, self.na), else, it will return a sparse matrix of shape = (self.na, self.na * self.n_s). One may figure out the connections via sc_index.

Examples

>>> Jij = tbt.orbital_transmission(-1.0, what="out") # orbital transmission @ E = -1 eV originating from electrode ``0``
>>> Jab1 = tbt.sparse_orbital_to_atom(Jij)[
>>> Jab2 = tbt.bond_transmission(-1.0, what="out")
>>> Jab1 == Jab2
True

See also

orbital_transmission

energy resolved transmission between orbitals

orbital_current

bias window integrated transmissions

bond_current

bias window integrated transmissions (orbital current summed over orbitals)

vector_transmission

an atomic field transmission for each atom (Cartesian representation of bond-transmissions)

vector_current

an atomic field current for each atom (Cartesian representation of bond-currents)

atom_transmission

energy resolved atomic transmission for each atom (scalar representation of bond-transmissions)

atom_current

the atomic current for each atom (scalar representation of bond-currents)

btd(elec: int | str | None = None)

Block-sizes for the BTD method in the device/electrode region

Parameters:

elec – the BTD block sizes for the device (if none), otherwise the downfolding BTD block sizes for the electrode

chemical_potential(elec: str | int) → float

Return the chemical potential associated with the electrode elec

close()

dir_file(filename=None, filename_base='')

File of the current Sile

eigenstate(molecule, k=None, all=True)

Return the eigenstate on the projected molecule

The eigenstate object will contain the geometry as the parent object. The eigenstate will be in the Lowdin basis:

\[|\psi'_i\rangle = \mathbf S^{1/2} |\psi_i\rangle\]

Parameters:

• molecule (str) – name of the molecule to retrieve the eigenstate from

• k (optional) – k-index for retrieving a specific k-point (default to all)

• all (bool, optional) – whether all states should be returned

Returns:

EigenstateElectron

electron_temperature(elec: str | int) → float

Electron bath temperature [Kelvin]

Parameters:

elec – electrode to extract the temperature from

See also

kT

bath temperature in [eV]

eta(elec: int | str | None = None) → float

The imaginary part used when calculating the self-energies in eV (or for the device

Parameters:

elec – electrode to extract the eta value from. If not specified (or None) the device region eta will be returned.

info(molecule=None)

Information about the calculated quantities available for extracting in this file

Parameters:

molecule (str or int) – the molecule to request information from

iter(group=True, dimension=True, variable=True, levels=-1, root=None)

Iterator on all groups, variables and dimensions.

This iterator iterates through all groups, variables and dimensions in the Dataset

The generator sequence will _always_ be:

1. Group

2. Dimensions in group

3. Variables in group

As the dimensions are generated before the variables it is possible to copy groups, dimensions, and then variables such that one always ensures correct dependencies in the generation of a new SileCDF.

Parameters:

• group (bool (True)) – whether the iterator yields Group instances

• dimension (bool (True)) – whether the iterator yields Dimension instances

• variable (bool (True)) – whether the iterator yields Variable instances

• levels (int (-1)) – number of levels to traverse, with respect to root variable, i.e. number of sub-groups this iterator will return.

• root (str (None)) – the base root to start iterating from.

Examples

Script for looping and checking each instance.

>>> for gv in self.iter():
...     if self.isGroup(gv):
...         # is group
...     elif self.isDimension(gv):
...         # is dimension
...     elif self.isVariable(gv):
...         # is variable

kT(elec: str | int) → float

Electron bath temperature [eV]

Parameters:

elec – electrode to extract the temperature from

See also

electron_temperature

bath temperature in [K]

kindex(k)

Return the index of the k-point that is closests to the queried k-point (in reduced coordinates)

Parameters:

k (array_like of float or int) – the queried k-point in reduced coordinates \(]-0.5;0.5]\). If int return it-self.

mu(elec: str | int) → float

Return the chemical potential associated with the electrode elec

n_btd(elec: int | str | None = None) → int

Number of blocks in the BTD partioning

Parameters:

elec – if None the number of blocks in the device region BTD matrix. Else the number of BTD blocks in the electrode down-folding.

na_down(elec: str | int) → int

Number of atoms in the downfolding region (without device downfolded region)

Parameters:

elec – Number of downfolding atoms for electrode elec

no_down(elec: str | int) → int

Number of orbitals in the downfolding region (plus device downfolded region)

Parameters:

elec – Number of downfolding orbitals for electrode elec

no_e(elec: str | int) → int

Number of orbitals in the downfolded region of the electrode in the device

Parameters:

elec – Specify the electrode to query number of downfolded orbitals

norm(atoms=None, orbitals=None, norm: Literal['none', 'atom', 'orbital', 'all'] = 'none') → int

Normalization factor depending on the input

The normalization can be performed in one of the below methods. In the following \(N\) refers to the normalization constant that is to be used (i.e. the divisor):

'none'

\(N=1\)

'all'

\(N\) equals the number of orbitals in the total device region.

'atom'

\(N\) equals the total number of orbitals in the selected atoms. If orbitals is an argument a conversion of orbitals to the equivalent unique atoms is performed, and subsequently the total number of orbitals on the atoms is used. This makes it possible to compare the fraction of orbital DOS easier.

'orbital'

\(N\) is the sum of selected orbitals, if atoms is specified, this is equivalent to the ‘atom’ option.

Parameters:

• atoms (array_like of int or bool, optional) – only return for a given set of atoms (default to all). NOT allowed with orbitals keyword

• orbitals (array_like of int or bool, optional) – only return for a given set of orbitals (default to all) NOT allowed with atoms keyword

• norm – how the normalization of the summed DOS is performed (see norm routine)

o2p(orbitals, elec: int | str | None = None)

Return the pivoting indices (0-based) for the orbitals, possibly on an electrode

Will warn if an orbital requested is not in the device list of orbitals.

Parameters:

• orbitals (array_like or int) – orbital indices (0-based)

• elec – electrode to return pivoting indices of (if None it is the device pivoting indices).

orbital_ACOHP(elec_mol_proj, E: str | float, kavg=True, isc=None, orbitals=None)

Orbital COHP analysis of the projected spectral function

This will return a sparse matrix, see scipy.sparse.csr_matrix for details. Each matrix element of the sparse matrix corresponds to the COHP of the underlying geometry.

The COHP analysis can be written as:

\[\mathrm{COHP}^{\mathbf A}_{ij} = \frac{1}{2\pi} \Re\big[\mathbf A_{ij} \mathbf H_{ij} \big]\]

Parameters:

• elec_mol_proj (str or tuple) – the electrode of the projected spectral function

• E – the COHP values corresponding to the energy.

• kavg (bool, int or array_like, optional) – whether the returned COHP is k-averaged, an explicit k-point or a selection of k-points

• isc (array_like, optional) – the returned COHP from unit-cell ([None, None, None]) to the given supercell, the default is all COHP for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].

• orbitals (array-like or dict, optional) – only retain COHP matrix elements for a subset of orbitals, all other are set to 0.

See also

atom_COHP_from_orbital

atomic COHP analysis from an orbital COHP

atom_ACOHP

atomic COHP analysis of the projected spectral function

atom_COOP_from_orbital

transfer an orbital COOP to atomic COOP

orbital_ACOOP

orbital resolved COOP analysis of the projected spectral function

atom_ACOOP

atomic COOP analysis of the projected spectral function

orbital_ACOOP(elec_mol_proj, E: str | float, kavg=True, isc=None, orbitals=None)

Orbital COOP analysis of the projected spectral function

This will return a sparse matrix, see scipy.sparse.csr_matrix for details. Each matrix element of the sparse matrix corresponds to the COOP of the underlying geometry.

The COOP analysis can be written as:

\[\mathrm{COOP}^{\mathbf A}_{ij} = \frac{1}{2\pi} \Re\big[\mathbf A_{ij} \mathbf S_{ji} \big]\]

The sum of the COOP DOS is equal to the DOS:

\[\mathrm{ADOS}_{i} = \sum_j \mathrm{COOP}^{\mathbf A}_{ij}\]

One can calculate the (diagonal) balanced COOP analysis, see JPCM 15 (2003), 7751-7761 for details. The DBCOOP is given by:

\[\begin{split}D &= \sum_i \mathrm{COOP}^{\mathbf A}_{ii} \\ \mathrm{DBCOOP}^{\mathbf A}_{ij} &= \mathrm{COOP}^{\mathbf A}_{ij} / D\end{split}\]

The BCOOP can be looked up in the reference above.

Parameters:

• elec_mol_proj (str or tuple) – the electrode of the spectral function

• E – the COOP values corresponding to the energy.

• kavg (bool, int or array_like, optional) – whether the returned COOP is k-averaged, an explicit k-point or a selection of k-points

• isc (array_like, optional) – the returned COOP from unit-cell ([None, None, None]) to the given supercell, the default is all COOP for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].

• orbitals (array-like or dict, optional) – only retain COOP matrix elements for a subset of orbitals, all other are set to 0.

Examples

>>> ACOOP = tbt.orbital_ACOOP('Left.C60.HOMO', -1.0) # COOP @ E = -1 eV from ``Left.C60.HOMO`` spectral function
>>> ACOOP[10, 11] # COOP value between the 11th and 12th orbital
>>> ACOOP.sum(1).A[tbt.o_dev, 0] == tbt.ADOS(0, sum=False)[tbt.Eindex(-1.0)]
>>> D = ACOOP.diagonal().sum()
>>> ADBCOOP = ACOOP / D

See also

atom_COOP_from_orbital

transfer an orbital COOP to atomic COOP

atom_ACOOP

atomic COOP analysis of the projected spectral function

atom_COHP_from_orbital

atomic COHP analysis from an orbital COHP

orbital_ACOHP

orbital resolved COHP analysis of the projected spectral function

atom_ACOHP

atomic COHP analysis of the projected spectral function

orbital_current(elec: str | int = 0, elec_other: str | int = 1, kavg=True, isc=None, what: str = 'all', orbitals=None) → csr_matrix

Orbital current originating from elec as a sparse matrix

This is the bias window integrated quantity of orbital_transmission. As such it represents how the current is flowing at an applied bias from a given electrode.

\[J_{ij} = \frac eh\int_{\mu_1}^{\mu_2} \!\mathrm dE\, T_{ij} [n_F(\mu_2, k_B T_2) - n_F(\mu_1, k_B T_1)]\]

with \(T_{\langle\rangle}\) being the electronic temperature of the respective reservoir.

Parameters:

• elec – the originating electrode

• elec_other – this electrode determines the other chemical potential. As such the orbital currents does not reflect the current going from elec to elec_other!

• kavg (bool, int, optional) – whether the returned orbital current is k-averaged, or an explicit (unweighed) k-point is returned

• isc (array_like, optional) – the returned bond currents from the unit-cell ([None, None, None]) to the given supercell, the default is all orbital currents for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].

• what ({"all"/"both"/"+-"/"inout", "+"/"out", "-"/"in"}) – which orbital currents to return, all, positive (outgoing) or negative (incoming). Default to "all" because it can then be used in the subsequent default arguments for sparse_orbital_to_atom and sparse_orbital_to_scalar.

• orbitals (array-like or dict, optional) – only retain orbital currents for a subset of orbitals.

Notes

Calculating the current between two electrodes with the same chemical potential will return a matrix filled with 0’s since there is no bias window.

The currents does not reflect the current going from elec_from to elec_other!

See also

orbital_transmission

energy resolved transmission between orbitals

bond_transmission

energy resolved transmissions between atoms

bond_current

bias window integrated transmissions (orbital current summed over orbitals)

vector_transmission

an atomic field transmission for each atom (Cartesian representation of bond-transmissions)

vector_current

an atomic field current for each atom (Cartesian representation of bond-currents)

atom_transmission

energy resolved atomic transmission for each atom (scalar representation of bond-transmissions)

atom_current

the atomic current for each atom (scalar representation of bond-currents)

orbital_transmission(E: str | float, elec_mol_proj, *args, **kwargs)

Transmission at energy E between orbitals originating from elec

Each matrix element of the sparse matrix corresponds to the orbital indices of the underlying geometry (including buffer and electrode atoms).

When requesting orbital-transmissions it is vital to consider how the data needs to be analysed before extracting the data. For instance, if only local transmission pathways are interesting one should use what="+" to retain the positive orbital transmissions. While if one is interested in the transmission between subset of orbitals, what="all" is the correct method to account for loop transmissions.

The orbital transmissions are calculated as described in the TBtrans manual:

\[T_{ij}(E) = i [ (\mathbf H_{ji} - E\mathbf S_{ji}) \mathbf A_{ij}(E) - (\mathbf H_{ij} - E\mathbf S_{ij}) \mathbf A_{ji}(E)],\]

It is easy to show that the above matrix obeys \(T_{ij}=-T_{ji}\).

For inexperienced users it is adviced to try out all three values of what to ensure the correct physics is obtained.

This becomes even more important when the orbital transmissions are calculated with magnetic fields. With \(\mathbf B\) fields local transmission loops may form and the pathways does not necessarily flow along the transport direction.

For correct interpretation of the orbital transmissions it is vital that one integrates the full Brillouin zone without any symmetry operations, see Section 5.4 in [10].

Parameters:

• E – the orbital transmission corresponding to the energy.

• elec – the electrode of originating electrons

• kavg (bool, int, optional) – whether the returned orbital transmission is k-averaged, or an explicit (unweighed) k-point is returned

• isc (array_like, optional) – the returned transmissions from the unit-cell ([None, None, None]) to the given supercell, the default is all transmissions for the supercell. To only get unit cell transmissions, pass [0, 0, 0].

• what ({"all"/"both"/"+-"/"inout", "+"/"out", "-"/"in"}) – which transmissions to return, all, positive (outgoing) or negative (incoming).

• orbitals (array-like or dict, optional) – only retain transmissions for a subset of orbitals (including their supercell equivalents)

Returns:

• A `scipy.sparse.csr_matrix containing the supercell transmission pathways`, or

• orbital transmissions.

Examples

>>> Jij = tbt.orbital_transmission(-1.0) # orbital current @ E = -1 eV originating from electrode ``0``
>>> Jij[10, 11] # orbital transmission from the 11th to the 12th orbital

>>> Jij = tbt.orbital_transmission(-1.0,
...     orbitals={tbt.geometry.atoms[0]: [0, 1]})

only retain transmissions from 1st and 2nd orbitals on first atom type (all atoms of that type in the entire structure.

See also

orbital_current

bias window integrated transmissions

bond_transmission

energy resolved transmissions between atoms

bond_current

bias window integrated transmissions (orbital current summed over orbitals)

vector_transmission

an atomic field transmission for each atom (Cartesian representation of bond-transmissions)

vector_current

an atomic field current for each atom (Cartesian representation of bond-currents)

atom_transmission

energy resolved atomic transmission for each atom (scalar representation of bond-transmissions)

atom_current

the atomic current for each atom (scalar representation of bond-currents)

pivot(elec: int | str | None = None, in_device: bool = False, sort: bool = False)

Return the pivoting indices for a specific electrode (in the device region) or the device

Parameters:

• elec – Can be None, to specify the device region pivot indices (default). Otherwise, it corresponds to the pivoting indicies in the downfolding region.

• in_device – If True the pivoting table will be translated to the device region orbitals. If sort is also true, this would correspond to the orbitals directly translated to the geometry self.geometry.sub(self.a_dev).

• sort – Whether the returned indices are sorted. Mostly useful if you want to handle the device in a non-pivoted order.

Examples

>>> se = tbtncSileTBtrans(...)
>>> se.pivot()
[3, 4, 6, 5, 2]
>>> se.pivot(sort=True)
[2, 3, 4, 5, 6]
>>> se.pivot(0)
[2, 3]
>>> se.pivot(0, in_device=True)
[4, 0]
>>> se.pivot(0, in_device=True, sort=True)
[0, 1]
>>> se.pivot(0, sort=True)
[2, 3]

See also

pivot_down

for the pivot table for electrodes down-folding regions

pivot_down(elec: str | int)

Pivoting orbitals for the downfolding region of a given electrode

Parameters:

elec – the corresponding electrode to get the pivoting indices for

plot.geometry(*args, data_kwargs={}, axes: Axes = ['x', 'y', 'z'], atoms: AtomsIndex = None, atoms_style: Sequence[AtomsStyleSpec] = [], atoms_scale: float = 1.0, atoms_colorscale: Colorscale | None = None, drawing_mode: Literal['scatter', 'balls', None] = None, bind_bonds_to_ats: bool = True, points_per_bond: int = 20, bonds_style: StyleSpec = {}, bonds_scale: float = 1.0, bonds_colorscale: Colorscale | None = None, show_atoms: bool = True, show_bonds: bool = True, show_cell: Literal['box', 'axes', False] = 'box', cell_style: StyleSpec = {}, nsc: tuple[int, int, int] = (1, 1, 1), atoms_ndim_scale: tuple[float, float, float] = (16, 16, 1), bonds_ndim_scale: tuple[float, float, float] = (1, 1, 10), dataaxis_1d: np.ndarray | Callable | None = None, arrows: Sequence[AtomArrowSpec] = (), backend='plotly') → GeometryPlot

Calls read_geometry and creates a GeometryPlot from its output.

Parameters:

• axes – The axes to project the geometry to.

• atoms – The atoms to plot. If None, all atoms are plotted.

• atoms_style – List of style specifications for the atoms. See the showcase notebooks for examples.

• atoms_scale – Scaling factor for the size of all atoms.

• atoms_colorscale – Colorscale to use for the atoms in case the color attribute is an array of values. If None, the default colorscale is used for each backend.

• drawing_mode – The method used to draw the atoms.

• bind_bonds_to_ats – Whether to display only bonds between atoms that are being displayed.

• points_per_bond – When the points are drawn using points instead of lines (e.g. in some frameworks to draw multicolor bonds), the number of points used per bond.

• bonds_style – Style specification for the bonds. See the showcase notebooks for examples.

• bonds_scale – Scaling factor for the width of all bonds.

• bonds_colorscale – Colorscale to use for the bonds in case the color attribute is an array of values. If None, the default colorscale is used for each backend.

• show_atoms – Whether to display the atoms.

• show_bonds – Whether to display the bonds.

• show_cell – Mode to display the cell. If False, the cell is not displayed.

• cell_style – Style specification for the cell. See the showcase notebooks for examples.

• nsc – Number of unit cells to display in each direction.

• atoms_ndim_scale – Scaling factor for the size of the atoms for different dimensionalities (1D, 2D, 3D).

• bonds_ndim_scale – Scaling factor for the width of the bonds for different dimensionalities (1D, 2D, 3D).

• dataaxis_1d – Only meaningful for 1D plots. The data to plot on the Y axis.

• arrows – List of arrow specifications to display. See the showcase notebooks for examples.

• backend – The backend to use to generate the figure.

See also

GeometryPlot

The plot class used to generate the plot.

read_geometry

The method called to get the data.

plot.pdos(geometry: Geometry | None = None, *, groups: Sequence[OrbitalStyleQuery] = [{'name': 'DOS'}], Erange: tuple[float, float] = (-2, 2), E_axis: Literal['x', 'y'] = 'x', line_mode: Literal['line', 'scatter', 'area_line'] = 'line', line_scale: float = 1.0, backend: str = 'plotly') → PdosPlot

Creates a PDOSData object and then plots a PdosPlot from it.

Parameters:

• geometry – Full geometry of the system (including scattering and electrode regions). Right now only used to get the basis of each atom, which is not stored in the TBT.nc file.

• groups – List of orbital specifications to filter and accumulate the PDOS. The contribution of each group will be displayed in a different line. See showcase notebook for examples.

• Erange – The energy range to plot.

• E_axis – Axis to project the energies.

• line_mode – Mode used to draw the PDOS lines.

• line_scale – Scaling factor for the width of all lines.

• backend – The backend to generate the figure.

See also

PdosPlot

The plot class used to generate the plot.

PDOSData

The class to which data is converted.

projections(molecule)

List of projections on molecule

Parameters:

molecule (str) – name of molecule to retrieve projections on

read(*args, **kwargs)

Generic read method which should be overloaded in child-classes

Parameters:

kwargs – keyword arguments will try and search for the attribute read_<> and call it with the remaining **kwargs as arguments.

read_data(*args, **kwargs)

Read specific type of data.

This is a generic routine for reading different parts of the data-file.

Parameters:

• geometry (bool, optional) – return the geometry

• vector_transmission (bool, optional) – return the bond transmissions as vectors

• vector_current (bool, optional) – return the bond currents as vectors

• atom_transmission (bool, optional) – return the atomic transmission flowing through an atom (the activity current)

• atom_current (bool, optional) – return the atomic current flowing through an atom (the activity current)

read_geometry(*args, **kwargs)

Returns Geometry object from this file

read_lattice() → Lattice

Returns Lattice object from this file

reflection(elec: str | int = 0, kavg=True, from_single: bool = False) → ndarray

Reflection into electrode elec

The reflection into electrode elec is calculated as:

\[R(E) = T_{\mathrm{bulk}}(E) - \sum_{\mathrm{to}} T_{\mathrm{elec}\to\mathrm{to}}(E)\]

Another way of calculating the reflection is via:

\[R(E) = T_{\mathrm{bulk}}(E) - \big\{i \mathrm{Tr}[(\mathbf G-\mathbf G^\dagger)\boldsymbol\Gamma_{\mathrm{elec}}] - \mathrm{Tr}[\mathbf G\boldsymbol\Gamma_{\mathrm{elec}}\mathbf G^\dagger\boldsymbol\Gamma_{\mathrm{elec}}]\big\}\]

Both are identical, however, numerically they may be different. Particularly when the bulk transmission is very large compared to the transmission to the other electrodes one should prefer the first equation.

Parameters:

• elec – the backscattered electrode

• kavg (bool, int, optional) – whether the returned reflection is k-averaged, or an explicit (unweighed) k-point is returned

• from_single – whether the reflection is calculated using the Green function and a single scattering matrix Eq. (2) above (true), otherwise Eq. (1) will be used (false).

See also

transmission

the total transmission

transmission_eig

the transmission decomposed in eigenchannels

transmission_bulk

the total transmission in a periodic lead

sparse_atom_to_vector(Dab) → ndarray

Reduce an atomic sparse matrix to a vector contribution of each atom

Notes

This routine may be moved to a sisl.utility at some point since it would be a generic routine usable for other parts of sisl.

Parameters:

Dab (scipy.sparse.csr_matrix) – the input sparse matrix in atomic indices

sparse_orbital_to_atom(Dij, uc: bool = False, sum_dup: bool = True) → csr_matrix

Reduce a sparse matrix in orbital sparse to a sparse matrix in atomic indices

This algorithm may keep the same non-zero entries, but will return a new csr_matrix with duplicate indices.

Notes

This routine may be moved to a sisl.utility at some point since it would be a generic routine usable for other parts of sisl.

Parameters:

• Dij (scipy.sparse.csr_matrix) – the input sparse matrix in orbital format

• uc – whether the returned data are only in the unit-cell. If True this will return a sparse matrix of shape = (self.na, self.na), else, it will return a sparse matrix of shape = (self.na, self.na * self.n_s). One may figure out the connections via sc_index.

• sum_dup – duplicates will be summed if this is true, in this case, no duplicates are present in the returned sparse matrix. If false, duplicates may exist for multi-orbital systems.

sparse_orbital_to_scalar(Dij, activity: bool = True) → ndarray

Atomic scalar contribution of atoms for a sparse orbital matrix

The atomic contribution is a single number specifying a figure of the magnitude of sparse matrix elements for each atom. It is thus not a quantity that can be related to any physical quantity that the sparse matrix may represent but is merely a number that provides an idea of how much this atom is governing the data in the matrix.

The atomic contribution may have two meanings based on these two equations

\[\begin{split}\mathbf a_I^{|a|} &=\frac 12 \sum_{\{J\}} \Big| \sum_{i\in I}\sum_{j\in J} \mathbf A_{ij} \Big| \\ \mathbf a_I^{|o|} &=\frac 12 \sum_{i\in I}\sum_{j\in\{J\}} \big| A_{ij} \big|\end{split}\]

If the activity is requested (activity=True) \(\mathbf a_I^{\mathcal A} = \sqrt{\mathbf a_I^{|a|} \mathbf a_I^{|o|} }\) is returned.

If activity=False \(\mathbf a_I^{|a|}\) is returned.

For geometries with all atoms only having 1-orbital, they are equivalent.

Parameters:

• Dij (scipy.sparse.csr_matrix) – the orbital sparse matrix.

• activity – True to return the atomic activity, see explanation above

Notes

This routine may be moved to a sisl.utility at some point since it would be a generic routine usable for other parts of sisl.

Examples

>>> Jij = tbt.orbital_current(0, -1.03, what="both") # orbital current @ E = -1 eV originating from electrode ``0``
>>> Ja = tbt.sparse_orbital_to_scalar(Jij)

sparse_orbital_to_vector(Dij, uc: bool = False, sum_dup: bool = True) → ndarray

Reduce an orbital sparse matrix to a vector contribution of each atom

Equivalent to calling sparse_orbital_to_atom and sparse_atom_to_vector.

Notes

This routine may be moved to a sisl.utility at some point since it would be a generic routine usable for other parts of sisl.

Parameters:

• Dij (scipy.sparse.csr_matrix) – the input sparse matrix

• uc – whether the returned data are only in the unit-cell. If True this will return a sparse matrix of shape = (self.na, self.na), else, it will return a sparse matrix of shape = (self.na, self.na * self.n_s). One may figure out the connections via sc_index.

• sum_dup – duplicates will be summed if this is true, in this case, no duplicates are present in the returned sparse matrix. If false, duplicates may exist for multi-orbital systems.

transmission(elec_mol_proj_from, elec_mol_proj_to, kavg=True)

Transmission from mol_proj_elec_from to mol_proj_elec_to

Parameters:

• elec_mol_proj_from (str or tuple) – the originating scattering projection (<electrode>.<molecule>.<projection>)

• elec_mol_proj_to (str or tuple) – the absorbing scattering projection (<electrode>.<molecule>.<projection>)

• kavg (bool, int or array_like, optional) – whether the returned transmission is k-averaged, an explicit k-point or a selection of k-points

See also

transmission_eig

projected transmission decomposed in eigenchannels

transmission_bulk(elec: str | int = 0, kavg=True) → ndarray

Bulk transmission for the elec electrode

The bulk transmission is equivalent to creating a 2 terminal device with electrode elec tiled 3 times.

Parameters:

• elec – the bulk electrode

• kavg (bool, int, optional) – whether the returned transmission are k-averaged, or an explicit (unweighed) k-point is returned

See also

transmission

the total transmission

transmission_eig

the transmission decomposed in eigenchannels

reflection

total reflection back into the electrode

transmission_eig(elec_mol_proj_from, elec_mol_proj_to, kavg=True)

Transmission eigenvalues from elec_mol_proj_from to elec_mol_proj_to

Parameters:

• elec_mol_proj_from (str or tuple) – the originating scattering projection (<electrode>.<molecule>.<projection>)

• elec_mol_proj_to (str or tuple) – the absorbing scattering projection (<electrode>.<molecule>.<projection>)

• kavg (bool, int or array_like, optional) – whether the returned transmission is k-averaged, an explicit k-point or a selection of k-points

See also

transmission

projected transmission

vector_current(elec: str | int = 0, elec_other: str | int = 1, kavg=True, isc=None, what: str = 'all', orbitals=None) → ndarray

Vector for each atom being the sum of bond currents times the normalized bond vector between the atoms

The vector current is defined as:

\[\mathbf J_I = \sum_J \frac{\mathbf r^{(J)} - \mathbf r^{(I)}}{|\mathbf r^{(J)} - \mathbf r^{(I)}|} \cdot J_{IJ}\]

Where \(J_{IJ}\) is the bond current between atom \(I\) and \(J\) and \(\mathbf r^{(\langle\rangle)}\) are the atomic coordinates.

Parameters:

• elec – the electrode of originating electrons

• elec_other – this electrode determines the other chemical potential. As such the vector currents does not reflect the current going from elec to elec_other!

• kavg (bool, int, optional) – whether the returned vector current is k-averaged, or an explicit (unweighed) k-point is returned

• isc (array_like, optional) – the returned currents from the unit-cell ([None, None, None]) to the given supercell, the default is all currents for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].

• what ({"all"/"both"/"+-"/"inout", "+"/"out", "-"/"in"}) – The outgoing currents may be retrieved by "out". The incoming currents may be retrieved by "in", while the average incoming and outgoing direction can be obtained with "both". In the last case the vector currents are divided by 2 to ensure the length of the vector is compatible with the other options given a pristine system.

• orbitals (array-like or dict, optional) – only retain currents for a subset of orbitals before calculating currents Passed directly to orbital_current.

Notes

Calculating the current between two electrodes with the same chemical potential will return a matrix filled with 0’s since there is no bias window.

The currents does not reflect the current going from elec_from to elec_other!

Returns:

numpy.ndarray – array of vectors per atom in the Geometry (only non-zero for device atoms)

See also

orbital_transmission

energy resolved transmission between orbitals

orbital_current

bias window integrated transmissions

bond_transmission

energy resolved transmissions between atoms

bond_current

bias window integrated transmissions (orbital current summed over orbitals)

vector_transmission

an atomic field transmission for each atom (Cartesian representation of bond-transmissions)

atom_transmission

energy resolved atomic transmission for each atom (scalar representation of bond-transmissions)

atom_current

the atomic current for each atom (scalar representation of bond-currents)

vector_transmission(E: str | float, elec: str | int = 0, kavg=True, isc=None, what='all', orbitals=None) → ndarray

Vector for each atom being the sum of bond transmissions times the normalized bond vector between the atoms

The vector transmission is defined as:

\[\mathbf T_I = \sum_J \frac{\mathbf r^{(J)} - \mathbf r^{(I)}}{|\mathbf r^{(J)} - \mathbf r^{(I)}|} \cdot T_{IJ}\]

Where \(T_{IJ}\) is the bond transmission between atom \(I\) and \(J\) and \(\mathbf r^{(\langle\rangle)}\) are the atomic coordinates.

Parameters:

• E – the vector transmission corresponding to the energy.

• elec – the electrode of originating electrons

• kavg (bool, int, optional) – whether the returned vector transmission is k-averaged, or an explicit (unweighed) k-point is returned

• isc (array_like, optional) – the returned vectors from the unit-cell ([None, None, None]) to the given supercell, the default is all vectors for the supercell. To only get unit cell vectors, pass [0, 0, 0].

• what ({"all"/"both"/"+-"/"inout", "+"/"out", "-"/"in"}) – The outgoing vectors may be retrieved by "out". The incoming vectors may be retrieved by "in", while the average incoming and outgoing direction can be obtained with "both". In the last case the vector transmissions are divided by 2 to ensure the length of the vector is compatible with the other options; given a pristine system.

• orbitals (array-like or dict, optional) – only retain transmissions for a subset of orbitals before calculating bond transmissions Passed directly to orbital_transmission.

Returns:

numpy.ndarray – array of vectors per atom in the Geometry (only non-zero for device atoms)

See also

orbital_transmission

energy resolved transmission between orbitals

orbital_current

bias window integrated transmissions

bond_transmission

energy resolved transmissions between atoms

bond_current

bias window integrated transmissions (orbital current summed over orbitals)

vector_current

an atomic field current for each atom (Cartesian representation of bond-currents)

atom_transmission

energy resolved atomic transmission for each atom (scalar representation of bond-transmissions)

atom_current

the atomic current for each atom (scalar representation of bond-currents)

write(*args, **kwargs)

Generic write method which should be overloaded in child-classes

Parameters:

**kwargs – keyword arguments will try and search for the attribute write_ and call it with the remaining **kwargs as arguments.

write_tbtav(*args, **kwargs)

Convert this to a TBT.AV.nc file, i.e. all k dependent quantites are averaged out.

This command will overwrite any previous file with the ending TBT.AV.nc and thus will not take notice of any older files.

Parameters:

file (str) – output filename

property E: ndarray

Sampled energy-points in file

property a_buf

Atomic indices (0-based) of device atoms

property a_dev

Atomic indices (0-based) of device atoms (sorted)

atom_COHP = None

atom_COOP = None

property base_file

File of the current Sile

property cell: ndarray

Unit cell in file

current = None

current_parameter = None

density_matrix = None

property elecs

List of electrodes

fano = None

property file

File of the current Sile

property geom

Same as geometry, but deprecated

property geometry: Geometry

The associated geometry from this file

property k: ndarray

Sampled k-points in file

property kpt: ndarray

Sampled k-points in file

property lasto: ndarray

Last orbital of corresponding atom

property molecules

List of regions where state projections may happen

property nE: int

Number of energy-points in file

property na: int

Returns number of atoms in the cell

property na_b: int

Number of atoms in the buffer region

property na_buffer: int

Number of atoms in the buffer region

property na_d: int

Number of atoms in the device region

property na_dev: int

Number of atoms in the device region

property na_u: int

Returns number of atoms in the cell

property ne: int

Number of energy-points in file

property nk: int

Number of k-points in file

property nkpt: int

Number of k-points in file

property no: int

Returns number of orbitals in the cell

property no_d: int

Number of orbitals in the device region

property no_u: int

Returns number of orbitals in the cell

noise_power = None

property o_dev

Orbital indices (0-based) of device orbitals (sorted)

See also

pivot

retrieve the device orbitals, non-sorted

orbital_COHP = None

orbital_COOP = None

plot

Plotting functions for the tbtprojncSileTBtrans class.

shot_noise = None

property wk: ndarray

Weights of k-points in file

property wkpt: ndarray

Weights of k-points in file

property xa: ndarray

Atomic coordinates in file

property xyz: ndarray

Atomic coordinates in file