Lattice 1 8 1

Lattice 1 8 1

Lattice 1 8 12
1.8.1 Minecraft
Lattice 1 8 1 4 In Fraction
Unit cell of a Bravais lattice, the basic building block of a tight-binding model
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This class describes the primitive vectors, positions of sublattice sites and hoppingparameters which connect those sites. All of this structural information is used tobuild up a larger system by translation.
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A few prebuilt lattices are available in the Material Repository.
Parameters:a1, a2, a3:array_likePrimitive vectors of a Bravais lattice. A valid lattice must have at leastone primitive vector (a1), thus forming a simple 1-dimensional lattice.If a2 is also specified, a 2D lattice is created. Passing values for allthree vectors will create a 3D lattice.
Attributes
hoppingsDict of names and HoppingFamily
min_neighborsMinimum number of neighbours required at each lattice site
ndimThe dimensionality of the lattice: number of primitive vectors
nhopNumber of hopping families
nsubNumber of sublattices
offsetGlobal lattice offset: sublattice offsets are defined relative to this
sublatticesDict of names and Sublattice
vectorsPrimitive lattice vectors
Methods
add_aliases(*aliases)Add multiple new aliases
add_hoppings(*hoppings)Add multiple new hoppings
add_one_alias(name, original, position)Add a sublattice alias - useful for creating supercells
add_one_hopping(relative_index, from_sub, …)Add a new hopping
add_one_sublattice(name, position[, …])Add a new sublattice
add_sublattices(*sublattices)Add multiple new sublattices
brillouin_zone()Return a list of vertices which form the Brillouin zone (1D and 2D only)
plot([axes, vector_position])Illustrate the lattice by plotting the primitive cell and its nearest neighbors
plot_brillouin_zone([decorate])Plot the Brillouin zone and reciprocal lattice vectors
plot_vectors(position[, scale])Plot lattice vectors in the xy plane
reciprocal_vectors()Calculate the reciprocal space lattice vectors
register_hopping_energies(mapping)Register a mapping of user-friendly names to hopping energies
site_radius_for_plot([max_fraction])Return a good estimate for the lattice site radius for plotting
with_min_neighbors(number)Return a copy of this lattice with a different minimum neighbor count
with_offset(position)Return a copy of this lattice with a different offset
__call__(name)¶Call self as a function.
add_aliases(*aliases)¶Add multiple new aliases
Parameters:*aliasesEach element should be a tuple containing the arguments foradd_one_alias(). Works just like add_sublattices().
add_hoppings(*hoppings)¶Add multiple new hoppings
Parameters:*hoppingsEach element should be a tuple containing the arguments fora add_one_hopping() method call. See example.
Examples
These three calls:
Can be replaced with a single call to:
add_one_alias(name, original, position)¶Add a sublattice alias - useful for creating supercells
Create a new sublattice called name with the same properties as original(same onsite energy) but with at a different position. The new name isonly used during lattice construction and the original will be used for thefinal system and Hamiltonian. This is useful when defining a supercell whichcontains multiple sites of one sublattice family at different positions.
Parameters:name:strUser-friendly identifier of the alias.
original:strName of the original sublattice. It must already exist.
position:array_likeCartesian position with respect to the origin. Usually different than the original.
add_one_hopping(relative_index, from_sub, to_sub, hop_name_or_energy)¶Add a new hopping
For each new hopping, its Hermitian conjugate is added automatically. Doing somanually, i.e. adding a hopping which is the Hermitian conjugate of an existingone, will result in an exception being raised.
Parameters:relative_index:array_like of intDifference of the indices of the source and destination unit cells.
from_sub:strName of the sublattice in the source unit cell.
to_sub:strName of the sublattice in the destination unit cell.
hop_name_or_energy:float or strThe numeric value of the hopping energy or the name of a previouslyregistered hopping.
add_one_sublattice(name, position, onsite_energy=0.0, alias=')¶Add a new sublattice
Parameters:name:strUser-friendly identifier. The unique sublattice ID can later be accessedvia this sublattice name as lattice[sublattice_name].
position:array_likeCartesian position with respect to the origin.
onsite_energy:floatOnsite energy to be applied only to sites of this sublattice.
alias:strDeprecated: Use add_one_alias() instead.
add_sublattices(*sublattices)¶Add multiple new sublattices
Parameters:*sublatticesEach element should be a tuple containing the arguments fora add_one_sublattice() method call. See example.
Examples
These three calls:
Can be replaced with a single call to:
brillouin_zone()¶Return a list of vertices which form the Brillouin zone (1D and 2D only)
Returns:List[array_like]
Examples
plot(axes='xy', vector_position='center', **kwargs)¶Illustrate the lattice by plotting the primitive cell and its nearest neighbors
Parameters:axes:strThe spatial axes to plot. E.g. ‘xy', ‘yz', etc.
vector_position:array_like or ‘center'Cartesian position to be used as the origin for the lattice vectors.By default the origin is placed in the center of the primitive cell.
**kwargsForwarded to System.plot().
plot_brillouin_zone(decorate=True, **kwargs)¶Plot the Brillouin zone and reciprocal lattice vectors
Parameters:decorate:boolLabel the vertices of the Brillouin zone and show the reciprocal vectors
**kwargsForwarded to plt.plot().
plot_vectors(position, scale=1.0)¶Plot lattice vectors in the xy plane
Parameters:position:array_likeCartesian position to be used as the origin for the vectors.
scale:floatMultiply the length of the vectors by this number.
reciprocal_vectors()¶Calculate the reciprocal space lattice vectors
Returns:list
Examples
register_hopping_energies(mapping)¶Register a mapping of user-friendly names to hopping energies
Parameters:mapping:dictKeys are user-friendly hopping names and values are the numeric valuesof the hopping energy.
site_radius_for_plot(max_fraction=0.33)¶Return a good estimate for the lattice site radius for plotting
Calculated heuristically base on the length (1D) or area (2D) of the unit cell.In order to prevent overlap between sites, if the computed radius is too large,it will be clamped to a fraction of the shortest inter-atomic spacing.

Parameters:	a1, a2, a3:array_like Primitive vectors of a Bravais lattice. A valid lattice must have at leastone primitive vector (`a1`), thus forming a simple 1-dimensional lattice.If `a2` is also specified, a 2D lattice is created. Passing values for allthree vectors will create a 3D lattice.

Parameters:	*aliases Each element should be a tuple containing the arguments for`add_one_alias()`. Works just like `add_sublattices()`.

Parameters:	*hoppings Each element should be a tuple containing the arguments fora `add_one_hopping()` method call. See example.

Parameters:	name:str User-friendly identifier of the alias. original:str Name of the original sublattice. It must already exist. position:array_like Cartesian position with respect to the origin. Usually different than the original.

Parameters:	relative_index:array_like of int Difference of the indices of the source and destination unit cells. from_sub:str Name of the sublattice in the source unit cell. to_sub:str Name of the sublattice in the destination unit cell. hop_name_or_energy:float or str The numeric value of the hopping energy or the name of a previouslyregistered hopping.

Parameters:	name:str User-friendly identifier. The unique sublattice ID can later be accessedvia this sublattice name as `lattice[sublattice_name]`. position:array_like Cartesian position with respect to the origin. onsite_energy:float Onsite energy to be applied only to sites of this sublattice. alias:str Deprecated: Use `add_one_alias()` instead.

Parameters:	*sublattices Each element should be a tuple containing the arguments fora `add_one_sublattice()` method call. See example.

Returns:	List[array_like]

Parameters:	axes:str The spatial axes to plot. E.g. ‘xy', ‘yz', etc. vector_position:array_like or ‘center' Cartesian position to be used as the origin for the lattice vectors.By default the origin is placed in the center of the primitive cell. **kwargs Forwarded to `System.plot()`.

Parameters:	decorate:bool Label the vertices of the Brillouin zone and show the reciprocal vectors **kwargs Forwarded to `plt.plot()`.

Parameters:	position:array_like Cartesian position to be used as the origin for the vectors. scale:float Multiply the length of the vectors by this number.

Returns:	list

Parameters:	mapping:dict Keys are user-friendly hopping names and values are the numeric valuesof the hopping energy.

Parameters:max_fraction:floatSet the upper limit of the calculated radius as this fraction of theshortest inter-atomic spacing in the lattice unit cell. Should be lessthan 0.5 to avoid overlap between neighboring lattice sites.
Returns:float
with_min_neighbors(number)¶Return a copy of this lattice with a different minimum neighbor count
Parameters:number:intThe minimum number of neighbors.
Returns:Lattice
with_offset(position)¶Return a copy of this lattice with a different offset
It must be within half the length of a primitive lattice vector
Parameters:position:array_likeCartesian offset in the same length unit as the lattice vectors.
Returns:Lattice
hoppings¶Dict of names and HoppingFamily
Lattice 1 8 12min_neighbors¶1.8.1 MinecraftMinimum number of neighbours required at each lattice site
When constructing a finite-sized system, lattice sites with less neighborsthan this minimum will be considered as 'dangling' and they will be removed.
ndim¶The dimensionality of the lattice: number of primitive vectors
nhop¶Number of hopping families
nsub¶Number of sublattices
Lattice 1 8 1 4 In Fractionoffset¶Global lattice offset: sublattice offsets are defined relative to this
It must be within half the length of a primitive lattice vector.
sublattices¶Dict of names and Sublattice
vectors¶Primitive lattice vectors

`hoppings`	Dict of names and `HoppingFamily`
`min_neighbors`	Minimum number of neighbours required at each lattice site
`ndim`	The dimensionality of the lattice: number of primitive vectors
`nhop`	Number of hopping families
`nsub`	Number of sublattices
`offset`	Global lattice offset: sublattice offsets are defined relative to this
`sublattices`	Dict of names and `Sublattice`
`vectors`	Primitive lattice vectors

`add_aliases`(*aliases)	Add multiple new aliases
`add_hoppings`(*hoppings)	Add multiple new hoppings
`add_one_alias`(name, original, position)	Add a sublattice alias - useful for creating supercells
`add_one_hopping`(relative_index, from_sub, …)	Add a new hopping
`add_one_sublattice`(name, position[, …])	Add a new sublattice
`add_sublattices`(*sublattices)	Add multiple new sublattices
`brillouin_zone`()	Return a list of vertices which form the Brillouin zone (1D and 2D only)
`plot`([axes, vector_position])	Illustrate the lattice by plotting the primitive cell and its nearest neighbors
`plot_brillouin_zone`([decorate])	Plot the Brillouin zone and reciprocal lattice vectors
`plot_vectors`(position[, scale])	Plot lattice vectors in the xy plane
`reciprocal_vectors`()	Calculate the reciprocal space lattice vectors
`register_hopping_energies`(mapping)	Register a mapping of user-friendly names to hopping energies
`site_radius_for_plot`([max_fraction])	Return a good estimate for the lattice site radius for plotting
`with_min_neighbors`(number)	Return a copy of this lattice with a different minimum neighbor count
`with_offset`(position)	Return a copy of this lattice with a different offset

Parameters:	max_fraction:float Set the upper limit of the calculated radius as this fraction of theshortest inter-atomic spacing in the lattice unit cell. Should be lessthan 0.5 to avoid overlap between neighboring lattice sites.
Returns:	float

Parameters:	number:int The minimum number of neighbors.
Returns:	`Lattice`

Parameters:	position:array_like Cartesian offset in the same length unit as the lattice vectors.
Returns:	`Lattice`