kwant.continuum.LandauLattice

class kwant.continuum.LandauLattice(grid_spacing, offset=None, name='', norbs=None)

Bases: Monatomic

A Monatomic lattice with a Landau level index per site.

Site tags (see SiteFamily) are pairs of integers, where the first integer describes the real space position and the second the Landau level index.

The real space Bravais lattice is one dimensional, oriented parallel to the magnetic field. The Landau level index represents the harmonic oscillator basis states used for the Landau quantization in the plane normal to the field.

Parameters:

• grid_spacing (float) – Real space lattice spacing (parallel to the magnetic field).

• offset (float (optional)) – Displacement of the lattice origin from the real space coordinates origin.

Methods

closest(pos)

Find the lattice coordinates of the site closest to position pos.

landau_index(tag)

n_closest(pos, n=1, group_by_length=False, rtol=1e-09)

Find n sites closest to position pos.

Returns:

sites – An array with sites coordinates.

Return type:

numpy array

neighbors(n=1, eps=1e-08)

Return n-th nearest neighbor hoppings.

Parameters:

• n (integer) – Order of the hoppings to return. Note that the zeroth neighbor is the site itself or any other sites with the same position.

• eps (float) – Tolerance relative to the length of the shortest lattice vector for when to consider lengths to be approximately equal.

Returns:

hoppings – The n-th nearest neighbor hoppings.

Return type:

list of kwant.builder.HoppingKind objects

Notes

The hoppings are ordered lexicographically according to sublattice from which they originate, sublattice on which they end, and their lattice coordinates. Out of the two equivalent hoppings (a hopping and its reverse) only the lexicographically larger one is returned.

normalize_tag(tag)

Return a normalized version of the tag.

Raises TypeError or ValueError if the tag is not acceptable.

pos(tag)

Return the real-space position of the site with a given tag.

shape(function, start)

Return a key for all the lattice sites inside a given shape.

The object returned by this method is primarily meant to be used as a key for indexing Builder instances. See example below.

Parameters:

• function (callable) – A function of real space coordinates that returns a truth value: true for coordinates inside the shape, and false otherwise.

• start (1d array-like) – The real-space origin for the flood-fill algorithm.

Returns:

shape_sites

Return type:

function

Notes

When the function returned by this method is called, a flood-fill algorithm finds and yields all the lattice sites inside the specified shape starting from the specified position.

A Symmetry or Builder may be passed as sole argument when calling the function returned by this method. This will restrict the flood-fill to the fundamental domain of the symmetry (or the builder’s symmetry). Note that unless the shape function has that symmetry itself, the result may be unexpected.

Examples

>>> def circle(pos):
...     x, y = pos
...     return x**2 + y**2 < 100
...
>>> lat = kwant.lattice.honeycomb()
>>> syst = kwant.Builder()
>>> syst[lat.shape(circle, (0, 0))] = 0
>>> syst[lat.neighbors()] = 1

vec(int_vec)

Return the coordinates of a Bravais lattice vector in real space.

Parameters:

vec (integer vector) –

Returns:

output

Return type:

real vector

wire(center, radius)

Return a key for all the lattice sites inside an infinite cylinder.

This method makes it easy to define cylindrical (2d: rectangular) leads that point in any direction. The object returned by this method is primarily meant to be used as a key for indexing Builder instances. See example below.

Parameters:

• center (1d array-like of floats) – A point belonging to the axis of the cylinder.

• radius (float) – The radius of the cylinder.

Notes

The function returned by this method is to be called with a TranslationalSymmetry instance (or a Builder instance whose symmetry is used then) as sole argument. All the lattice sites (in the fundamental domain of the symmetry) inside the specified infinite cylinder are yielded. The direction of the cylinder is determined by the symmetry.

Examples

>>> lat = kwant.lattice.honeycomb()
>>> sym = kwant.TranslationalSymmetry(lat.a.vec((-2, 1)))
>>> lead = kwant.Builder(sym)
>>> lead[lat.wire((0, -5), 5)] = 0
>>> lead[lat.neighbors()] = 1

Attributes

prim_vecs

(sequence of vectors) Primitive vectors

prim_vecs[i]` is the i-th primitive basis vector of the lattice displacement of the lattice origin from the real space coordinates origin.