erlab.plotting.bz

Utilities for plotting Brillouin zones.

Functions

plot_bz(basis, *[, reciprocal, rotate, ...])	Plot a Brillouin zone, given the basis vectors.
plot_hex_bz([a, reciprocal, rotate, offset, ax])	Plot a 2D hexagonal BZ overlay on the specified axes.
plot_in_plane_bz(bvec, *[, kz, angle, ...])	Plot Brillouin-zone boundaries on a constant-kz plane.
plot_out_of_plane_bz(bvec, *[, k_parallel, ...])	Plot Brillouin-zone boundaries on an out-of-plane momentum slice.

erlab.plotting.bz.plot_bz(basis, *, reciprocal=False, rotate=0.0, offset=(0.0, 0.0), ax=None, **kwargs)

Plot a Brillouin zone, given the basis vectors.

Parameters:

• basis (ndarray[tuple[Any, ...], dtype[floating]]) – A 2D or 3D numpy array with shape (N, N) where N = 2 or 3, containing the basis vectors of the lattice. If N is 3, only the upper left 2x2 submatrix is used.

• reciprocal (bool, default: False) – If True, the basis vectors are interpreted as reciprocal lattice vectors.

• rotate (float, default: 0.0) – Rotation angle in degrees to apply to the BZ.

• offset (tuple[float, float], default: (0.0, 0.0)) – Offset for the Brillouin zone center in the form of a tuple (x, y).

• ax (Axes | None, default: None) – The axes to plot the BZ on. If None, the current axes are used.

• **kwargs – Additional keyword arguments passed to matplotlib.patches.Polygon.

erlab.plotting.bz.plot_hex_bz(a=3.54, *, reciprocal=False, rotate=0.0, offset=(0.0, 0.0), ax=None, **kwargs)

Plot a 2D hexagonal BZ overlay on the specified axes.

Parameters:

• a (float, default: 3.54) – Lattice constant of the hexagonal lattice.

• reciprocal (bool, default: False) – If True, a is interpreted as the periodicity of the reciprocal lattice.

• rotate (float, default: 0.0) – Rotation angle in degrees to apply to the BZ.

• offset (tuple[float, float], default: (0.0, 0.0)) – Offset for the Brillouin zone center in the form of a tuple (x, y).

• ax (Axes | None, default: None) – The axes to plot the BZ on. If None, the current axes are used.

• **kwargs – Additional keyword arguments passed to matplotlib.patches.RegularPolygon.

erlab.plotting.bz.plot_in_plane_bz(bvec, *, kz=0.0, angle=0.0, bounds=None, ax=None, vertices=False, midpoints=False, vertex_kwargs=None, midpoint_kwargs=None, **line_kwargs)

Plot Brillouin-zone boundaries on a constant-kz plane.

Parameters:

• bvec (ndarray[tuple[Any, ...], dtype[floating]]) – Reciprocal lattice basis vectors.

• kz (float, default: 0.0) – Out-of-plane momentum of the slice.

• angle (float, default: 0.0) – Rotation angle in degrees about the kz axis.

• bounds (tuple[float, float, float, float] | None, default: None) – (kx_min, kx_max, ky_min, ky_max) bounds. If None, bounds are inferred from the current axes limits.

• ax (Axes | None, default: None) – The axes to plot the BZ boundaries on. If None, the current axes are used.

• vertices (bool, default: False) – If True, also mark BZ vertices.

• midpoints (bool, default: False) – If True, also mark segment midpoints.

• vertex_kwargs (dict[str, Any] | None, default: None) – Additional keyword arguments passed to matplotlib.axes.Axes.scatter() for vertices and midpoints.

• midpoint_kwargs (dict[str, Any] | None, default: None) – Additional keyword arguments passed to matplotlib.axes.Axes.scatter() for vertices and midpoints.

• **line_kwargs – Additional keyword arguments passed to matplotlib.axes.Axes.plot().

Returns:

tuple – Line artists, vertex scatter artist, and midpoint scatter artist.

Return type:

tuple[tuple[Line2D, …], PathCollection | None, PathCollection | None]

erlab.plotting.bz.plot_out_of_plane_bz(bvec, *, k_parallel=0.0, angle=0.0, bounds=None, ax=None, vertices=False, midpoints=False, vertex_kwargs=None, midpoint_kwargs=None, **line_kwargs)

Plot Brillouin-zone boundaries on an out-of-plane momentum slice.

Parameters:

• bvec (ndarray[tuple[Any, ...], dtype[floating]]) – Reciprocal lattice basis vectors.

• k_parallel (float, default: 0.0) – Fixed in-plane momentum component along angle.

• angle (float, default: 0.0) – Angle in degrees of the fixed in-plane momentum direction.

• bounds (tuple[float, float, float, float] | None, default: None) – (kp_min, kp_max, kz_min, kz_max) bounds. If None, bounds are inferred from the current axes limits.

• ax (Axes | None, default: None) – The axes to plot the BZ boundaries on. If None, the current axes are used.

• vertices (bool, default: False) – If True, also mark BZ vertices.

• midpoints (bool, default: False) – If True, also mark segment midpoints.

• vertex_kwargs (dict[str, Any] | None, default: None) – Additional keyword arguments passed to matplotlib.axes.Axes.scatter() for vertices and midpoints.

• midpoint_kwargs (dict[str, Any] | None, default: None) – Additional keyword arguments passed to matplotlib.axes.Axes.scatter() for vertices and midpoints.

• **line_kwargs – Additional keyword arguments passed to matplotlib.axes.Axes.plot().

Returns:

tuple – Line artists, vertex scatter artist, and midpoint scatter artist.

Return type:

tuple[tuple[Line2D, …], PathCollection | None, PathCollection | None]