PAOFLOW.pyskeaf.slice_ops

Construction of 2D energy slices perpendicular to the magnetic-field axis.

Reproduces the per-slice grid construction at the top of sliceext (skeaf_v1p3p0_r149.F90 lines 3853–3886) and the slice-frame setup at lines 1249–1264 of the main program.

Geometry

The slicing frame has axes (x’, y’, z’) with z’ = magnetic-field direction. In terms of (theta, phi) — both in radians, where phi is the polar angle from +z and theta the azimuth in the xy-plane — the H-vector in the BZ frame is

Ĥ = (cos θ sin φ, sin θ sin φ, cos φ).

The Fortran builds the rotation matrix from slicing → BZ frame using

p = sin θ, q = cos θ, s = sin φ, c = cos φ, u = 1 − cos φ

via the explicit form

     | p²u + c    −p q u    q s |
R =  | −p q u     q²u + c   p s |
     | −q s       −p s      c   |

so that (p1, p2, p3) = R · (X', Y', Z') with the columns being the BZ-frame images of the slicing x’, y’, z’ axes.

Supercell sampling

The orbit-detection supercell has

numx = numy = numslices = 4·(numint − 1) + 1

points along each side, with spacing

Δk = maxlreciplat / (numint − 1) (Å^-1)

where maxlreciplat = max(|b_1|, |b_2|, |b_3|). The slicing-frame coordinates of grid index i ∈ [1, numx] are

X’_i = ((i − 1) / (numint − 1) − 1) · maxlreciplat

i.e. the supercell spans [−1, +3] · maxlreciplat in each slicing direction (asymmetric: matches Fortran). The total supercell side length is xlength = ylength = 4 · maxlreciplat.

After rotating each (X’, Y’, Z’) sample into the BZ frame, the result is mapped to BXSF fractional grid indices and wrapped periodically with mod (n − 1) (the same trick as floor(fintpoint/(n-1))*(n-1) in sliceext).

Classes

SliceGeometry	Geometric metadata for one slicing configuration (independent of slice index).
Slice2D	Energies sampled on a 2D (numx × numy) slice perpendicular to H.

Functions

rotation_matrix(theta, phi)	Return the 3×3 rotation matrix from slicing-frame to BZ-frame.
make_slice_geometry(bxsf, numint, theta, phi)	Pre-compute the slice geometry for given (theta, phi) and numint.
build_slice(bxsf, geom, slice_index)	Build the 2D energy slice at index slice_index (1-based, in [1, numx]).

Module Contents

class PAOFLOW.pyskeaf.slice_ops.SliceGeometry

Geometric metadata for one slicing configuration (independent of slice index).

theta: float

phi: float

numint: int

numx: int

xkseparation: float

ykseparation: float

zkseparation: float

xlength: float

ylength: float

maxlreciplat: float

rotation: numpy.ndarray

h_vector: numpy.ndarray

plr_inverse: numpy.ndarray

class PAOFLOW.pyskeaf.slice_ops.Slice2D

Energies sampled on a 2D (numx × numy) slice perpendicular to H.

geometry: SliceGeometry

slice_index: int

z_prime: float

energies: numpy.ndarray

PAOFLOW.pyskeaf.slice_ops.rotation_matrix(theta, phi)

Return the 3×3 rotation matrix from slicing-frame to BZ-frame.

Reproduces the parameterisation at lines 1260–1264 of the Fortran source (p, q, s, c, u) exactly; see module docstring for the formula.

PAOFLOW.pyskeaf.slice_ops.make_slice_geometry(bxsf, numint, theta, phi)

Pre-compute the slice geometry for given (theta, phi) and numint.

Mirrors the bookkeeping at Fortran lines 669–688 plus 1249–1264.

PAOFLOW.pyskeaf.slice_ops.build_slice(bxsf, geom, slice_index)

Build the 2D energy slice at index slice_index (1-based, in [1, numx]).

Each of the numx · numy sample points is independently rotated into the BZ frame and Lagrange-interpolated. Memory usage: O(numx²) scratch for fractional indices.