API Reference: Topology

The Python surface exposes topology routines at top level (from pysicrs import berry_phase). See also Algorithms: Topology.

import pysicrs

Berry phase & curvature

berry_phase

berry_phase(states_real: list[list[float]], states_imag: list[list[float]]) -> float

Discrete Berry phase around a closed loop of parameter points. states_real[k] / states_imag[k] are the wavefunction components sampled along the loop.

berry_phase_bloch

berry_phase_bloch(theta: float) -> float

Berry phase accumulated by a two-level (Bloch) system along a parameter path at polar angle theta.

Chern / winding / skyrmion numbers

chern_number

chern_number(berry_curvature: list[list[float]], dk: float) -> float

\(C = \frac{1}{2\pi}\int \Omega\,d^2k\) over the Brillouin zone mesh.

winding_number

winding_number(f1: list[float], f2: list[float]) -> float

\(w = \frac{1}{2\pi i}\oint g'/g\,dz\) for \(g = f_1 + i f_2\) sampled on a closed contour.

skyrmion_number

skyrmion_number(n_field: list[list[list[float]]], dx: float, dy: float) -> float

Degree of the map \(\mathbb R^2 \to S^2\) from the spin texture n_field on an (x, y, 3) grid.

Rust-only (not yet bound)

function	purpose
berry_curvature	curvature at a point
chern_number_discrete	lattice flux version
winding_number_discrete	discrete encirclement count