Concept Guide — Observables & Spectral Analysis

Analyse bands, densities of states, Berry curvature, and linear-response coefficients using the Spectrum, LinearResponse, and Plotting modules.

Spectrum essentials

Spectrum.getbands(hops, ks, op=nothing) computes eigenvalues and, if an operator is supplied, expectation values along the k-path.
Spectrum.getdos(hops, emin, emax; klin, Γ, format) returns density-of-states estimates. For large systems use format=:sparse.
Spectrum.chern and related routines derive topological invariants from eigenvectors or Wilson loops.

Berry phases & Wilson loops

lat = Geometries.honeycomb()
hops = Operators.graphene(lat)
loops = Spectrum.wilsonloop(hops; nk=200, bands=1:2)

Inspect the SSH×SSH example (extra/examples/SSHxSSH/wilsonloop.jl) for a working script.
Normalise phases to maintain continuity; unwrap when plotting.

Linear response

LinearResponse.opticalconductivity and friends evaluate conductivities using Kubo formulas. See extra/examples/graphene/opticalconductivity.jl.
Pay attention to broadening parameters and sum-rule checks.

Plotting recipes

Plotting.plot(bands; kwargs...) produces band plots with colour bars, annotated symmetry points, and legend customisation.
For density-of-states, combine Plots with returned arrays to overlay multiple datasets.

Best practices

Cache k-paths and operators when scanning parameters to avoid recomputation.
For extensive sweeps, stream results to disk (HDF5, JLD2) and perform plotting in a separate step to decouple compute from rendering.
Document numerical tolerances (Γ, nk, integration step) alongside figures so others can reproduce them.