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Concept Guide — Geometry & Lattices

This guide expands on Tutorial 1 with additional context about how LatticeQM represents lattices, handles dimensionality, and exposes helper utilities.

Core types

  • Structure.Lattice: stores primitive vectors (A), fractional coordinates, and optional extra dimensions (e.g. layer labels, z offsets).
  • Structure.Geometries: collection of convenience constructors for common lattices (honeycomb, triangular, square, multilayer stacks).
  • Structure.Lattices: lower-level factory supporting programmatic lattice generation.

Constructing lattices

lat = Lattice([1 0; 0 1], [[0, 0] [0.5, 0.5]])   # square lattice with two sites
lat3d = Lattice([[1,0,0] [0,1,0] [0,0,1]])       # cubic lattice
twisted = Geometries.honeycomb_twisted(13)       # moiré honeycomb (θ ≈ 1.05°)
  • Use the optional extra_dimensions keyword to attach metadata: Lattice(A, coords; extra_dimensions=["layer"]).
  • Prefer Geometries helper functions for well-tested configurations; inspect their docstrings for supported keywords (strain, offsets, stacking).

Neighbours and symmetry

  • Structure.getneighbors(lat; cutoff, order) returns neighbour shells with displacement vectors—essential for building hoppings.
  • Structure.brillouinzone(lat) and Structure.highsymmetrypoints(lat) help generate k-paths aligned with lattice symmetries.
  • Structure.symmetries(lat) (where available) exposes point-group data; leverage it to reduce computational workloads.

Visualisation

using Plots
plot(lat; repeat=[0:1, 0:1], bonds=true, legends=false)
  • For multilayer systems, use the LayeredLayouts recipes in Plotting to separate layers vertically.
  • Export figures alongside scripts (mkpath("output"); savefig("output/lat.svg")) to keep provenance.

Best practices

  • Avoid mutating lattice internals directly; instead use Structure.update_spacecoordinates! or Structure.update_A!.
  • Document any custom lattice constructors and add them to Geometries when stable so users can discover them via the API reference.
  • Cross-reference the extra/examples/ scripts to showcase non-standard lattices (e.g. TMDs, triangular Hubbard models).