Tight-binding operators

This page describes the tight-binding (TB) files and the operator container of WannierIO.

At a high level, WannierIO provides:

• reading and writing the Wannier90 *_tb.dat, *_hr.dat, *_r.dat and *_wsvec.dat files, exactly as stored,

• OperatorPack, a container of named operators on a common set of R-vectors,

• sparse/compressed storage of an OperatorPack in HDF5, JLD2, Zarr and zipped Zarr files, see Sparse storage.

Wannier90 files

Wannier90 TB files store each operator on the Wigner–Seitz R-vectors with degeneracy weights (Rdegens), and *_wsvec.dat optionally adds the translation vectors and degeneracies (Tvectors, Tdegens) of the minimum-distance replica selection (MDRS). WannierIO reads and writes these fields as they are, without applying them:

• TbDat: *_tb.dat, the Hamiltonian and position operators,

• HrDat: *_hr.dat, the Hamiltonian only (no lattice),

• RDat: *_r.dat, the position operator only,

• WsvecDat: *_wsvec.dat, with optional MDRS information.

using WannierIO

tbdat = read_w90_tb_dat("silicon_tb.dat")
wsvec = read_w90_wsvec_dat("silicon_wsvec.dat")

write_w90_tb_dat("silicon_copy_tb.dat", tbdat)
write_w90_wsvec_dat("silicon_copy_wsvec.dat", wsvec)

Absorbing the degeneracies and MDRS replicas into the operators is Wannier interpolation, not file IO, and is done by Wannier.jl: its read_w90_tb(prefix) and TightBindingModel(tbdat; wsvec) return a model whose operators are a plain inverse Fourier transform away from any kpoint.

Operator container

An OperatorPack holds a header, the lattice, unique R-vectors and an ordered dictionary of named operators. Each operator is an array n_wann × n_wann × … × n_Rvecs: a scalar operator such as the Hamiltonian is n_wann × n_wann × n_Rvecs, a vector operator such as the Berry connection is n_wann × n_wann × 3 × n_Rvecs. The R-vectors carry no degeneracy weights, so an operator at a kpoint is the plain sum  .

The container stores data and checks shapes; it does not interpret the operators. Build one directly,

using WannierIO
using OrderedCollections: OrderedDict

operators = OrderedDict("hamiltonian" => H)  # n_wann × n_wann × n_Rvecs
pack = OperatorPack("my model", lattice, Rvectors, operators)

or export a Wannier.jl tight-binding model with OperatorPack(tb), which names the operators after the model's ("hamiltonian", "berry_connection", …).

For all related type/function signatures, see the tight-binding API reference.