ValleyScope

中文说明

ValleyScope is a high-throughput post-processing workflow for valley projection, valley-projected irreps, and reduced EBR analysis in two-dimensional moire materials. It extracts selected VASP wavefunctions, resolves their parent-layer momentum-valley content, identifies the symmetry of each valley-projected subspace, and prepares or solves reduced-dimensional EBR problems using reviewed Bilbao/irreptables conventions.

ValleyScope reports physical evidence and explicit blockers. It does not turn high valley weight or a few symmetry eigenvalues into an automatic topology label.

Supported Scope

The primary supported and validated calculation domain is:

• VASP plane-wave wavefunctions, read from WAVECAR or a ValleyScope HDF5 intermediate;
• nonmagnetic, spin-orbit-coupled two-dimensional moire systems with parent time-reversal symmetry (TRS) and the default VASP Cartesian spin frame SAXIS=[0,0,1];
• selected moire high-symmetry points (HSPs), target bands, parent-layer valley centers, and a moire or bilayer structure for symmetry detection.

The workflow is general in lattice, space group, HSP set, valley orbit, and valley-projected subspace space group. Real materials are validation fixtures, not branches in the production method.

The calculation assumptions above are not fully recoverable from a WAVECAR or compact HDF5 file alone. Users must ensure that the source calculation belongs to this domain. Magnetic systems, spin-space-group treatments, non-SOC noncollinear calculations, and arbitrary spin axes are not currently claimed as validated production inputs.

Physical Workflow

VASP WAVECAR / ValleyScope HDF5
-> q-cut momentum-valley projection
-> valley mapping and valley-projected subspace symmetry
-> HSP little group and valley-preserving subgroup
-> symmetry representations restricted to the valley-preserving subgroup
-> valley-preserving irreps
-> reduced-dimensional EBR data in Bilbao/irreptables conventions
-> exact-integer reduced EBR decomposition

Momentum-Valley Projection

For a moire Bloch state at momentum (\mathbf k_M), each plane-wave component has momentum

$$\mathbf q = \mathbf k_M + \mathbf G_M .$$

ValleyScope compares the in-plane component of (\mathbf q) with configured parent-layer valley centers modulo the corresponding monolayer reciprocal lattice. A q-cut window defines a seed projector (P_a^0) for valley (a). For a normalized state,

$$W_a = \langle\psi|P_a^0|\psi\rangle, \qquad W_{\rm val} = \sum_a W_a .$$

This is momentum-space parent-valley projection, not full monolayer Bloch-state unfolding. W_val depends on the physical valley centers and q-cut, and is not a topological invariant.

For near-degenerate target bands, individual VASP eigenvectors are gauge-dependent. ValleyScope therefore analyzes the whole target subspace, including its projected valley matrices and a valley-adapted basis. Detailed subspace weights, assignments, and projector-quality evidence are retained by the debug profile.

Two projector modes are available:

• fixed_center (default) uses fixed parent-layer valley centers. These seed projectors enter symmetry and irrep readiness.
• k_resolved_parent_valley uses dynamic centers for parent-valley weight reporting across the moire Brillouin zone. It does not replace the fixed-center projectors in irrep or EBR readiness.

Valley-Preserving Symmetry

For an HSP (k), the HSP little group is

$$G_k = \{g \mid gk = k + G_M\}.$$

If (\pi_g(a)) is the valley mapping induced by operation (g), the valley-preserving subgroup for valley (a) is

$$G_k^{(a)} = \{g \in G_k \mid \pi_g(a)=a\}.$$

The seed-projector covariance test is

$$D_g P_a^0 D_g^\dagger \approx P_{\pi_g(a)}^0 .$$

An operation that maps (a) to another valley is a valley-changing operation. It contributes valley-orbit and valley sewing matrix data; it must not be forced into the single-valley irrep of (G_k^{(a)}). When an independently validated unitary valley sewing operation connects an observed source row to an unsampled row, ValleyScope can transport the actual projected subspace, re-match the target representation, and complete the valley-resolved unitary irrep vector. This completion requires recomputable coefficient, projector, affine-operation, and reciprocal-grid evidence.

ValleyScope restricts each symmetry representation to the actual valley-preserving operation set and matches double-valued irreps for SOC wavefunctions. Matching uses a validated standard-setting certificate that relates the computed affine space-group operations and reciprocal coordinates to the Bilbao/irreptables convention. Rotation matrices or user labels alone do not establish this convention.

Time Reversal

Parent TRS does not imply that a one-valley subspace is TR-invariant. In general, time reversal relates distinct time-reversed valleys:

• a single-valley irrep is a unitary irrep of its valley-preserving subgroup;
• unitary valley-sewing completion is distinct from time reversal;
• time-reversal completion is a separate inter-valley construction;
• a one-valley result is not matched to a grey group by default;
• joint grey-group data are used only when the required antiunitary and inter-valley evidence is present and validated.

Enable analysis.time_reversal.enabled only for input known to come from a parent-TRS calculation. Missing or inconsistent sewing evidence remains an explicit blocker.

Reduced EBR Analysis

Raw three-dimensional EBR data are not a ValleyScope answer. ValleyScope uses reviewed Bilbao/irreptables source conventions and reduces them to the same physical basis used by the valley calculation:

source EBR data
-> certified valley-projected subspace space group
-> sampled source-HSP basis
-> restriction to the valley-preserving subgroup
-> multiplicities in the matched valley-preserving irrep basis
-> reduced EBR matrix

The resulting integer vector is solved with the pure Python/SymPy exact integer solver. Results distinguish an exact nonnegative EBR combination, membership in the integer span without a nonnegative witness, exclusion from the integer span, an indeterminate bounded search, and a blocked calculation. None of these classifications alone is a Chern-number statement.

Trust Criteria

High valley purity is useful but not sufficient for a trusted irrep or EBR result. Promotion also requires the relevant evidence to pass, including:

• target-subspace closure and representation unitarity;
• seed-projector covariance under the full valley mapping;
• a well-defined valley-projected subspace and (G_k^{(a)});
• complete, unambiguous operation and source-HSP mappings;
• a validated standard setting and reviewed irrep/EBR provenance;
• conservative spinful and, when used, antiunitary sewing evidence.

A clean fixed-center seed basis may be used directly. Otherwise ValleyScope may construct a symmetry-adapted valley basis. Failed or incomplete evidence stays diagnostic-only or blocked; tolerances should not be relaxed merely to obtain a label.

Installation

ValleyScope requires Python 3.10 or newer.

git clone https://github.com/gawcista/valley-proj.git
cd valley-proj
python -m pip install -e .

Check the installed commands:

valleyscope --help
valleyscope analyze-hsp --help

From a source checkout, python -m valleyscope.cli --help is equivalent.

Quick Start

The normal workflow extracts a compact HDF5 file once, then analyzes that file.

1. Extract Selected WAVECAR Data

Create extract.yaml:

input:
  wavecar: ./WAVECAR

extract:
  kpoints:
    - name: GammaM
      vasp_index: 1
    - name: KM
      vasp_index: 2
  bands_vasp: [101, 102]

output:
  wavefunction_h5: ./wavefunctions.h5

vasp_index and bands_vasp are one-based VASP indices.

valleyscope extract-wavecar extract.yaml

2. Analyze the HSP Wavefunctions

Create analyze.yaml:

input:
  wavefunction_h5: ./wavefunctions.h5
  monolayer_poscars:
    parent: ./monolayer.vasp

analysis:
  kpoints: [GammaM, KM]
  iband: [101, 102]
  time_reversal:
    enabled: true

valley_centers:
  coordinate_mode: layer_frac
  centers:
    - name: valley_a
      layer: parent
      frac: [0.333333333333, 0.333333333333, 0.0]
    - name: valley_b
      layer: parent
      frac: [-0.333333333333, -0.333333333333, 0.0]

valley_subspaces:
  - name: valley_a
    centers: [valley_a]
  - name: valley_b
    centers: [valley_b]

projection:
  projector_mode: fixed_center
  qcut_fraction: 0.20

symmetry:
  operations:
    structure_file: ./moire.vasp

output:
  directory: ./valley_analysis
  profile: standard

Replace the HSPs, bands, valley centers, structures, and q-cut with values derived from the actual system. For multilayers, define each layer's reciprocal frame and transform consistently; for commensurate structures, integer supercell transforms are preferable to a twist angle alone.

valleyscope analyze-hsp analyze.yaml

Example screen summary

The standard profile prints the same result-first text written to valley_summary.txt. Its main sections are:

Run and projection context
Valley projection by sampled state
Valley-projected subspace space group and trusted HSP irreps
Authoritative reduced EBR results
Readiness blockers and warnings
Public output files

The run context includes lines such as qcut mode: and the effective q-cut. The standard Valley projection summary is the compact valley_projection_summary; the same record also keeps canonical valley_resolved_irreps, reduced_ebr_summary, and readiness_blocker_summary. Common projection states include fixed_center_not_captured, not_derived, and unreliable. The debug profile retains Valley subspace analysis; S_min is the minimum target-valley-subspace weight, alongside min_concentration, assigned_valleys, and valley_weights_adapted.

Inputs and Configuration

An analysis needs:

• a ValleyScope HDF5 file containing selected coefficients, reciprocal vectors, k points, energies, and VASP band indices;
• monolayer reciprocal-lattice information and physically defined valley centers, including layer transforms when needed;
• target HSP labels and analysis.iband values that exist in the HDF5 file;
• a moire or bilayer POSCAR/CONTCAR at symmetry.operations.structure_file for spglib operation detection.

The monolayer structure defines parent-layer reciprocal coordinates; the moire or bilayer structure defines the symmetry operations. They are not interchangeable.

Use output.profile: standard for routine runs and output.profile: debug when detailed projector, representation, closure, HSP-star, or sewing evidence is needed. Advanced source-table and standard-setting overrides are intentionally omitted here: use the current CLI help and parser in valleyscope/io/config.py when preparing reviewed inputs.

Outputs

The standard profile emphasizes these public surfaces:

File	Purpose
valley_summary.txt	Result-first human-readable summary; read this first
valley_summary.json	Compact machine-readable record with projection, canonical irrep, authoritative reduced-EBR, and blocker summaries
valley_weights.csv	Quick scan of raw per-(kpoint, VASP band) valley weights
valley_ebr_export_bundle.json	Written only when at least one ready bundle exists
valley_reduced_ebr_mapping.json	Written only when reduced EBR mapping is enabled and evaluated

valley_resolved_irreps contains one canonical record per sampled (kpoint, valley), including the valley-projected subspace space group, HSP little group, valley-preserving operation IDs, readiness, blockers, and irrep_multiplicities.

Raw rows in valley_weights.csv are useful for screening, but individual rows inside a near-degenerate band subspace are gauge-dependent. Interpret them together with the subspace and readiness information in the summary.

The debug profile retains detailed JSON/HDF5 evidence such as diagnostics.h5, symmetry reports, restricted representation data, and irrep/EBR provenance. These are debugging surfaces, not files that every user must inspect. Database ingestion reads complete EBR bundle and mapping evidence from the standalone public files; the compact summary does not duplicate those payloads. Some debug tables may be header-only when no row satisfies their physical scope; that alone is not a run failure.

Running Reduced EBR Mapping

analysis.reduced_ebr.enabled is off by default. For ready canonical bundles, the analyzer can build reviewed reduced tables from the installed irreptables source, or consume a user-supplied validated reduced table or reviewed mapping specification. All paths must pass the same group, setting, spin, HSP, irrep, and provenance checks before the exact solver runs.

Authoritative evaluation runs inside analyze-hsp, where the producer-owned representation evidence is available for recomputation. An exported JSON bundle retains identity links for audit and downstream transport, but those links alone cannot re-establish numerical trust. Therefore the standalone command is a fail-closed compatibility audit when given only serialized JSON; it does not promote an identity-only bundle to an authoritative solution:

valleyscope map-reduced-ebr \
  valley_ebr_export_bundle.json \
  validated_reduced_ebr_table.json \
  --output valley_reduced_ebr_mapping.json

ValleyScope does not ship ad hoc or unreviewed production EBR tables.

Limits and Non-Goals

ValleyScope currently does not provide:

• raw three-dimensional EBR decomposition as a valley-resolved result;
• built-in unreviewed EBR tables or heuristic floating-point EBR fitting;
• compatibility relations;
• Berry curvature, Wilson loops, or Chern numbers;
• automatic full-moire-Brillouin-zone valley-goodness validation;
• a topology conclusion from HSP data alone.

Development

Install the test dependency and run the suite:

python -m pip install -e ".[test]"
python -m pytest -q

The public command surface is defined in valleyscope/cli.py, configuration parsing in valleyscope/io/config.py, and public output selection in valleyscope/reports/analysis_outputs.py.