Structural-Spillage-Package

This work builds off Structural spillage: an efficient method to identify non-crystalline topological materials (https://link.aps.org/doi/10.1103/PhysRevResearch.5.L042011) with a more efficient implementation of the structural spillage calculations.

Method

The quasi-Bloch structural spillage at UC k-point k (paper eq. 2b):

$$ \gamma_{\mathrm{qB}}(\mathbf{k}) = \frac{1}{2}\left\lbrace \left[\sum_{G\alpha} P^{\alpha\alpha}_{\mathbf{k+G},\mathbf{k+G}}\right] + \tilde{n}_{\mathrm{occ}}(\mathbf{k}) - \sum_{G\alpha}\sum_{G'\beta}\left[P^{\alpha\beta}_{\mathbf{k+G},\mathbf{k+G'}}\tilde{P}^{\beta\alpha}_{\mathbf{k+G'},\mathbf{k+G}} + \tilde{P}^{\alpha\beta}_{\mathbf{k+G},\mathbf{k+G'}}P^{\beta\alpha}_{\mathbf{k+G'},\mathbf{k+G}}\right] \right\rbrace $$

where $P$ is the occupied-subspace projector of the crystalline reference (--xtal-sc) and $\tilde{P}$ is the projector of the comparison system (--amor-sc), both expressed in the plane-wave basis and unfolded onto the UC k-mesh (--xtal-uc). This is implemented in compute_structural_spillage in structural_spillage.py: p4 is $\sum_{G\alpha} P^{\alpha\alpha}$, aa is $\tilde{n}_{\mathrm{occ}}(\mathbf{k})$, and p1/p2 are the two cross terms $P\tilde{P}$ and $\tilde{P}P$.

Currently only $\gamma_{\mathrm{qB}}(\mathbf{k})$ itself (the structural spillage from the paper) is implemented. The band-resolved outputs (per-band structural spillage, per-band spin-orbit spillage, and the Appendix D spin-orbit plane-wave spillage) are not yet implemented.

Requirements

Python 3.9+ (uses the walrus operator). Install dependencies with:

pip install -r requirements.txt

Test cases

Bismuthene bi-layer

We provide the commands to calculate structural spillage for Bismuthene bi-layer for example.

• uc/2nd/WAVECAR — crystalline unit cell, 5×5×1 k-mesh, SOC (vasp_type=ncl)
• supercell/WAVECAR — crystalline 50-atom supercell, gamma-only, SOC
• dis/WAVECAR — the same supercell disordered (amorphized), gamma-only, noSOC

Run:

python structural_spillage.py \
  --xtal-uc  /global/cfs/cdirs/m4590/spillage_data/Bi_data/uc/2nd/WAVECAR \
  --uc-soc \
  --xtal-sc  /global/cfs/cdirs/m4590/spillage_data/Bi_data/supercell/WAVECAR \
  --amor-sc  /global/cfs/cdirs/m4590/spillage_data/Bi_data/dis/WAVECAR \
  --out-spillage tests/bi_smoke/spillage.txt

--uc-soc is required because the UC WAVECAR was written with LSORBIT=.TRUE..

We confirm that the value at the $\Gamma$ point (2.37) matches the original spillage code.

Bi2Se3 (crystalline)

Unlike the bismuthene case above, this compares the crystalline SOC supercell against the same nominal structure without SOC — no actual disorder — so it isolates the SOC-driven band inversion at $\Gamma$ that makes Bi2Se3 a topological insulator. This should yield the same value as pymatgen's spin orbit spillage.

python structural_spillage.py \
  --xtal-uc  /global/cfs/cdirs/m5222/ehof12/AmorphousTDA/r2scan_uc_nosoc/WAVECAR \
  --xtal-sc  /global/cfs/cdirs/m4590/spillage_data/DOS_crys_supercell/soc/WAVECAR \
  --amor-sc  /global/cfs/cdirs/m4590/spillage_data/DOS_crys_supercell/noSOC/WAVECAR \
  --out-spillage tests/bi2se3_smoke/spillage.txt

We confirm that the value at the $\Gamma$ point (2.7) matches pymatgen spin orbit spillage.