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SOF-8014: tutorial for twisted MoS2 bilayer band structure - #396

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SOF-8014 — tutorial: band structure of twisted MoS2 bilayers

Companion to mat3ra/api-examples#358, which adds the notebooks this page describes.

Reproduces the electronic-structure result of Liu et al., Evolution of interlayer coupling in
twisted molybdenum disulfide bilayers
, Nat. Commun. 5, 4966 (2014)

10.1038/ncomms5966: the indirect gap of a MoS2 bilayer is set
by the interlayer distance, while the K-valley direct gap barely moves.

Contents

  • the manuscript's result, and that Kohn-Sham gaps are not the photoluminescence peaks it also
    reports
  • the prerequisite structure-creation tutorial, which builds and names the materials
  • the structures computed, and that the interlayer distances are inputs taken from Table S1 rather
    than relaxed here
  • which stacking registry a 0° or 60° build produces, since the builder has no registry parameter
  • computational settings and where they differ from the manuscript's
  • results: gaps against twist angle, on the manuscript's own axes

Where it differs from the manuscript

The manuscript used LDA with norm-conserving pseudopotentials. The platform carries none for Mo or S
under LDA, so the tutorial uses the ultrasoft GBRV set at the same functional — keeping LDA matters,
since it is what binds this bilayer. Absolute gaps land ~0.2 eV low as a result; differences between
structures computed with identical settings are much less affected, and the page says so.

Verified

  • measured on two structures differing only in interlayer distance: indirect gaps 1.098 eV at 6.1 Å
    and 1.297 eV at 6.5 Å, a +0.199 eV shift against the manuscript's +0.20 eV, with the
    K-valley gap moving 0.012 eV
  • every relative link, the image, the jupyterlite_embed target and the @Liu2014 citation resolve
  • registered in both mkdocs.yml and mkdocs-guide.yml, matching the sibling simulation tutorial;
    both parse

Not rendered locally — mkdocs is not installed in this worktree, so the build is unverified beyond
the checks above.

🤖 Generated with Claude Code

Reproduces the electronic-structure result of Liu et al., Nat. Commun. 5,
4966 (2014): the indirect gap of a MoS2 bilayer is set by the interlayer
distance, while the K-valley direct gap barely moves.

Covers the prerequisite structure notebook, the structures computed, where
the settings differ from the manuscript's and why, and the results.

Registered in both mkdocs.yml and mkdocs-guide.yml, as the sibling
simulation tutorial is.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
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VsevolodX and others added 5 commits August 18, 2026 18:31
The out-of-plane cell is now 20 A as in the manuscript, so it is no longer
a divergence. The cutoff row is: 140 Ry is a norm-conserving wavefunction
cutoff and is not comparable with an ultrasoft one, which converges lower
and needs a higher charge-density cutoff instead.

Drop the walkthrough of the Mo-Mo to sulfur-plane conversion; the notebook
prints the resulting separation and cell height for checking.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
The band-structure page did not read as the second half of the MoS2
manuscript reproduction:

- nav titled it "Twisted Bilayer MoS2 Band Structure" instead of the
  structure page's title plus "(Band Structure)", the form already used
  for the graphene pair
- in mkdocs-guide.yml it sat seven rows above its own structure page,
  directly under the graphene pair
- overview.md still advertised its Properties entry as "Coming Soon"

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Follows the _SIMULATION rename in api-examples. Two references in the
page - the GitHub source path and the jupyterlite_embed notebook_name.
The page slug is unchanged, so no published URL moves.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
The cost-lever paragraph still named INTERFACE_VACUUM, which no longer
exists - the structure notebook takes TOTAL_CELL_HEIGHT and derives the
builder's vacuum from it. It also framed the cell as more generous than
the manuscript's, which stopped being true when it moved to 20 A.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Sections 3 and 4 documented create_twisted_interface_with_commnesurate_
lattices.ipynb, while section 5 embeds
specific_examples/interface_bilayer_twisted_commensurate_lattices_
molybdenum_disulfide.ipynb. None of the variables the page told the
reader to set - TARGET_TWIST_ANGLE, INTERFACE_DISTANCE, INTERFACE_VACUUM,
MAX_SUPERCELL_MATRIX_INT, USE_CONVENTIONAL_CELL, STACKING_DIRECTION -
exist in the embedded notebook, so the prerequisite step of the band
structure tutorial could not be followed as written.

Rewritten against the embedded notebook: the INTERFACE_PARAMETERS list
replaces the one-angle-at-a-time walkthrough, TOTAL_CELL_HEIGHT replaces
INTERFACE_VACUUM, and the six angle snippets become uncommented entries.

Two things the old text got wrong about the physics, now called out:
d_mo_mo is the Mo-Mo separation Table S1 tabulates, not a gap - passing
6.5 A through as a gap separates the layers ~3 A too far; and the
interlayer distance belongs to the stacking registry, 6.1-6.2 A for
AA1/AB1 and AA2/AB2 against 6.8 A for AA3/AB3.

Atom counts, Mo-Mo separations, cell heights and the two registry
classifications in the new text were built and measured, not inferred.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
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