unPHold

unPHold unfolds phonon band structures from a supercell calculation onto a primitive-cell Brillouin zone and characterizes each mode.

GitHub repo: sabia-group/unPHold

What unPHold does

A supercell has a smaller Brillouin zone than the primitive cell it is built from, so its phonon branches appear as folded copies of the primitive-cell dispersion. Unfolding reverses this down-folding: from a supercell phonon calculation it recovers the effective primitive-cell dispersion.

Folded TBG bands Unfolded TBG spectrum

Unfolding twisted bilayer graphene phonon bands. Left: the raw phonon bands of the moiré supercell, where every mode is folded into the small moiré Brillouin zone, giving dense, hard-to-read bands. Right: unfolding onto one layer's primitive cell (blue) recovers the effective dispersion. The spetral function matches the Bernal bilayer reference (red).

Beyond unfolding supercell phonon bands, unPHold also characterizes individual modes and visualizes their real-space displacement pattern.

Layer-breathing mode of twisted bilayer graphene

A special layer-breathing mode (LBM) of twisted bilayer graphene at Γ. The bottom layer (left) and the top layer (right) move antiphase out-of-plane (colour, red for +z and blue for -z), with moiré-modified amplitude at AA and AB stacking regions.

Scope

  • 3D and 2D supercells, moiré superlattices, defected structures
  • Relaxed / deregistered structures
  • Phonon mode characterization

Features

  • Atom matching for defective, deregistered, and layer-resolved systems.
  • Per-mode unfolding weights and unfolded band structure visualization.
  • Mode-character metrics: acoustic participation ratio (APR), longitudinality (L), and out-of-plane verticality (V).
  • Built on phonopy: unPHold reuses phonopy's force constants and structural metadata, so it works with any force-constant source, including DFT codes and machine-learning interatomic potentials (MLIPs).

Getting started