What if electrons
had a neighborhood?
Choose a material. Tune the energy. Discover where electronic
states spread out—and where they gather.
A smooth neighborhood
Regular atoms create a repeating environment.
The bright dots illustrate a relatively spread-out state.
The energy dial
TUNE INThink of energy as a radio frequency. Peaks indicate where more electronic states are available to tune into.
Recomputed from the repository’s 48-site Hamiltonian. Gaussian broadening σ = 0.065; normalized per Hamiltonian basis state.
Spread out or clustered?
EXPLOREEach point represents a near-Fermi eigenstate. Higher means its probability is more concentrated across model sites.
The inverse participation ratio (IPR) increases as a state becomes more concentrated. Computed from twelve near-Fermi eigenstates per model; not physical travel distances.
What does it mean?
An ordered crystal has a regular repeating atomic pattern. Some of its modeled electronic states extend across many sites.
Stay curious. Try a little experiment.
Switch from blue to green. Move across a peak. Tap a high dot, then a low one.
What changes—and what stays the same?
Behind the model Sources, assumptions & scientific context ＋
Original scientific plots
These graphs are recomputed from research/bismuth_heterostructure/run.py: a 48-site, four-state-per-site Hamiltonian, seed 83, with Gaussian DOS broadening σ = 0.065. The right chart shows the twelve eigenstates nearest zero energy per model. They are model proxies, not experimental spectra.
Blue: bulk A7 Bi proxy. Orange: ideal Bi/Mg superlattice proxy. Green: disordered Bi-Pb / Mg-Zn proxy. Energy is in model units.
Reproduce the browser dataset with python app/export_model.py. Within degenerate subspaces, eigenvectors and individual-state IPR can vary across numerical libraries; these charts use one reproducible exported basis. The animation maps each of the 48 model sites to patches of a conceptual 2D lattice. Selected eigenstates use their exported site weights; the energy dial controls an illustrative surface when no state is selected. The underlying Hamiltonian is a 1D chain. It does not reproduce the model geometry or depict electron trajectories.