Multilayer Graphene Band Structure Calculator

Calculating the bands of few layer graphite in a TB model, beyond the nearest neighbour. THIS IS JUST FOR VISUALIZATION PURPOSES! The parameters were not fitted to ab initio, or checked regarding the final structure of the low energy bands.

Simple example

import multilayer_graphene as mlg

# Tell it what you want
mlg.set_parameters(N_layers=3, stacking='abc')

# Plot some beautiful bands
mlg.plot_bands()

# Want to see how different layer numbers compare? No problem!
mlg.plot_panel_comparison(range(1, 9))

Settings

Hoppings in eV

Don't worry, the defaults are sensible! But if you're feeling adventurous:

• gamma0: How carbons talk within a layer (default: 3.0)
• E0: Energy offset (default: 0)
• Delta: A vs B asymmetry (default: 0)

The System Stuff

• N_layers: How many layers? (default: 3)
• stacking: 'abc' for rhombohedral or 'aba' for Bernal (default: 'abc')

The k-Space Details

• K_point: Where's the K point? (default: [1/3, 1/3])
• n_k: How many k-points along the default path (default: 1500)
• d_cc: Carbon-carbon bond length in Å (default: 1.42)

By default, band plots now use the high-symmetry path Γ → K → M, and the x-axis is the arc length along this path with the K point centered at 0 (Γ at negative x, M at positive x). You can override x-limits via the xlim argument.

Movie Generation

• make_movie.py [framerate] [stacking_type] [max_layers]: Creates both WebM video and animated GIF for maximum compatibility.
  • python make_movie.py 2 abc - 2 fps, ABC stacking, 30 layers
  • python make_movie.py 5 aba 20 - 5 fps, ABA stacking, 20 layers
  • python make_movie.py 1 abc 5 - Quick test with 5 layers
  • Requires: ffmpeg (for WebM) and Pillow (for GIF)

What Can You Do With It?

Set Things Up

• set_parameters(**kwargs): Change whatever you want
• get_info(): See what you've got configured
• get_parameters(): Get all the current settings

Calculate

• calculate_bands(...)

Plotting

• plot_bands(...): Single band structure plot
• plot_panel_comparison(...): Side-by-side comparison panels
• plot_band_density(...): Density plot of a selected band.

Brillouin Zone helpers

• get_brillouin_zone(plot=True, ax=None, annotate=True, figsize=(4,4), save_as=None, show=True): Returns a dictionary with reciprocal vectors (b1, b2), Γ, K and M points (both fractional and Cartesian), and the first Brillouin zone hexagon vertices (Å⁻¹). If plot=True, it also draws the BZ hexagon and marks Γ, K, and M; you can pass an existing Matplotlib ax to draw into, or let it create one.

Based on the work from Grüneiss et al. (Physical Review B 78, 205425, 2008).

mlg.set_parameters(N_layers=N, stacking='abc', **params)
E, k_mag = mlg.calculate_bands()

# Same deal for ABA:
mlg.set_parameters(N_layers=N, stacking='aba', **params)
E, k_mag = mlg.calculate_bands()

What You Need

• NumPy (for the math)
• Matplotlib (for the pretty plots)