Twisted Bilayer Boron Nitride Commensurate Lattice Structure Creation.

1. Introduction

This tutorial demonstrates the process of creating a periodic twisted bilayer hexagonal boron nitride (h-BN) structure based on the work presented in the following manuscript.

Manuscript

Lede Xian, Dante M. Kennes, Nicolas Tancogne-Dejean, Massimo Altarelli, and Angel Rubio, "Multiflat Bands and Strong Correlations in Twisted Bilayer Boron Nitride: Doping-Induced Correlated Insulator and Superconductor" Nano Lett. 19, 4934–4940 (2019) DOI: 10.1021/acs.nanolett.9b00986 ¹

We use the Materials Designer to create the periodic twisted bilayers at 7.34°, one of the cells the manuscript computes (Fig. 1g; text p. 4936). Each built cell has 244 atoms.

The manuscript's two configurations, α and β, share one moiré cell and their twist angles differ by 60° (p. 4935). With the h-BN from Standata, a twist of 60° + 7.34° gives configuration α and 7.34° gives β; this tutorial builds both.

Figure 1a,b of the manuscript shows both configurations (left); the cells built in this tutorial are shown next to them in the same top view (right).

2. Load and preview h-BN structure

First, we navigate to Materials Designer and import the h-BN monolayer from the Standata.

Standata's lattice constant of 2.509 Å is used as is; the manuscript uses 2.512 Å (Supporting Information, p. 2).

Then we will use the JupyterLite environment to create the twisted h-BN bilayers.

3. Create the h-BN bilayers

3.1. Launch JupyterLite Session

Select the "Advanced > JupyterLite Transformation" menu item to launch the JupyterLite environment.

3.2. Open and modify the notebook

Open specific_examples/interface_bilayer_twisted_commensurate_lattices_boron_nitride.ipynb — the notebook embedded in section 4 below.

The first cell lists the configurations to build, each a name and a twist angle, and sets the interlayer distance:

# Uncomment a line to build that configuration as well: α is twisted by 60° + θ, β by θ. The angles are those of
# Xian et al. 2019 Fig. 1g; smaller angles have larger cells (6.01°: 364 atoms, 5.08°: 508, 3.89°: 868, 2.64°: 1876).
INTERFACE_PARAMETERS = [
    {"name": "h-BN bilayer 7.34deg alpha d3.23", "angle": 60 + 7.34},
    {"name": "h-BN bilayer 7.34deg beta d3.23", "angle": 7.34},
    # {"name": "h-BN bilayer 6.01deg alpha d3.23", "angle": 60 + 6.01},
    # {"name": "h-BN bilayer 6.01deg beta d3.23", "angle": 6.01},
    # {"name": "h-BN bilayer 5.08deg alpha d3.23", "angle": 60 + 5.08},
    # {"name": "h-BN bilayer 5.08deg beta d3.23", "angle": 5.08},
    # {"name": "h-BN bilayer 3.89deg alpha d3.23", "angle": 60 + 3.89},
    # {"name": "h-BN bilayer 3.89deg beta d3.23", "angle": 3.89},
    # {"name": "h-BN bilayer 2.64deg alpha d3.23", "angle": 60 + 2.64},
    # {"name": "h-BN bilayer 2.64deg beta d3.23", "angle": 2.64},
]
INTERFACE_DISTANCE = 3.23  # Å, the article's
MONOLAYER_NAME = "h-BN monolayer"  # the Standata monolayer, saved as is (Fig. 1d)

The defaults build α and β at 7.34°.

The interlayer distance of 3.23 Å is the manuscript's, the optimized distance of the bilayer without twist (p. 4935–4936).

The second cell holds the vacuum and visualization parameters:

VACUUM = 20.0  # Å of empty space above the top layer; paper: not stated

# Visualization parameters
SHOW_INTERMEDIATE_STEPS = True
VISUALIZE_REPETITIONS = [3, 3, 1]

3.3. Run the Notebook

After setting the parameters, run the notebook to build every active configuration.

3.4. Check the geometry

For each structure the notebook prints the atom count, the composition, the cell, the interlayer distance, and the target twist angle:

h-BN bilayer 7.34deg alpha d3.23: 244 atoms (B122N122), a = 19.596 Å, gamma = 120.0°, interlayer distance 3.230 Å, target twist 67.34°
h-BN bilayer 7.34deg beta d3.23: 244 atoms (B122N122), a = 19.596 Å, gamma = 120.0°, interlayer distance 3.230 Å, target twist 7.34°

3.5. View results and pass to Materials Designer

The notebook shows the bilayers from the top and from the side. Each structure is saved to the uploads folder under its name, and can also be passed to the Materials Designer for further analysis. The Standata monolayer is saved as h-BN monolayer. The right column of the figure in section 1 shows these cells, rotated to the orientation of the manuscript's Fig. 1a,b.

Once the structures exist, the band structure tutorial loads them by name and computes the width of their top valence flat bands.

4. Interactive JupyterLite Notebook

The interactive JupyterLite notebook for creating the twisted bilayer h-BN structure can be accessed below. To run the notebook, click the "Run All" button.

⛶ Full Screen

5. References

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1. Lede Xian, Dante M. Kennes, Nicolas Tancogne-Dejean, Massimo Altarelli, and Angel Rubio. Multiflat bands and strong correlations in twisted bilayer boron nitride: doping-induced correlated insulator and superconductor. Nano Lett., 19(8):4934–4940, 2019. URL: https://doi.org/10.1021/acs.nanolett.9b00986. ↩