This repository provides a Python implementation for calculating and visualizing the electronic band structure of monolayer molybdenum disulfide (MoS₂) using the Slater–Koster Tight-Binding (TB) formalism. The implementation is developed in Jupyter Notebook and demonstrates the construction of the Tight-Binding Hamiltonian together with the numerical calculation of the energy dispersion along the high-symmetry path of the first Brillouin zone.
Monolayer MoS₂ is a representative transition metal dichalcogenide (TMD) with remarkable electronic and optical properties, including a direct band gap, strong spin–orbit coupling, and excellent potential for applications in nanoelectronics, optoelectronics, valleytronics, and photonics.
The electronic structure is described using an eleven-orbital Slater–Koster Tight-Binding model.
Each primitive unit cell contains:
- One Molybdenum (Mo) atom
- Two Sulfur (S) atoms
The Hamiltonian is constructed by considering:
- Mo d-orbitals
- S p-orbitals
- Nearest-neighbor hopping interactions
- Slater–Koster overlap parameters
The eigenvalue problem is solved for each k-point along the high-symmetry path (Γ–K–M–Γ) to obtain the electronic band structure.
- Python implementation of the Slater–Koster Tight-Binding model for monolayer MoS₂
- Construction of the Hamiltonian matrix using orbital interactions
- Implementation of Slater–Koster hopping parameters
- Numerical diagonalization of the Hamiltonian
- Calculation of electronic energy bands
- Band structure visualization using Matplotlib
- Well-documented Jupyter Notebook suitable for educational and research purposes
The implementation includes the following hopping integrals:
- (V_{pp\pi})
- (V_{pp\sigma})
- (V_{pd\sigma})
- (V_{pd\pi})
- (V_{dd\sigma})
- (V_{dd\pi})
- (V_{dd\delta})
These parameters are used to construct the interaction matrices between Mo and S orbitals.
band-structure-MoS2-2D
│
├── MoS2.ipynb # Main notebook
├── README.md # Project documentation
├── requirements.txt # Python dependencies
├── figures/ # Generated figures
└── LICENSE
The notebook requires the following Python packages:
- numpy
- matplotlib
Install the required packages using:
pip install -r requirements.txt- Clone the repository.
git clone https://github.com/your_username/band-structure-MoS2-2D.git- Navigate to the project directory.
cd band-structure-MoS2-2D- Launch Jupyter Notebook.
jupyter notebook- Open MoS2.ipynb and execute the notebook cells sequentially.
The notebook calculates the eigenvalues of the Tight-Binding Hamiltonian and plots the electronic band structure of monolayer MoS₂ along the high-symmetry path of the first Brillouin zone.
A typical output is shown below.
This project can be used for:
- Tight-Binding model development
- Electronic structure calculations
- Two-dimensional materials research
- Condensed matter physics education
- Photonics and optoelectronic device studies
- Validation of DFT and Quantum ESPRESSO calculations
-
Liu, G.-B., Shan, W.-Y., Yao, Y., Yao, W., & Xiao, D. Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides.
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Cappelluti, E., Roldán, R., Silva-Guillén, J. Á., Ordejón, P., & Guinea, F. Tight-binding model and direct-gap/indirect-gap transition in single-layer and multilayer MoS₂.
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Ridolfi, E., et al. A tight-binding model for MoS₂ monolayers.
Potential extensions of this project include:
- Spin–Orbit Coupling (SOC)
- Density of States (DOS)
- Projected Density of States (PDOS)
- Effective mass calculation
- Berry curvature
- Valley polarization
- Comparison with Density Functional Theory (DFT)
- Extension to other transition metal dichalcogenides (WS₂, MoSe₂, WSe₂)
This project is released under the MIT License.
Shahnaz Mohammadi
