Tight-Binding Model
Also known as: TB model, hopping model
The Tight-Binding (TB) model is a simplified semi-empirical approach for computing electronic band structures and properties of solids. Formulated by Slater and Koster in 1954, TB treats electron hopping between atomic sites as the dominant interaction, enabling efficient calculations of band dispersion for a wide variety of materials.
Key highlights
- Computationally very cheap; diagonalization of small matrices.
- Provides clear physical intuition for electronic structure.
- Captures band structure features and band gaps qualitatively.
- Useful for extended systems where DFT calculations are prohibitive.
- Foundation for understanding topological properties and anomalies.
Intuition
This section is available to Pro members. Upgrade to Pro
How it works
This section is available to Pro members. Upgrade to Pro
When to use it
TB is used for qualitative understanding of band structure and for quick estimates of electronic properties. It is especially valuable for novel materials (graphene, topological insulators) where accurate ab initio methods are expensive.
Strengths & limitations
- Computationally very cheap; diagonalization of small matrices.
- Provides clear physical intuition for electronic structure.
- Captures band structure features and band gaps qualitatively.
- Useful for extended systems where DFT calculations are prohibitive.
- Foundation for understanding topological properties and anomalies.
- Semi-empirical: parameters often fitted to experiment or ab initio results.
- Cannot reliably predict absolute energies or many-body effects.
- Poor description of orbital character mixing and hybridization.
- Parameterization depends heavily on system; not transferable universally.
- Excited states not accessible; TB is inherently single-particle.
Common pitfalls
This section is available to Pro members. Upgrade to Pro
Applications
This section is available to Pro members. Upgrade to Pro
Frequently asked
How are tight-binding parameters determined?
Parameters can be fitted to DFT band structures, experimental spectra, or extracted from first-principles calculations using Wannier functions. Literature values for common materials are available.
What is the difference between TB and DFT?
DFT is ab initio (no free parameters) and accurate for many properties. TB is semi-empirical, faster but less accurate. TB is useful for intuition and rapid estimates; DFT for quantitative predictions.
Can TB include electron interactions?
Standard TB is non-interacting. The Hubbard model adds on-site repulsion. Mean-field approximations (Hartree-Fock on the TB Hamiltonian) include electron-electron effects partially.
Is TB suitable for excited states?
Standard TB gives single-particle excitations (band structure). Many-body excitations require extensions like Bethe-Salpeter equation or many-body perturbation theory.
How accurate are TB band gaps?
TB band gaps at the fitted k-points are usually accurate. Away from fitted points, accuracy depends on parameterization. Absolute band gaps often differ by 20–50% from experiment.
Sources
- 1.Slater, J. C., Koster, G. F. (1954). Simplified LCAO method for the periodic potential problem. Physical Review, 94, 1498–1524.
- 2.Ashcroft, N. W., Mermin, N. D. (1976). Solid State Physics. Holt, Rinehart and Winston.
- 3.Mahan, G. D. (2000). Many-Particle Physics (3rd ed.). Kluwer Academic/Plenum Publishers.
You have read it. What now?
Cite this page
ScholarGate. (2026, June 3). Tight-Binding Model. ScholarGate. https://scholargate.app/quantum-computing/tight-binding-model