Wannier90

A practical step-by-step guide to building, checking, and using Wannier tight-binding models

Author: Dmitry Skachkov

Content

Wannier90 is a powerful software package that transforms the delocalized Bloch states of a crystal into compact and physically intuitive Wannier functions. In many cases, these functions resemble atomic orbitals or chemical bonds, providing a direct real-space picture of the electronic structure.

One of the most remarkable features of Wannier90 is that it does not solve the electronic structure problem again. Instead, it takes the Bloch wave functions obtained from a first-principles calculation—such as density functional theory (DFT)—and transforms them into an equivalent, but much more compact and intuitive representation.

In this representation, the electronic structure is described by a Hamiltonian expressed in a localized Wannier basis. Unlike the original Bloch representation, this Hamiltonian is compact, easy to interpret, and computationally efficient, making it an ideal starting point for tight-binding models and many advanced electronic-structure calculations.

Because the Wannier Hamiltonian retains first-principles accuracy while containing only the physically relevant degrees of freedom, it can be used to efficiently interpolate electronic band structures and investigate a wide range of material properties, including topology, transport, optical response, superconductivity, excitons, and many-body phenomena.

Motivation

A typical first-principles calculation may produce dozens or even hundreds of electronic bands, many of which are not essential for describing the physical properties of interest. In many materials, the low-energy physics is governed by only a small number of electronic states located near the valence-band maximum (VBM) and the conduction-band minimum (CBM).

The challenge is to identify these relevant states and construct a compact model that accurately reproduces the first-principles electronic structure. Wannier90 provides a systematic solution to this problem by transforming the original Bloch states into a small set of localized Wannier functions and the corresponding Wannier Hamiltonian.

As a result, a large first-principles Hamiltonian containing hundreds of Bloch states can often be replaced by an effective tight-binding Hamiltonian involving only a few orbitals. This reduced Hamiltonian preserves the essential physics of the material while being much easier to interpret and dramatically more efficient for subsequent calculations.

In the following sections, we will see how Wannier90 constructs such compact Hamiltonians and how they can be used to accurately reproduce electronic band structures and serve as the foundation for many advanced computational methods.

Why Should Students Learn Wannier90?

Wannier90 has become one of the standard tools in modern computational materials science. It is routinely used in research on semiconductors, topological materials, superconductors, two-dimensional materials, and strongly correlated systems.

Learning Wannier90 provides much more than the ability to construct Wannier functions. It teaches how first-principles electronic-structure calculations can be transformed into compact and physically transparent models that are easier to understand, analyze, and reuse.

The Wannier Hamiltonians generated by Wannier90 are widely used to interpolate electronic band structures, calculate Berry-phase-related quantities, build realistic tight-binding models, and serve as input for many advanced simulation packages studying transport, topology, electron–phonon interactions, superconductivity, excitons, and many-body phenomena.

For students entering the field of computational materials science, Wannier90 is therefore not only a useful software package but also an important conceptual tool for connecting first-principles calculations with physical intuition.

About This Tutorial

This tutorial is intended for students and researchers who are new to Wannier90 and would like to become familiar with its basic concepts and practical workflow as quickly as possible. No prior knowledge of Wannier functions is assumed.

Rather than covering every feature of the package, we focus on the fundamental ideas behind Wannier90 and illustrate them through a series of simple, hands-on examples. Starting from first-principles electronic-structure calculations, we will learn how to construct Maximally Localized Wannier Functions (MLWFs), build Hamiltonians in the Wannier basis, and understand how these Hamiltonians can be used to reproduce electronic band structures with first-principles accuracy.

By the end of this tutorial, readers will understand the physical meaning of Wannier functions, know how to perform Wannierization for simple materials, construct compact tight-binding models, and appreciate why Wannier90 has become one of the most widely used tools in modern computational materials science.

This tutorial is an independent educational resource developed by Delta Science Institute. For official Wannier90 documentation, software releases, and developer resources, please visit the official Wannier90 website.

Next: What Can Wannier90 Do?

Afterword

This tutorial introduced the basic ideas behind Wannier functions and showed how Wannier90 can transform first-principles electronic-structure calculations into compact and physically transparent tight-binding models.

Starting from Bloch states obtained from DFT, we learned how localized Wannier functions can be constructed and how they can be used to build effective Hamiltonians for realistic materials. Using monolayer MoS2 as an example, we compared minimal and extended Wannier models and saw how the choice of orbitals controls the accuracy and physical content of the resulting model.

The main message of this tutorial is that Wannier90 is not only a technical post-processing tool. It is a bridge between first-principles calculations and intuitive model Hamiltonians. Once a reliable Wannier Hamiltonian is obtained, it can be used to study band structures, density of states, topology, transport, optical response, electron–phonon interactions, excitons, and many other properties of materials.

This tutorial is intended as a starting point and covers the basic concepts and practical steps needed to get started with Wannier90. The next step is to apply Wannier90 to new materials, test different orbital projections and energy windows, compare Wannier-interpolated bands with the original DFT bands, and use the resulting Hamiltonians for more advanced physical simulations. Additional examples and extended workflows are available in the accompanying GitHub repository: https://github.com/DS-RF/Wannier90_examples 

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© 2026 Delta Science Institute
This tutorial is freely available as an open educational resource.
Unless otherwise stated, the tutorial materials are licensed under the
Creative Commons Attribution 4.0 International License (CC BY 4.0).
Preferred citation: Skachkov, D. (2026). Wannier90 Tutorial. Delta Science Institute. Available at: https://www.DSedu.org/tutorials/wannier90