WannierTools: An open-source software package for novel topological materials

Abstract: We present an open-source software package WannierTools, a tool for investigation of novel topological materials. This code works in the tight-binding framework, which can be generated by another software package Wannier90. It can help to classify the topological phase of given materials by calculating the Wilson loop and can get the surface state spectrum which is detected by angle-resolved photoemission (ARPES) and in scanning tunneling microscopy (STM) experiments. It also identifies positions of Weyl/Dirac points and nodal line structures, calculates the Berry phase around a closed momentum loop and Berry curvature in a part of the Brillouin zone.

• The paper introduces a robust method using the Wilson loop technique to compute topological invariants like Chern numbers for phase classification.
• The paper details an iterative Green’s function approach to accurately calculate surface state spectra, aligning with ARPES and STM experimental observations.
• The paper further employs advanced algorithms for nodal point and line detection alongside Berry curvature calculations to explore the electronic topology of semimetals.

An Overview of WannierTools: Software for Topological Material Analysis

The paper presents WannierTools, a computational tool designed to explore the properties of novel topological materials within the framework of tight-binding (TB) models derived using Wannier90. The tool provides functionalities to classify the topological phases and analyze the electronic properties of these materials through the calculation of surface state spectra, amongst other features. This paper provides a comprehensive description of the tool's capabilities, methodologies, and its application to real-world materials, emphasizing its significance in the exploration of topological phases of matter.

Key Features and Techniques

WannierTools is an open-source software package implemented in Fortran90, which leverages the power of the tight-binding model to provide a detailed analysis of topological materials. The core capabilities of WannierTools include:

1. Topological Phase Classification: By employing the Wilson loop method, which is synonymous with the calculation of Wannier charge centers, WannierTools facilitates the classification of the topological phases in crystalline systems. The tool can compute topological invariants such as the $\mathbb{Z}_2$ and Chern numbers, which are critical to distinguishing topological materials from trivial ones.
2. Surface State Spectrum Calculation: The surface states, which are a hallmark of topological materials, can be scrutinized through WannierTools. The package uses iterative Green’s function methods to derive surface state spectra for semi-infinite systems, providing insights into the surface electronic structure observable in ARPES and STM experiments.
3. Nodal Point and Line Searches: WannierTools incorporates an algorithm to search for Weyl/Dirac points and nodal line structures within the Brillouin zone (BZ), pertinent to the identification of semimetals. The convergence of the nodal search is verified by successive refinement of the initial mesh points.
4. Berry Phase and Curvature Calculations: The software offers numerical methods for calculating Berry phases and curvatures, integral for understanding the quantum geometric aspects of topological bands.

Numerical Results and Examples

The paper illustrates the application of WannierTools with the analysis of new topological materials such as the HfPtGe compound. Numerical results demonstrate the tool's capability to accurately compute band structures, density of states, and topological invariants, alongside the visualization of surface state spectra and spin textures. The nodal line semimetal characteristic of HfPtGe is supported by the nodal line structure and energy gap calculations, showcasing WannierTools' efficacy in unearthing topological attributes of materials.

Implications and Future Directions

WannierTools bridges the gap between theoretical predictions and experimental validations in the field of topological materials. By enabling efficient classification and analysis of topological phases, it plays a pivotal role in aiding the discovery and research of materials with nontrivial topological characteristics. Future developments may focus on extending the versatility of WannierTools to accommodate evolving theoretical models and supporting broader classes of materials with complex topological properties.

In conclusion, WannierTools stands as a robust computational package for researchers probing the electronic topology of materials within a TB model framework. Its integration with first-principle calculation tools and its focus on both bulk and surface phenomena mark its significance in the continuous exploration of topological materials.