Understanding Dirac, Weyl and nodal-line semimetals: a step-by-step guide through model Hamiltonians

Area of Science:

• Condensed Matter Physics
• Materials Science
• Solid State Physics

Background:

• Graphene's unique electronic properties inspire research into 3D materials.
• Topological semimetals exhibit exotic electronic states.
• Low-energy effective Hamiltonians are key tools for studying these materials.

Purpose of the Study:

• To explore electronic band structures of Dirac semimetals (DSM), Weyl semimetals (WSM), and nodal line semimetals (NLS).
• To provide an accessible framework using model Hamiltonians for beginners.
• To connect theoretical insights with experimental realizations and educational applications.

Main Methods:

• Utilizing low-energy effective Hamiltonians.
• Solving for density of states and effective masses.
• Adopting pedagogical approaches with model Hamiltonians.

Main Results:

• Exact solutions for density of states and effective masses of DSM, WSM, and NLS.
• A clear framework for understanding topological semimetal physics.
• Connections drawn between theoretical models and experimental observations.

Conclusions:

• The study deepens the appreciation for novel band structures in condensed matter physics.
• It encourages integrating research perspectives into undergraduate education.
• The framework aims to foster curiosity and innovation in students exploring cutting-edge concepts.