Topological classification and stability of Fermi surfaces

Area of Science:

• Condensed matter physics
• Quantum mechanics
• Topology

Background:

• The Cartan classification provides a framework for understanding Hamiltonians.
• Fermi surfaces in materials exhibit topological properties.
• Topological charges are key to classifying these properties.

Purpose of the Study:

• Establish a topological classification of Fermi surfaces using topological charges.
• Investigate the relationship between topological charges, Hamiltonian classification, and Fermi surface properties.
• Explore the role of topological charges in protecting Fermi surfaces.

Main Methods:

• Utilizing the Cartan classification of Hamiltonians.
• Defining topological charges based on Fermi surface codimension and Hamiltonian class.
• Analyzing the structure of topological charges concerning chiral symmetry.

Main Results:

• A topological classification of Fermi surfaces is established.
• Six types of topological charges are identified.
• These charges form two distinct groups related to chiral symmetry, each with an original charge and two descendants.
• Nontrivial topological charges confer robust protection to Fermi surfaces.

Conclusions:

• Topological charges offer a powerful tool for classifying Fermi surfaces.
• The identified topological charges explain the robust protection of Fermi surfaces against perturbations.
• This classification deepens the understanding of topological phases of matter.