Punctured-Chern Topological Invariants for Semimetallic Band Structures

Area of Science:

• Condensed Matter Physics
• Materials Science
• Quantum Mechanics

Background:

• Topological insulators classify gapped electronic bands, but nontrivial topology exists in systems with multiple gap-closing points.
• Existing methods struggle to capture the complex topology of systems with multiple bands and gapless points.

Purpose of the Study:

• To introduce a general wave-function-based invariant, the "punctured-Chern" invariant, for classifying nontrivial band topology.
• To demonstrate the invariant's applicability to diverse gapless topological systems.
• To provide a unified framework for understanding topological phase transitions and semimetallic nodal defects.

Main Methods:

• Construction of a general wave-function-based "punctured-Chern" invariant.
• Analysis of a two-dimensional fragile topological model to study band-topological transitions.
• Analysis of a three-dimensional triple-point nodal defect model to characterize semimetallic topology.

Main Results:

• The "punctured-Chern" invariant successfully captures nontrivial topology in systems with multiple bands and gap-closing points.
• The invariant characterizes topological transitions in a 2D fragile topological model.
• The invariant describes the semimetallic topology of a 3D triple-point nodal defect, yielding half-integer topological charges relevant to anomalous transport.

Conclusions:

• The "punctured-Chern" invariant offers a powerful tool for classifying complex topological phases beyond traditional topological insulators.
• The invariant provides a unified approach to understanding diverse gapless topological phenomena.
• The classification of Nexus triple points (Z×Z) is confirmed under specific symmetry conditions.