Real-space representation of the second Chern number
arXiv:2502.14299 · doi:10.1103/ztk4-ckj1
Abstract
We extend Kitaev's real-space formulation of the first Chern number to the second Chern number and establish a computational framework for its evaluation. To test its validity, we apply the derived formula to the disordered Wilson-Dirac model and analyze its ability to capture topological properties in the presence of disorder. Our results demonstrate that the real-space approach provides a viable method for characterizing higher-dimensional topological phases beyond momentum-space formulations.
8 pages, 5 figures, v2: final version
References in corpus (12)
- Classification of topological insulators and superconductors in three spatial dimensions
- Topological Field Theory of Time-Reversal Invariant Insulators
- Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
- Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
- Orbital magnetization in periodic insulators
- Hyperbolic band topology with non-trivial second Chern numbers
- Symmetry and topology of hyperbolic Haldane models
- Topological meaning of Z numbers in time reversal invariant systems
- Haldane model on the Sierpiński gasket
- Topological magnetoelectric pump in three dimensions
- Flow of unitary matrices: Real-space winding numbers in one and three dimensions
- Streda formula for the Hofstadter-Wilson-Dirac model in two and four dimensions