2015/10/27 by Ralph M. Kaufmann, Dan Li, Kaufmann, Ralph M. +3 · 1 citation
Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Other Condensed Matter (cond-mat.other) #Quantum optics and atomic interactions #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.1510.08001
openalex publication_date 2015/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyze the topological ℤ2 invariant, which characterizes time reversal invariant topological insulators, in the framework of index theory and K-theory. The topological ℤ2 invariant counts the parity of generalized Majorana zero modes, which can be interpreted as an analytical index. As we show, it fits perfectly into a mod 2 index theorem, and the topological index provides an efficient way to compute the topological ℤ2 invariant. Finally, we give a new version of the bulk-boundary correspondence which yields an alternative explanation of the index theorem and the topological ℤ2 invariant. Here the boundary is not the geometric boundary of a probe, but an effective boundary in the momentum space.