2016/05/31 by Ralph M. Kaufmann, Dan Li, Kaufmann, Ralph M. +3
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Other Condensed Matter (cond-mat.other)
paper · pdf · doi:10.48550/arxiv.1605.09470
openalex publication_date 2016/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We generalize the ℤ2 invariant of topological insulators using noncommutative differential geometry in two different ways. First, we model Majorana zero modes by KQ-cycles in the framework of analytic K-homology, and we define the noncommutative ℤ2 invariant as a topological index in noncommutative topology. Second, we look at the geometric picture of the Pfaffian formalism of the ℤ2 invariant, i.e., the Kane--Mele invariant, and we define the noncommutative Kane--Mele invariant over the fixed point algebra of the time reversal symmetry in the noncommutative 2-torus. Finally, we are able to prove the equivalence between the noncommutative topological ℤ2 index and the noncommutative Kane--Mele invariant.