2021/07/22 by Jianfeng Lu, Kevin D. Stubbs, Lu, Jianfeng +1 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum and electron transport phenomena #Spectral Theory in Mathematical Physics #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2107.10699
openalex publication_date 2021/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For gapped periodic systems (insulators), it has been established that the insulator is topologically trivial (i.e., its Chern number is equal to 0) if and only if its Fermi projector admits an orthogonal basis with finite second moment (i.e., all basis elements satisfy ∫ |\boldsymbolx|2 |w(\boldsymbolx)|2 \textrmd\boldsymbolx < ∞). In this paper, we extend one direction of this result to non-periodic gapped systems. In particular, we show that the existence of an orthogonal basis with slightly more decay (∫ |\boldsymbolx|2+ε |w(\boldsymbolx)|2 \textrmd\boldsymbolx < ∞ for any ε> 0) is a sufficient condition to conclude that the Chern marker, the natural generalization of the Chern number, vanishes.