2024/10/06 by Giuseppe De Nittis, De Nittis, Giuseppe, Jaime Gomez +3 · 2 citations
Mathematics · Computer Science · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2410.04531
In the tight-binding approximation, an Iwatsuka magnetic field is modeled by a function on ℤ2 with constant, but distinct values in the two parts of the lattice separated by a straight line of slope α∈ [-∞,∞]. In this paper, the K-theory of the magnetic C^*-algebras generated by an Iwatsuka magnetic field for any possible α is computed. One interesting aspect concerns the analysis of the behavior of the system in the transition from rational to irrational α. It turns out that when α is irrational, the magnetic hull associated with the flux operator forms a Cantor set. On the other hand, for rational α this set coincides with the two-point compactification of ℤ. This characterization, along with the use of the Pimsner-Voiculescu exact sequence, is the main ingredient for the computation of the K-theory. Once the K-theory is known, with the use of the index theory one can deduce the bulk-interface correspondence for tight-binding Hamiltonians subjected to an Iwatsuka magnetic field. Notably, it occurs that the topological quantization of the interface currents remains independent of the slope α.