Delocalized spectra of Landau operators on helical surfaces

Abstract

On a flat surface, the Landau operator, or quantum Hall Hamiltonian, has spectrum a discrete set of infinitely degenerate Landau levels. We consider surfaces with asymptotically constant curvature away from a possibly non-compact submanifold, the helicoid being our main example. The Landau levels remain isolated, provided the spectrum is considered in an appropriate Hilbert module over the Roe algebra of the surface delocalized away from the submanifold. Delocalized coarse indices may then be assigned to them. As an application, we prove that Landau operators on helical surfaces have no spectral gaps above the lowest Landau level.

arXiv comment35 pages, 1 figure, new Background section added, to appear in CMP

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Cited by in corpus (3)

• Bulk-interface correspondences for one dimensional topological materials with inversion symmetry
• Large-scale geometry obstructs localization
• A vanishing theorem in $K$-theory for spectral projections of a non-periodic magnetic Schrödinger operator