Delocalized Spectra of Landau Operators on Helical Surfaces
Date
2022
Authors
Kubota, Y.
Ludewig, M.
Thiang, G.C.
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Journal article
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Communications in Mathematical Physics, 2022; 395(3):1211-1242
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Yosuke Kubota, Matthias Ludewig, Guo Chuan Thiang
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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.
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Published online: 15 July 2022
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© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022