Quantum Hall effect and Landau levels without spatial long-range correlations

Abstract

The spectrum of charged particles in translation-invariant systems in a magnetic field is characterized by the Landau levels, which play a fundamental role in the thermodynamic and transport properties of solids. The topological nature and the approximate degeneracy of the Landau levels are known to also survive on crystalline lattices with discrete translation symmetry when the magnetic flux through a primitive cell is small compared to the flux quantum. Here we show that the notion of Landau levels and the quantum Hall effect can be generalized to 2d non-crystalline lattices without spatial long-range order. Remarkably, even when the spatial correlations decay over microscopic distances, 2d systems can exhibit a number of well-resolved Landau-like bands. The existence of these bands imply that non-crystalline systems in magnetic fields can support the hallmark quantum effects which have been typically associated with crystalline solids.

5 pages + 2.5-page appendix, 4+1 figures

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Cited by in corpus (5)

• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
• Structural spillage: an efficient method to identify non-crystalline topological materials
• Tensor network method for real-space topology in quasicrystal Chern mosaics
• Three-Dimensional Quantum Hall Effect in Topological Amorphous Metals