Topologically protected edge states, immune to various disorders, have been realized in a range of topological insulators. In this article we demonstrate that Landau levels in aperiodic acoustic structures can be realized under different pseudomagnetic fields (PMFs). The resulting zero-order Landau modes (ZOLMs) can propagate along the channels at the interior or exterior of the inhomogeneous array, referred to as “bulk-transport states” (BTSs) and “edge-transport states” (ETSs), respectively. Unlike conventional valley edge states, the ZOLMs exhibit a fascinating self-collimation feature. Additionally, when a pseudoelectric field (PEF) is introduced, the combination of a PMF and PEF leads to the formation of bulk or edge Landau rainbows, where the zeroth Landau modes are distributed at various positions within the bulk or boundary of the sample at different frequencies. These synthetic-gauge-field-controlled topological states enable full control over robust transmission, utilizing the entire footprint of a topological lattice. Our findings not only significantly advance the understanding of topological phase matter but also open up new possibilities for the design of topological acoustic devices.

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• Landau levels
• 2-dimensional systems
• Acoustic metamaterials