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When electrons moving in two-dimensions (2D) are subjected to a stronguniform magnetic field, they form flat bands called Landau levels, which arethe basis for the quantum Hall effect. Landau levels can also arise frompseudomagnetic fields (PMFs) induced by lattice distortions; for example,mechanically straining graphene causes its Dirac quasiparticles to form acharacteristic set of unequally-spaced Landau levels, including a zeroth Landaulevel. In three-dimensional (3D) systems, there has thus far been noexperimental demonstration of Landau levels or any other type of flat band. Forinstance, applying a uniform magnetic field to materials hosting Weylquasiparticles, the 3D generalizations of Dirac quasiparticles, yields bandsthat are non-flat in the direction of the field. Here, we report on theexperimental realization of a flat 3D Landau level in an acoustic crystal.Starting from a lattice whose bandstructure exhibits a nodal ring, we design aninhomogeneous distortion corresponding to a specific pseudomagnetic vectorpotential (PVP) that causes the nodal ring states to break up into Landaulevels, with a zeroth Landau level that is flat along all three directions.These findings point to the possibility of using nodal ring materials togenerate 3D flat bands, to access strong interactions and other interestingphysical regimes in 3D.

Three-dimensional flat Landau levels in an inhomogeneous acoustic crystal