Three-dimensional flat Landau levels in an inhomogeneous acoustic crystal

TL;DR

This paper demonstrates the first experimental realization of three-dimensional flat Landau levels in an acoustic crystal by engineering inhomogeneous distortions that induce pseudomagnetic fields, enabling flat bands in 3D systems.

Contribution

It introduces a method to create 3D flat Landau levels in an acoustic crystal through specific lattice distortions, expanding the understanding of flat bands beyond 2D systems.

Findings

Successfully realized 3D flat Landau levels in an acoustic crystal.

Engineered inhomogeneous distortions to induce pseudomagnetic vector potentials.

Observed zeroth Landau level flatness along all three spatial directions.

Abstract

When electrons moving in two-dimensions (2D) are subjected to a strong uniform magnetic field, they form flat bands called Landau levels, which are the basis for the quantum Hall effect. Landau levels can also arise from pseudomagnetic fields (PMFs) induced by lattice distortions; for example, mechanically straining graphene causes its Dirac quasiparticles to form a characteristic set of unequally-spaced Landau levels, including a zeroth Landau level. In three-dimensional (3D) systems, there has thus far been no experimental demonstration of Landau levels or any other type of flat band. For instance, applying a uniform magnetic field to materials hosting Weyl quasiparticles, the 3D generalizations of Dirac quasiparticles, yields bands that are non-flat in the direction of the field. Here, we report on the experimental realization of a flat 3D Landau level in an acoustic crystal. Starting from a lattice whose bandstructure exhibits a nodal ring, we design an inhomogeneous distortion corresponding to a specific pseudomagnetic vector potential (PVP) that causes the nodal ring states to break up into Landau levels, with a zeroth Landau level that is flat along all three directions. These findings point to the possibility of using nodal ring materials to generate 3D flat bands, to access strong interactions and other interesting physical regimes in 3D.