Transport evidence for chiral surface states from three-dimensional Landau bands

Abstract Strong magnetic fields applied to metals confine electrons into Landau orbits, except at the boundaries at which frequent surface collisions disrupt their cyclotron motion. In two-dimensional systems, these boundary states form dissipationless chiral edge channels in the quantum Hall regime. By contrast, the quantum limit of three-dimensional (3D) metals is traditionally thought to differ fundamentally and instead contains gapless Landau bands, lacking quantized Hall conductance or dissipationless transport. Here we demonstrate enhanced surface conduction in the quantum limit of the 3D semimetal bismuth, characterized by the counterintuitive increase in conductivity as material is removed by micropatterning. The conductance of the 3D chiral boundary states—3D analogues of quantum Hall states in two dimensions—naturally accounts for this behaviour and for the highly non-local transport observed in micrometre-sized crystalline bismuth structures. These findings introduce an approach for engineering and exploiting chiral conduction on the surfaces of 3D materials, offering a design space for geometries beyond the simple one-dimensional boundary modes of two-dimensional systems.