Quantum Hall effect in wedge-shaped samples

The quantum Hall effect (QHE) is broadly studied in the films of semiconductors, conductors, topological insulators, and topological semimetals. Wedge-shaped samples, guaranteeing the uniform properties of materials, bring obscure characteristics connected to the sample geometry. Here we study the QHE in wedge-shaped samples by using a simple electron gas model. We find that the Hall resistance shows anomalous behaviors: the Hall plateau value shifts when measuring from different lateral terminals, the Hall resistances in positive and negative magnetic fields are not equal, and the Hall resistance depends on the direction of the tilted magnetic field. In addition, the longitudinal resistance also has anomalous characteristics in wedge-shaped samples. These results are very similar to the QHE based on the Weyl orbits observed in a recent experiment, although they are different in origin. These anomalous behaviors in the trivial wedge-shaped sample originate from the spatial redistribution of Landau levels; that is, the edge state can follow an equal-thickness path in the bulk.