Fractional Quantum Conductance Plateaus in Mosaic‐Like Conductors and Their Similarities to the Fractional Quantum Hall Effect

Abstract

A simple route to generate magnetotransport data is reported that results in fractional quantum Hall plateaus in the conductance without invoking strongly correlated physics. Ingredients to the generating model are conducting tiles with integer quantum Hall effect and metallic linkers, further Kirchhoff rules. When connecting few identical tiles in a mosaic, fractional steps occur in the conductance values. Richer spectra representing several fractions occur when the tiles are parametrically varied. Parts of the simulation data are supported with purposefully designed graphene mosaics in high magnetic fields. The findings emphasize that the occurrence of fractional conductance values, in particular in two-terminal measurements, does not necessarily indicate interaction-driven physics. The importance of an independent determination of charge densities is underscored and similarities with and differences to the fractional quantum Hall effect are critically discussed.

Effects of domain walls in bilayer graphene in an external magnetic field

“…It is argued that transport energy gaps in the meV regime are not caused by an electronic instability due to electronic interactions as typically assumed [39; 40], but simply due to the structure of transport across LSWs and, in particular, due to "hot" charge carrying LSWs [41]. A similar argument for the presence of plateaus at fractional fillings [42][43][44] in BLG is made in [45], where arbitrary fractional plateaus are engineered in artificial SLG mosaics interconnected with metallic strips. It is proposed that there is an ambiguity in two-terminal transport experiments between the purely single-particle plateaus at fractional fillings due to LSWs and fractional plateaus originating from electron-electron interactions.…”