Hall coefficient sign reversal in metamaterials, and double ordinary, integral and fractional quantum Hall effects in a single specimen
ABSTRACT :
The Hall-effect remains broadly important nearly 140 years after its initial discovery. In science, the integral- and fractional- quantum Hall effects have revolutionized condensed matter physics with novel insights into the role of topological protection in the observed exact quantization and “novel quantum fluids with fractionally charged excitations.†Meanwhile, the ordinary Hall-effect remains a vital semiconductor characterization tool and proven contactless-sensing technology for numerous real world applications. Recent work,[1] claims novel sign reversal of the Hall-coefficient in chain-mail-like 3D metamaterials, whereby an n-type semiconductor mimics the Hall-effect of a p-type semiconductor. The result carried great impact because the authors claimed a new discovery in a very old effect.[2] Hall-effect sign-inversion is an interesting effect that was investigated in 2D- or 3D- semiconductor plates including a hole with current and voltage contacts placed on the interior boundary of the hole.[3] Studies of such “anti-hall bars†demonstrated a sign reversed Hall-effect with respect to the standard geometry. A Hall-bar including a single supplementary hole can be transformed into an “anti-hall-bar†by turning the sample inside out, see Fig. 1. This transformation shifts the exterior boundary and contacts to the sample interior while moving the hole-boundary to the exterior.[3] For a fixed direction of the magnetic field, B, device-inversion leads to sign-reversal of the Hall-effect in “anti-hall bars†since the device-orientation becomes flipped with respect to B. Here, we discuss the relation between such sign inversion and the reported sign reversal of the Hall coefficient in metamaterials.[1] We also demonstrate the possibility of configuration superposition where an antihall bar is placed inside a Hall bar, two currents are simultaneously injected into the specimen, in order to realize two ordinary, integral quantum, and fractional quantum Hall effects at once, in one specimen.